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OPTICAL FIBER
Introduction
Fiber optics deals with the light propagation through thin glass fibers.
Fiber optics plays an important role in the field of communication to transmit voice,
television and digital data signals fro one place to another. The transmission of light
along the thin cylindrical glass fiber by total internal reflection was first demonstrated
by John Tyndall in 1870 and the application of this phenomenon in the field of
communication is tried only from 1927. Today the applications of fiber optics
are also extended to medical field in the form of endoscopes and to instrumentation
engineering in the form of optical sensors.
The Basic principle of optical fiber
Principle:
The basic principle of optical fiber in the transmission of optical signal is total
internal reflection.
Total internal reflection:-
When the light ray travels from denser medium to rarer medium the refracted
ray bends away from the normal. When the angle of incidence is greater than the
critical angle, the refracted ray again reflects into the same medium. This
phenomenon is called total internal reflection.
The refracted ray bends towards the normal as the ray travels from rarer medium
to denser medium. The refracted ray bends away from the normal as it travels
from denser medium to rarer medium.
Conditions for Total Internal Reflection
(a) the refractive index n1 of the core must always be greater than the refractive index n2
of the cladding.
(b) The angle of incidence i must be greater than critical angle C
it can be define as when light travels from a more optically dense material [larger index of
refraction] to a less dense material the angle of refraction is larger than the incident angle.
Because the refracted angle is always larger than the incident angle, it is possible for the
refracted angle to reach 90° before the incident angle reaches 90°. If the light were to refract out
of the denser medium, it would then run along the surface. Larger angles would then yield
situations which would force the sine function to be larger than 1.00, which is mathematically
impossible.
When the incident angle reaches the condition whereby the refracted ray would bend to an angle
of 90°, it is called the CRITICAL ANGLE. The critical angle obeys the following equation:
This reflected ray changes in intensity as we vary the angle of incidence. At small incident
angles (almost perpendicular to the surface) the reflected ray is weak and the refracted ray is
strong.
Construction of optical fiber:-
The optical fiber mainly consists the following six parts as shown in figure
Core:
A typical glass fiber consists of a central core material. Generally core
diameter is 50 . The core is surrounded by cladding. The core medium
refractive is always greater than the cladding refractive index.
Cladding
Cladding refractive index is lesser than the cores refractive index. The
over all diameter of cladding is 125 to 200 .
Silicon Coating
Silicon coating is provided between buffer jacket and cladding. It
improves the quality of transmission of light.
Buffer Jacket
Silicon coating is surrounded by buffer jacket. Buffer jacket is made of
plastic and protects the fiber cable from moisture.
Strength Member
Buffer jacket is surrounded by strength member. It provides strength to the
fiber cable.
Outer Jacket
Finally the fiber cable is covered by polyurethane outer jacket. Because
of this arrangement fiber cable will not be damaged during pulling,
bending, stretching and rolling through the fiber cable is made up of glasses.
NA & ACCEPTANCE ANGLE DERIVATION
“In optics, the numerical aperture (NA) of an optical system is a dimensionless number
that characterizes the range of angles over which the system can accept or emit light.”
optical fiber will only propagate light that enters the fiber within a certain cone, known as
the acceptance cone of the fiber. The half-angle of this cone is called the acceptance angle,
θmax. on
where n1 is the refractive index of the fiber core, and n2 is the refractive index of the cladding.
When a light ray is incident from a medium of refractive index n to the core of index n1, Snell's
law at medium-core interface gives
From the above figure and using trigonometry, we get :
Where is the critical angle for total internal reflection, since
Substituting for sin θr in Snell's law we get:
By squaring both sides
Thus,
from where the formula given above follows.
θmax =
This has the same form as the numerical aperture in other optical systems, so it has become
common to define the NA of any type of fiber.
Definition:-
Acceptance angle:-
Acceptance angle is defined as the maximum angle of incidence at the interface
of air medium and core medium for which the light ray enters into the core and
travels along the interface of core and cladding.
Acceptance Cone:-
There is an imaginary cone of acceptance with an angle .The light that enters the fiber at
angles within the acceptance cone are guided down the fiber core
Numerical aperture:-
Numerical aperture is defined as the light gathering capacity of an optical fiber and it is
directly proportional to the acceptance angle.
Numerically it is equal to the sin of the acceptance angle
Classification of fibers:-
Based on the refractive index of core medium, optical fibers are classified into
two categories.
i. Step index fiber
ii. Graded index fiber
Based on the number of modes of transmission, optical fibers are classified into
two categories
i. Single mode fiber
ii. Multimode fiber
Based on the material used, optical fibers are may broadly classified into four
categories
i. All glass fibers
ii. All plastic fibers
iii. Glass core with plastic cladding fibers iv.
Polymer clad silica fibers.
Step index fiber:-
In step index fibers the refractive index of the core medium is uniform and
undergoes an abrupt change at the interface of core and cladding as shown in figure.
The diameter of core is about 10micrometers in case of single mode fiber and 50 to 200
micrometers in multi mode fiber.
Attenuation is more for step index multi mode fibers but less in step index single
mode fibers
Numerical aperture is more for step index multi mode fibers but it is less in step
index single mode fibers
Graded index fiber:-
In graded index fibers, the refractive index of the core medium is varying in the
parabolic manner such that the maximum refractive index is present at the center
of the core.
The diameter of the core is about 50 micro meters.
Attenuation is very less in graded index fibers Numerical aperture is less in graded index
fibers
Graded index Figure Two types of fiber: (Top) step index fiber; (Bottom) Graded index fiber
Single mode optical fiber
In single mode optical fibers only one mode of propagation is possible.In case of single mode
fiber the diameter of core is about 10micrometers.The difference between the refractive
indices of core and cladding is very small. In single mode fibers there is no dispersion,
so these are more suitable for
Communication. The single mode optical fibers are costly, because the fabrication is
difficult.The process of launching of light into single mode fibers is very difficult.
Multi mode optical fiber
In multi mode optical fibers many mummer of modes of propagation are possible. In case of
in multi mode fiber the diameter of core is 50 to 200 micrometers. The difference between
the refractive indices of core and cladding is also large compared to the single mode
fibers. Due to multi mode transmission, the dispersion is large, so these fibers are not used
for communication purposes. The multi mode optical fibers are cheap than single mode
fibers, because the fabrication is easy. The process of launching of light into single mode
fibers is very easy.
Based on the material:-
Three common type of fiber in terms of the material used:
Glass core with glass cladding –all glass or silica fiber
Glass core with plastic cladding –plastic cladded/coated silica (PCS)
Plastic core with plastic cladding – all plastic or polymer fib
Attenuation:-
Definition: a loss of signal strength in a lightwave, electrical or radio signal usually related to
the distance the signal must travel.
Attenuation is caused by:
Absorption
Scattering
Radiative loss
Losses:-
Losses in optical fiber result from attenuation in the material itself and from scattering,
which causes some light to strike the cladding at less than the critical angle
Bending the optical fiber too sharply can also cause losses by causing some of the light to
meet the cladding at less than the critical angle
Losses vary greatly depending upon the type of fiber
Plastic fiber may have losses of several hundred dB per kilometer
Graded-index multimode glass fiber has a loss of about 2–4 dB
per kilometer
Single-mode fiber has a loss of 0.4 dB/km or less
Macrobending Loss:
The curvature of the bend is much larger than fiber diameter. Lightwave suffers sever loss due
to radiation of the evanescent field in the cladding region. As the radius of the curvature
decreases, the loss increases exponentially until it reaches at a certain critical radius. For any
radius a bit smaller than this point, the losses suddenly becomes extremely large. Higher order
modes radiate away faster than lower order modes.
Microbending Loss:
microscopic bends of the fiber axis that can arise when the fibers are incorporated into cables.
The power is dissipated through the microbended fiber, because of the repetitive coupling of
energy between guided modes & the leaky or radiation modes in the fiber.
Dispersion:-
The phenomenon in an optical fibre whereby light photons arrive at a distant point in different
phase than they entered the fibre. Dispersion causes receive signal distortion that ultimately
limits the bandwidth and usable length of the fiBer cable
The two main causes of dispersion are:
Material (Chromatic) dispersion
Waveguide dispersion
Intermodal delay (in multimode fibres)
Dispersion in fiber optics results from the fact that in multimode propagation, the signal travels
faster in some modes than it would in others.Single-mode fibers are relatively free from
dispersion except for intramodal dispersion .Graded-index fibers reduce dispersion by taking
advantage of higher-order modes.One form of intramodal dispersion is called material
dispersion because it depends upon the material of the core.Another form of dispersion is called
waveguide dispersion .Dispersion increases with the bandwidth of the light source
The advantage of fiber optic cable over metallic cable:-
1. Extremely wide (large) bandwidth.
The bandwidth available with a single glass fibre is more than 100GHZ. With such a large
bandwidth, it is possible to transmit thousands of voice conversations or dozens of video signals
over the same fibre simultaneously. Irrespective of whether the information is voice, data or
video or a combination of these, it can be transmitted easily over the optical fibre. Less no of
independent signals alone can be sent through metallic cables.
2. Immunity to electrostatic interference.
As optical fibres are being made of either glass or plastic external electric noise and lightning
do not affect the energy in a cable. The result is noise free transmission. While this is not true
for metallic cables made up of metals, as they are good conductors of electricity.
3. Elimination of cross Talk.
Fibre systems are immune to cross talk between cables caused by magnetic induction. Whereas
in a metallic cable cross talk results from the electromagnetic coupling between two adjacent
wires.
4. Lighter weight and smaller size.
Fibres are very smaller in size. This size reduction makes fibre the ideal transmission medium
for ships, aircraft and high rise buildings where bulky copper cables occupy to much space.
Reduction in size so reduction in weight also.
5. Lower cost.
The material used in fibres is silica glass or silicon dioxide which is one of the most abundant
materials on earth. So available in lower cost.
6. Security.
Fibre cables are more secure than metallic cables. Due to its immunity to electromagnetic
coupling and radiation, optical fibre can be used in most secure environment. Although it can be
intercepted or tapped, it is very difficult to do so because, at the receiving users end an alarm
would be sounded.
7. Greater safety.
In many wired system the potential hazard of short circuits requires precautionary designs.
Whereas, the dielectric nature of optical fibres eliminates the spark hazard.
8. Corrosion
Fibre cables are more resistive to environmental extremes. They operate over large temperature
variation than their metallic counter parts, and are less affected by corrosive liquids and gases.
9. Longer life span and ease of maintenance.
A longer life span of 20 to 30 years is predicted for the fibre optic cables as compare to 12to 15
years of metallic cables.
Differences between step index fibers and graded index fibers:-
Step index fiber Graded index fiber
1. In step index fibers the refractive index of the
core medium is uniform through and
undergoes an abrupt change at the interface of
core and cladding.
1. In graded index fibers, the refractive index of
the core medium is varying in the parabolic
manner such that the maximum refractive index
is present at the center of the core.
2. The diameter of core is about
10micrometers in case of single mode fiber and
50 to 200 micrometers in multi mode fiber.
2. The diameter of the core is about 50 micro meters.
3. The transmitted optical signal will cross the
fiber axis during every reflection at the core
cladding boundary.
3. The transmitted optical signal will never cross
the fiber axis at any time.
4. The shape of propagation of the optical
signal is in zigzag manner.
4. The shape of propagation of the optical signal
appears in the helical or spiral manner
5. Attenuation is more for multi mode step
index fibers but Attenuation is less in single
mode step index fibers
5. Attenuation is very less in graded index fibers
6. Numerical aperture is more for multi
mode step index fibers but it is less in single
mode step index fibers
6. Numerical aperture is less in graded index fibers
Differences between single mode fibers and Multy mode fibers:-
Single mode fiber Multimode fiber
Single Mode cable is a single strand (most
applications use 2 fibers) of glass fiber with a
diameter of 8.3 to 10 microns that has one mode of
transmission.
Multi-Mode cable has a little bit bigger diameter,
with a common diameters in the 50-to-100 micron
range for the light carry component
Single Modem fiber is used in many applications
where data is sent at multi-frequency (WDM
Wave-Division-Multiplexing) so only one cable is
needed
Most applications in which Multi-mode fiber is used,
2 fibers are used (WDM is not normally used on
multi-mode fiber).
Example:- step index fiber Example:- multimode step index fiber
The small core and single light-wave virtually
eliminate any distortion that could result from
overlapping light pulses, providing the least signal
attenuation and the highest transmission speeds of
any fiber cable type.
multiple paths of light can cause signal distortion at
the receiving end, resulting in an unclear and
incomplete data transmission
Applications of optical fibers
1. Optical fibers are extensively used in communication system.
2. Optical fibers are in exchange of information between different computers
3. Optical fibers are used for exchange of information in cable televisions,
space vehicles, submarines etc.
4. Optical fibers are used in industry in security alarm systems, process control
and industrial auto machine.
5. Optical fibers are used in pressure sensors in biomedical and engine control.
6. Optical fibers are used in medicine, in the fabrication in endoscopy for
the visualization of internal parts of the human body.
7. Sensing applications of optical fibers are
Displacement sensor
Fluid level detector Liquid
Temperature and pressure sensor
Chemical sensors
8. Medical applications of optical fibers are
Gastroscope
Orthoscope Couldo
EXAMPLE:-
1.
A silica optical fiber has a core of refractive index 1.55 and a cladding of refractive index
1.47. Determine (i) the critical angle at the core-cladding interface (ii) the numerical
aperture for the fiber and (iii) the acceptance angle in the air for the fiber.
Given,
n1=1.55,
n2=1.47
Øin(max)=?
NA=?
Øc=?
Acceptance angle Øin(max)= sin-1
(n1
2
– n2
2
)1/2
Øin(max)= sin-1
(1.552
–1.472
)1/2
= sin-1
(2.41-2.16)1/2
= sin-1
(0.25)1/2
= sin-1
(0.316)
Øin(max) =30°00’
Numerical aperture NA= (n1
2
– n2
2
)1/2
= 1.552
–1.472
)1/2
= (2.41-2.16)1/2
= (0.25)1/2
= 0.316
critical angle Øc = sin-1
(n2 / n1)
= sin-1
(1.47 / 1.55)
= sin-1
(0.9483)
= 71°.55’
2.
An optical fiber has refractive index of core and cladding is 1.514 and 1.48 Respectively.
Calculate the acceptance angle and the fractional index Change
Given
,n1=1.514,
n2=1.48
Øin(max)=? ∆=?
Acceptance angle Øin(max ) = sin-1
(n1
2
– n2
2
)1/2
Øin(max) = sin-1
(1.5142
–1.482
)1/2
= sin-1
(2.29-2.19)1/2
= sin-1
(0.1)1/2
= sin-1
(0.316)
Øin(max)=18°42’
Numerical aperture NA= (n1
2
– n2
2
)1/2
=(1.5142
–1.482
)1/2
=(2.29-2.19)1/2
=(0.1)1/2
=0.316
NA=n1√2∆
0.316/1.514=√2∆
(0.2087)2
=2∆
∆=0.0435/2
∆=0.0217
Dielectrics
 Introduction
Dielectrics are the materials having electric dipole moment permanently.
Dipole: A dipole is an entity in which equal positive and negative charges are separated by a small distance..
DIPOLE moment (µEle ):The product of magnitude of either of the charges and separation distance b/w them
is called Dipole moment.
µe = q . x  coulmb.m
All dielectrics are electrical insulators and they are mainly used to store electrical energy.
Ex: Mica, glass, plastic, water & polar molecules…
 Dielectric const. of medium
The relative permittivity(εr) is often known as dielectric const. of medium it can given by,
εr=ε/ε0
Dielectric constant is ratio of permittivity of medium to permittivity of free space.
The value of capacitance of capacitor is given by,
C0=εrε0A/d
By this eqn
we can say that high εr increases capacity of capacitor.
 Polar and Nonpolarized Molecules
Non-polar Molecules : The Dielectric material in which there is no permanent dipole existence in absence
of an external field is …..
2 – Compounds made of molecules which are symmetrically shaped
Polar Molecules :The Dielectric material in which there is permanent dipole existence even in absence of
an external field is …..
Polarization of Dielectrics
As shown in fig. when an electric field is applied to dielectric material their negative & positive charges tend
to align in equilibrium position.
 Gauss’s Law In Dielectrics
In absence of dielectric In presence of dielectric
0 0
d
0
0
0 0
0 0 0
0
0
E V
k
E V
E q
E
k kA
q q '
E
A A
q q q '
S o,
kA A A
1
then , q ' q (1 )
k
S o, E.ds
V E d
S
q q '
1
q q (1 )
k
q
k
k E.ds q
o,
N ow
This relation true is for parallel plate capacitor Which is Gauss’s law for dielectrics.
0
0
0
0
0
E.ds q
q
E A
q
E
A
0
0 0
0 0
E.ds q q '
q q '
EA
q q '
E
A A
 Three Electric vectors
The resultant dielectric field is given by,
Where,
E=Electric field
D=Flux Density or
Displacement vector
P=Polarization
 Electric susceptibility:
The polarization vector P is proportional to the total electric flux density and direction of
electric field.
Therefore the polarization vector can be written as:
 Relation between εr &
Displacement vector,
 Types of polarization
1. Electron polarization
2. Ionic polarization
3. Orientation polarization
4. Space charge polarization
0 0
0 0
0
0
'
'
,
,
, D
p
q q
E
A A
q
now P
A
q P
E
A
q
E P
A
q
now D
A
So E P
0
0
0
0
( 1)
1
e
e
r
e r
P E
P
E
E
E
0
0
0
r 0 0
0
D E P
Now,P=
( - ) E P
(or) ( . - ) E P
( 1) . P
W here,( 1)
r
r
E
E
1. Electronic polarization
When no external field is applied nucleus of atom is like in fig. (a)
When external field is applied, displacement in opposite direction is observed between nucleus &
electrons due to this dipole moment is induced.
This type of polarization is called Electronic polarization.
Ex. Germanium, Silicon, Diamond etc…
2. Ionic polarization
Some materials like ionic crystal does not possess permanent dipole moment.
Fig. (a) shows natural arrangement of ionic crystal. When Ele. Field is applied on this type of
material displacement of ions is observed.
Due to an external electric field a positive & negative ion displaces in the direction opposite to
each other due to which distance between them is reduced & ionic polarization is generated.
Ionic polarization is observed in materials like NaCl, KBr, KCl etc…
Let us consider simple example of NaCl crystal.
As shown in fig. when crystal is placed in an external electric field Na+
ion displaces in one
direction & Cl-
ion goes in opposite direction.
3. Orientation polarization
Some molecules like H2O, HCl having permanent dipole moment p0.
In the absence of a field, individual dipoles are arranged in random way, so net average dipole
moment in a unit volume is zero as shown in fig. (b).
A dipole such as HCl placed in a field experiences a torque that tries to rotate it to align p0 with
the field E.
In the presence of an applied field, the dipoles try to rotate to align parallel to each other in
direction of electric field fig (d).
This type of polarization is Orientation polarization.
This type of polarization occurs only in polar substances like H2O, CH3Cl when they are placed
in external field.
4. Space charge polarization (Interfacial polarization)
A crystal with equal number of mobile positive ions and fixed negative ions.
In the absence of a field, there is no net separation between all the positive charges and all the
negative charges.
In the presence of an applied field, the mobile positive ions migrate toward the negative charges
and positive charges in the dielectric.
The dielectric therefore exhibits Space charge or interfacial polarization.
 Energy stored in dielectric field
Work done is, .
?
.
.
dW F dr
F
dW qE dr
dW E dp
p p
P
lA V
0
0
0
2
0
2
0
( 1) .
. .( 1) .
. .( 1) .
1
( 1) E
2
1
( 1) E
2
?
r
r
r
r
r
p PV
dW EVdP
P E
dW E V dE
dW E V dE
W V
W
V
U
Band Theory of Solid
 Objectives
• Effective Mass of electron
• Concept of Holes
• Energy Band Structure of Solids:
 Conductors, Insulators and Semiconductors
• Semiconductors
 Intrinsic and Extrinsic Semiconductors
• Type of diodes
 Simple Diode
 Zener Diode
 Effective Mass of electron
 An electron moving in the solid under the influence of the crystal potential is subjected to
an electric field.
 We expect an external field to accelerate the electron, increasing E and k and change the
electron’s state.
------ (1)
But, dx/dt = vg ------ (2)
------ (3)
dk
d
gv


1

gv
dx
dV
e
dt
dk
dk
d


----- (4)
------ (5)
------ (6)
------ (7)
----- (8)
 Concept of Holes
Consider a semiconductor with a small number of electrons excited from the valence
band into the conduction band.
 If an electric field is applied,
• The conduction band electrons will participate in the electrical current
• The valence band electrons can “move into” the empty states, and thus can also
contribute to the current.
 If we describe such changes via “movement” of the “empty” states – the picture will be
significantly simplified. This “empty space” is called a Hole.
 “Deficiency” of negative charge can be treated as a positive charge.
dx
dV
ek
dt
d
gv
dx
dV
e
dt
dk
gv




eEk
dt
d

dt
dk
dk
d
dk
d
dk
d
dt
d
dt
dv
a
g















11




















k
dt
d
dk
d
dt
dk
dk
d


2
2
22
2
11 
 Holes act as charge carriers in the sense that electrons from nearby sites can “move” into
the hole.
 Holes are usually heavier than electrons since they depict collective behavior of many
electrons.
 To understand hole motion, one requires another view of the holes, which represent them
as electrons with negative effective mass m*.
 For example the movement of the hole think of a row of chairs occupied by people with
one chair empty, and to move all people rise all together and move in one direction, so the
empty spot moves in the same direction.
 Energy Band Structure of Solids Conductor, Semiconductor and Insulator
 In isolated atoms the electrons are arranged in energy levels.
 Energy Band in Solid
The following are the important energy band in solids:
 Valence band
 Conduction band
 Forbidden energy gap or Forbidden band
 Valance band
The band of energy occupied by the valance electrons is called valence band. The
electrons in the outermost orbit of an atom are known as valance electrons. This band may be
completely or partial filled.
Electron can be move from one valance band to the conduction band by the
application of external energy.
 Conduction band
The band of energy occupied by the conduction electrons is called conduction
band. This is the uppermost band and all electrons in the conduction band are free electrons.
The conduction band is empty for insulator and partially filled for conductors.
 Forbidden Energy Gap or Forbidden band
The gap between the valance band and conduction band on energy level diagram
known as forbidden band or energy gap.
Electrons are never found in the gap. Electrons may jump from back and forth
from the bottom of valance band to the top of the conduction band. But they never come to rest
in the forbidden band.
 According to the classical free electron theory, materials are classified in to three types:
 Conductors
 Semiconductors
 Insulators
 Conductors
There is no forbidden gap and the conduction band and valence band are
overlapping each other between and hence electrons are free to move about. Examples are Ag,
Cu, Fe, Al, Pb ….
 Conductor are highly electrical conductivity
 So, in general electrical resistivity of conductor is very low and it is of the order of 10-6
Ω
cm.
 Due to the absence of the forbidden gap, there is no structure for holes.
 The total current in conductor is simply a flow of electrons.
 For conductors, the energy gap is of the order of 0.01 eV.
 Semiconductors:
Semiconductors are materials whose electrical resistivity lies between insulator
and conductor. Examples are silicon (Si), germanium (Ge) ….
 The resistivity of semiconductors lies between 10-4
Ω cm to 103
Ω cm at room
temperature.
 At low temperature, the valence band is all most full and conduction band is almost
empty. The forbidden gap is very small equal to 1 eV.
 Semiconductor behaves like an insulator at low temperature. The most commonly used
semiconductor is silicon and its band gap is 1.21 eV and germanium band gap is 0.785
eV.
When a conductor is heated its resistance increases; the atoms vibrate more and
the electrons find it more difficult to move through the conductor but, in a semiconductor
the resistance decreases with an increase in temperature. Electrons can be excited up to the
conduction band and Conductivity increases.
 Insulators
 Here the valence band is full but the conduction band is totally empty. So, a free electron
from conduction band is not available.
 In insulator the energy gap between the valence and conduction band is very large and
it’s approximately equal to 5 eV or more.
 Hence electrons cannot jump from valence band to the conduction band. So, a very high
energy is required to push the electrons to the conduction band.
 Therefore the electrical conductivity is extremely small.
 The resistivity of insulator lie between 103
to 1017
Ωm, at the room temperature
 Examples are plastics, paper …..
 Types of semiconductors
 Intrinsic Semiconductor
The intrinsic semiconductors are pure semiconductor materials. These
semiconductors possess poor conductivity. The elemental and compound semiconductor can be
intrinsic type. The energy gap in semiconductor is very small. So, even at the room temperature,
some of electrons from valance band can jump to the conduction band by thermal energy.
The jump of electron in conduction band adds one conduction electron in
conduction band and creates a hole in the valence band. The process is called as “generation of
an electron–hole pair”.
In pure semiconductor the no. of electrons in conduction band and holes in holes
in valence bands are equal.
 Extrinsic Semiconductor
Extrinsic semiconductor is an impure semiconductor formed from an intrinsic
semiconductor by adding a small quantity of impurity atoms called dopants.
The process of adding impurities to the semiconductor crystal is known as doping.
This added impurity is very small of the order of one atom per million atoms of
pure semiconductor.
Depending upon the type of impurity added the extrinsic semiconductors are
classified as:
• p – type semiconductor
• n – type semiconductor
p – type semiconductor
The addition of trivalent impurities such as boron, aluminum or gallium to
an intrinsic semiconductor creates deficiencies of valence electrons, called "holes". It is typical to
use B2H6 di-borane gas to diffuse boron into the silicon material.
n – type semiconductor
The addition of pentavalent impurities such as antimony, arsenic or phosphorous
contributes free electrons, greatly increasing the conductivity of the intrinsic semiconductor.
Phosphorous may be added by diffusion of phosphine gas (PH3).
 Simple Diode
The two terminals are called Anode and Cathode. At the instant the two materials
are “joined”, electrons and holes near the junction cross over and combine with each other.
Holes cross from P-side to N-side and free electrons cross from N-side to P-side.
At P-side of junction, negative ions are formed.
At N-side of junction, positive ions are formed.
Depletion region is the region having no free carriers. Further movement of
electrons and holes across the junction stops due to formation of depletion region. Depletion
region acts as barrier opposing further diffusion of charge carriers. So diffusion stops within
no time. Current through the diode under no-bias condition is zero.
Reverse bias
Positive of battery connected to n-type material (cathode).
Negative of battery connected to p-type material (anode).
Free electrons in n-region are drawn towards positive of battery; Holes in p-region
are drawn towards negative of battery.
Depletion region widens, barrier increases for the flow of majority carriers.
Majority charge carrier flow reduces to zero.
Minority charge carriers generated thermally can cross the junction – results in a
current called “reverse saturation current” Is , Is is in micro or nano amperes or less. Is does
not increase “significantly” with increase in the reverse bias voltage
 Zener Diode
A diode which is heavily doped and which operates in the reverse breakdown
region with a sharp breakdown voltage is called a Zener diode.
This is similar to the normal diode except that the line (bar) representing the cathode is bent
at both side ends like the letter Z for Zener diode. In simple diode the doping is light; as a
result, the breakdown voltage is high and not sharp. But if doping is made heavy, then the
depletion layers becomes very narrow and even the breakdown voltage gets reduced to a
sharp value.
 Working Principle
The reverse breakdown of a Zener diode may occur either due to Zener effect or
avalanche effect. But the Zener diode is primarily depends on Zener effect for its working.
When the electrical field across the junction is high due to the applied voltage, the
Zener breakdown occurs because of breaking of covalent bonds. This produces a large
number of electrons and holes which constitute a steep rise in the reverse saturation current
(Zener current IZ). This effect is called as Zener effect.
Zener current IZ is independent of the applied voltage and depends only on the
external resistance.
The I-V characteristic of a Zener diode is shown in this figure. The forward
characteristic is simply that of an ordinary forward biased junction diode.
Under the reverse bias condition, the breakdown of a junction occurs. Its depends
upon amount of doping. It can be seen from above figure as the reverse voltage is increased
the reverse current remains negligibly small up to the knee point (K) of the curve.
At point K, the effect of breakdown process beings. The voltage corresponding to
the point K in figure is called the Zener breakdown voltage or simply Zener voltage (VZ),
which is very sharp compared to a simple p-n junction diode. Beyond this voltage the
reverse current (IZ) increases sharply to a high value.
The Zener diode is not immediately burnt just because it has entered the
breakdown region.
The Zener voltage VZ remains constant even when Zener current IZ increases
greatly. This ability of a diode is called regulating ability and it enables us to use Zener
diode for voltage regulation.
The maximum value of current is denoted by IZ max and the minimum current to
sustain breakdown is denoted by IZ min. By two points A and B on the reverse VI
characteristic, the Zener resistance is given by the relation
rz = ( Δ VZ / Δ IZ). ------- (1)
 Zener diode Applications:
1) Zener diodes are used as a voltage regulator.
2) They are used in shaping circuits as peak limiters or clippers.
3) They are used as a fixed reference voltage in transistor biasing and for
comparison purpose.
4) They are used for meter protection against damage from accidental application
of excessive voltage.
LASER
Light Amplification by Stimulated Emission of Radiation
 Introduction
The full form of LASER is Light Amplification by Stimulated Emission of
Radiation.
Laser light is highly powerful and it is capable of propagating over long distances
and it is not easily absorbed by water.
 Light having following Properties:
• Wavelength
• Frequency
• Amplitude
• Phase
• Coherence/Incoherence
• Velocity
• Direction
The characteristics or properties of Laser Light are:
• Coherence
• High Intensity
• High directionality
• High monochromaticity
 Absorption
According to Bohr’s law atomic system is characterized by discrete energy level. When
atoms absorb or release energy it transit upward or downward.
Here lower level is E1 and excited level is E2, the photon energy hƒ = E2 – E1.
The atom absorbed an incident photon. As the result of absorption atom absorbed energy
and the atom jumped to excited state E2. This transition is called absorption. It is also referred to
as induced absorption.
We may express the process as,
A + hν = A*
Where A is an atom in lower state and A* is an excited atom.
The rate of absorption depends on no. of atoms N1 present in E1 and spectral energy density u(ƒ)
of radiation.
P12 α N1 u(ƒ) -----(1)
So, P12 = B12N1 u(ƒ) -----(2)
In each absorption transition event, an atom in the medium is excited and one photon is
subtracted from the incident beam, which result in attenuation of light in the medium.
 Spontaneous Emission
An atom cannot stay in the excited state for a longer time. Ina time of 10-8
sec, the atom
come back to the ground state by releasing a photon of energy hν, and hν = E = E2 – E1. Where
E1 = Ground State and E2 = Excited State.
The emission of photon by an atom without any external impetus is called spontaneous
emission.
We may write the process as,
A* → hν + A
Here system having atoms in excited state. Atom goes to downward transition with emitting
photons, hƒ = E1 – E2.
Emission is random, so if not in same phase becomes incoherent.
The transition depends on atoms in excited state N2.
P12 (spont) α N2 = A21 N2 ------- (1)
Where, A21 = Einstein coefficient for spontaneous Emission. We get Incoherent radiation forms
heat by light amplification of radiation by spontaneous emission.
 Stimulated Emission
An atom in the excited state need not wait for spontaneous emission of photon. Well before
the atom can make a spontaneous transition, it may interacts with a photon with energy hν = E2 –
E1, and make a downward transition. The photon is said to stimulated of induced the excited
atom to emit a photon of energy hν = E2 – E1. The passing photon does not disappear and in
addition to it there is a second photon which is emitted by the excited atom.
The phenomenon of forced photon emission by an excited atom due to the action of an
external energy is called stimulated emission or induced emission.
The process may be expressed as,
A* + hν → A + 2hν
Here system having atoms in excited state. The atom goes to downward transition with
emitting photons.
2hƒ = E1 – E2. After applying photon energy hƒ.
Emission is depends on energy density u(ƒ) & No. of atoms in excited state N2
P12 (stimul) α u(ƒ) N2 - -------- (1)
= B21 N2 u(ƒ) -------- (2)
Where, B21 = Einstein coefficient for Stimulated Emission.
Thus one photon of energy hƒ stimulates two photons of energy hƒ in same phase & directions.
So, we get coherent light amplification of radiation by stimulated emission.
 Population Inversion
It is the process of increasing exited electrons in higher energy levels. Due to this
process the production of laser is possible. The energy level between the ground state E1 (1st
level) and exited state E3 (3rd
level) is known as metastable state E2 (2nd
level).
By the optical pumping electrons from ground state jumps to excited state by
absorbing photons. The electrons remain only for 10-8
sec in exited state E3, so most of them
jump back to the ground state E1 by emitting photons. But some of them jump to the
metastable state E2.
They (electron) stay in metastable state for more then 10-3
sec. So electron density
increases in metastable state. Thus the transitions are possible it takes more no. of electrons
together and ν – (knew)
12 photon beam is produced which constitute laser beam.
 Optical Pumping
There are no of techniques for pumping a collection of atoms to an inverted state.
•Optical pumping
• Electrical discharge
• Direct conversion
When photon of blue green light incident on Ruby crystal, electrons from ground
state absorbs and exited and jumps on higher energy state levels and comes back to metastable
state. They increase population of electrons in metastable state.
This process is called “optical pumping” which is done by flash tube.
 Relation between Einstein’s ‘A’ and ‘B’ coefficients
Einstein obtained a mathematical expression for the existence of two different kinds of
processes,
(1) Spontaneous emission
(2) Stimulated emission
Consider all atoms r in thermal equilibrium at T and radiation of frequency (ƒ) and energy
density u(ƒ). Here N1 and N2 r atoms in E1 and E2 respectively.
In equilibrium absorption rates and emission rates must be same. i.e.
B12 N1 u(ƒ) = A21 N2+ B21 N2 u(ƒ)
→ A21 N2= u(ƒ) [B12N1 – B21N2]
→ u(f) = [A21 N2 / (B12 N1 – B21 N2)] --------- (1)
---------- (2)
So Boltzmann distribution law is,
---------- (3)
21
21
12 1
21 2
( )
[ ]
ƒ
1
A
B
u
B N
B N
1
2
/
1 0
/
2 0
E kT
E kT
N N e
N N e
And
----------- (4)
But, E2 – E1 = hf ----------- (5)
So, ----------- (6)
------------ (7)
According to plank’s radiation formula,
------------ (8)
Where, B12 = B21 & A21 / B21 = 8∏hf3
/c3
------------ (9)
So, Ratio of spontaneous to stimulated emission:
----------- (10)
So,
------------ (11)
------------ (12)
R = e hf/KT
- 1 -------------- (13)
So,
• If hƒ << kT, in thermal equilibrium,
Then R = ehf/KT
- 1 << 1
• hƒ<<kT – Stimulated emission
– Valid in microwave region (MASER)
• hƒ>>kT – Spontaneous emission
– Valid in visible region, incoherent Valid
2 1( )/1
2
E E kTN
e
N
h /1
2
ƒ kTN
e
N
21
21
ƒ12
21
h /
ƒ
1
( )
[ ]
kT
e
A
B
u
B
B
3
3 ƒh /
8 1
( ) ( )
[ ]
ƒ
ƒ
1
kT
u
c
h
e
2 21 21
2 21 21
3
3
8
( ) ( ) ( )
ƒ
ƒ ƒ ƒ
N A A h
R
B u B u ucN
3
3 /
3
3
ƒh
8
( )
8
ƒ
ƒ
&
ƒ
ƒ
1
1
( ) ( )
[ ]
kT
h
u
c
u
R
h
e
c
 Types of LASER
There are three types of lasers
1. Solid Laser (Ruby Laser)
2. Liquid Laser
3. Gas Laser ( He – Ne Laser, CO2 Laser)
Ruby Laser
To produce laser from solid, Ruby crystal is used. Ruby is an aluminum oxide crystal
(Al
2
O
3
) in which some of the aluminum atoms have been replaced with Cr
+3
chromium atoms
(0.05% by weight).
It was the first type of laser invented, and was first operated by Maiman in research
laboratories on 1960.
Chromium gives ruby its characteristic pink or red color by absorbing green and blue
light.
For a ruby laser, a crystal of ruby is formed into a cylinder. The ruby laser is used as a
pulsed laser, producing red light at 6943 Å.
Ruby crystal is surrounded by xenon tube. Ruby crystal is fully silvered at one side and
partially silvered at the other end.
A strong beam of blue green light is made to fall up on crystal from xenon tube and this
light is absorbed by the crystal.
Because of this, many electrons from ground state or normal state are raised to the
excited state or higher state and electron falls to metastable state.
During this transition photon is not emitted but excess energy of the electrons absorbed in
crystal lattice.
As electron drops to metastable state they remain there for certain time ~ 10-6
sec.
Thus, the incident blue green light from tube increases the number of electron in
metastable state and then the population inversion can be achieved.
If a light of different frequency is allowed to fall on this material, the electrons move
back and forth between silvered ends of the crystal.
While moving through they get stimulated and exited electrons radiate energy.
Thus readia photon has the same frequency as that of incident photon and is also in
exactly same phase.
When the intensity of light beam is increased the same process is repeated.
Finally extremely intensified beam of light energies from the semi silvered side of the
crystal.
This way it is possible to get extremely intensified and coherent beam of light from the
crystal. This beam is nothing but higher energetic beam – ie. LASER beam.
Applications of Ruby Laser
Ruby lasers have declined in use with the discovery of better lasing media. They are still
used in a number of applications where short pulses of red light are required. Holography's
around the world produce holographic portraits with ruby lasers, in sizes up to a meter squared.
Many non-destructive testing labs use ruby lasers to create holograms of large objects
such as aircraft tires to look for weaknesses in the lining.
Ruby lasers were used extensively in tattoo and hair removal.
Drawbacks of Ruby Laser
The laser requires high pumping power because the laser transition terminates at the
ground state and more than half of ground state atoms must be pumped to higher state to achieve
population inversion.
The efficiency of ruby laser is very low because only green component of the pumping
light is used while the rest of components are left unused.
The laser output is not continues but occurs in the form of pulses of microseconds
duration.
The defects due to crystalline imperfections are also present in this laser.
Gaseous Laser (He – Ne Laser)
Helium - neon laser, usually called a He-Ne laser, is a type of small gas laser. He-Ne
lasers have many industrial and scientific uses, and are often used in laboratory demonstrations
of optics.
He-Ne laser is an atomic laser which employs a four-level pumping scheme.
The active medium is a mixture of 10 parts of helium to 1 part of neon.
Neon atoms are centers and have energy levels suitable for laser transitions while helium
atoms help efficient excitation of neon atoms.
The most common wavelength is 6328 Å. These lasers produced powers in the range 0.5
to 50 mW in the red portion of the visible spectrum.
They have long operating life of the order of 50,000 hrs.
Construction
It consists of a glass discharge tube of about typically 30 cm long and 1.5 cm diameter.
The tube is filled with a mixture of helium and neon gases in the 10:1.
Electrodes are provided in the tube to produce a discharge in the gas.
They are connected to a high voltage power supply. The tube is hermetically sealed with
glass windows oriented at Brewster angle to the tube. The cavity mirrors are arranged externally.
Working
When the power is switched on, a high voltage of about 10 kV is applied across the gas.
It is sufficient to ionize the gas.
The electrons and ions are produced in the process of discharge are accelerated toward
the anode and cathode respectively.
The electron have a smaller mass, they acquire a higher velocity. They transfer their
kinetic energy to helium atoms through inelastic collisions.
The initial excitation effects only the helium atoms. They are in metastable state and
cannot return in ground state by the spontaneous emission.
The excited helium atoms can return to the ground state by transforming their energy to
neon atoms through collision. These transformations take place when two colliding atoms have
initial energy state. It is called resonant transfer of energy.
So, the pumping mechanism of He-Ne Laser is when the helium atom in the metastable
state collides with neon atom in the ground state the neon atom is excited and the helium atom
drops back to the ground state.
The role of helium atom is thus to excite neon atom and cause, population inversion. The
probability of energy transfer from helium atoms to neon atoms is more as there are 10 atoms of
helium per 1 neon atom in gas mixture.
Without the Brewster windows, the light output is unpolarized; because of it laser output
to be linearly polarized.
When the excited Ne atom passes from metastable state (3s) to lower level (2p), it emits
photon of wavelength 632 nm.
This photon travels through the gas mixture parallel to the axis of tube; it is reflected
back and forth by the mirror ends until it stimulates an excited Ne atom and causes it to emit a
photon of 632 nm with the stimulating photon.
The stimulated transition from (3s) level to (2p) level is laser transition.
Although 6328 Å is standard wavelength of He-Ne Laser, other visible wavelengths 5430
Å (Green) 5940 Å (yellow-orange), 6120 Å (red-orange) can also produce.
Overall gain is very low and is typically about 0.010 % to 0.1 %.
The laser is simple practical and less expensive.
The Laser beam is highly collimated, coherent and monochromatic.
Applications of He-Ne Laser
The Narrow red beam of He-Ne laser is used in supermarkets to read bar codes.
The He-Ne Laser is used in Holography in producing the 3D images of objects.
He-Ne lasers have many industrial and scientific uses, and are often used in laboratory
demonstrations of optics.
 Semiconductor Laser (Diode Laser)
A semiconductor laser is a laser in which a semiconductor serves as a photon source.
The most common semiconductor material that has been used in lasers is gallium
arsenide.
Einstein’s Photoelectric theory states that light should be understood as discrete lumps of
energy (photons) and it takes only a single photon with high enough energy to knock an electron
loose from the atom it's bound to.
Stimulated, organized photon emission occurs when two electrons with the same energy
and phase meet. The two photons leave with the same frequency and direction.
 P-type Semiconductors
In the compound GaAs, each Ga atom has three electrons in its outermost shell of
electrons and each As atom has five.
When a trace of an impurity element with two outer electrons, such as Zn (zinc), is added
to the crystal.
The result is the shortage of one electron from one of the pairs, causing an imbalance in
which there is a “hole” for an electron but there is no electron available. This forms a p-type
semiconductor.
 N-type Semiconductors
When a trace of an impurity element with six outer electrons, such as Se (selenium), is
added to a crystal of GaAs, it provides on additional electron which is not needed for the
bonding.
This electron can be free to move through the crystal. Thus, it provides a mechanism for
electrical conductivity. This type is called an n-type semiconductor.
Under forward bias (the p-type side is made positive) the majority carriers, electrons in
the n-side, holes in the p-side, are injected across the depletion region in both directions to create
a population inversion in a narrow active region. The light produced by radioactive
recombination across the band gap is confined in this active region.
 Application of Lasers
1. Laser beam is used to measure distances of sun, moon, stars and satellites very
accurately.
2. It can be used for measuring velocity of light, to study spectrum of matters, to study
Raman effect.
3. It can be is used for increasing speed and efficiency of computer.
4. It is used for welding.
5. It is used in biomedical science.
6. It is used in 3D photography.
7. It is used for communication, T. V. transmission, to search the objects under sea.
8. It can be used to predict earthquake.
9. Laser tools are used in surgery.
10. It is used for detection and treatment of cancer.
11. It is used to aline straight line for construction of dam, tunnels etc.
12. It is used in holography.
13. It is used in fiber optic communication.
14. It is also used in military, like LIDAR.
15. It is used to accelerate some chemical reactions.
Special Theory of Relativity
 Introduction to Relativity
o The dependence of various physical phenomena on relative motion of the observer
and the observed objects, especially regarding the nature and behaviour of light,
space, time, and gravity is called relativity.
o When we have two things and if we want to find out the relation between their
physical property i.e.velocity,accleration then we need relation between them that
which is higher and which is lower.In general way we reffered it to as a relativity.
o The famous scientist Einstein has firstly found out the theory of relativity and he has
given very useful theories in relativity.
o In 1905, Albert Einstein determined that the laws of physics are the same for all non-
accelerating observers, and that the speed of light in a vacuum was independent of the
motion of all observers. This was the theory of special relativity.
 FRAMES OF REFERENCE
o A Reference Frame is the point of View, from which we Observe an Object.
o A Reference Frame is the Observer it self, as the Velocity and acceleration are
common in Both.
o Co-ordinate system is known as FRAMES OF REFERENCE
o Two types:
1. Inertial Frames Of Reference.
2. non-inertial frame of reference.
o We have already come across idea of frames of reference that move with constant
velocity. In such frames, Newton’s law’s (esp. N1) hold. These are called
inertial frames of reference.
o Suppose you are in an accelerating car looking at a freely moving object (I.e., one
with no forces acting on it). You will see its velocity changing because you are
accelerating! In accelerating frames of reference, N1 doesn’t hold – this is a non-
inertial frame of reference.
 Galilean Transforms
o Parallel axes (for convenience)
o K’ has a constant relative velocity in the x-direction with respect to K
o Time (t) for all observers is a
Fundamental invariant,
i.e., the same for all inertial observers
o Galilean Transformation Inverse Relations
o Step 1. Replace with .
o Step 2. Replace “primed” quantities with
“unprimed” and “unprimed” with “primed.”
o General Galilean Transformations
o Newton’s Eqn of Motion is same at face-value in both reference frames
 Einstein’s postulates of special theory of relativity
o The First Postulate of Special Relativity
 The first postulate of special relativity states that all the laws of nature are the
same in all uniformly moving frames of reference.
o The Second Postulate of Special Relativity
 The second postulate of special relativity states that the speed of light in empty
space will always have the same value regardless of the motion of the source
or the motion of the observer.
 The speed of a light flash emitted by either the spaceship or the space station is
measured as c by observers on the ship or the space station. Everyone who measures
the speed of light will get the same value, c.
 The Ether
o Light is a wave.
o Waves require a medium through which to propagate.
o Medium as called the “ether.” (from the Greek aither, meaning upper air)
o Maxwell’s equations assume that light obeys the Newtonian-Galilean transformation.
 The Ether: Since mechanical waves require a medium to propagate, it was generally
accepted that light also require a medium. This medium, called the ether, was
assumed to pervade all mater and space in the universe.
 The Michelson-Morley Experiment
o Experiment designed to measure small changes in the speed of light was performed
by Albert A. Michelson (1852 – 1931, Nobel ) and Edward W. Morley (1838 – 1923).
o Used an optical instrument called an interferometer that Michelson invented.
o Device was to detect the presence of the ether.
o Outcome of the experiment was negative, thus contradicting the ether hypothesis.
o Michelson developed a device called an inferometer.
o Device sensitive enough to detect the ether.
o Apparatus at rest wrt the ether.
o Light from a source is split by a half silvered mirror (M)
o The two rays move in mutually perpendicular directions
o The rays are reflected by two mirrors (M1 and M2) back to M where they recombine.
o The combined rays are observed at T.
o The path distance for each ray is the same (l1=l2).
o Therefore no interference will be observed
o Apparatus at moving through the ether.
o First consider the time required for the parallel ray
o Distance moved during the first part of the path is
o Similarly the time for the return trip is
o The total time
o For the perpendicular ray ,we can write, from fig.
||
L
t
(c u )
ct L ut
L
t
(c u )
||
2 2
2 2
( ) ( )
2
( )
2 /
1
L L
t
c u c u
Lc
c u
L c
u c
o The return path is the same as the initial leg therefore the total time is
o The time difference between the two rays is,
o The expected time difference is too small to be measured directly!
o Instead of measuring time, Michelson and Morley looked for a fringe change.
o as the mirror (M) was rotated there should be a shift in the interference fringes.
 Results of the Experiment
 A NULL RESULT
o No time difference was found!
o Hence no shift in the interference patterns
 Conclusion from Michelson-Morley Experiment
o the ether didn’t exist.
 The Lorentz Transformation
 We are now ready to derive the correct transformation equations between two inertial
frames in Special Relativity, which modify the Galilean Transformation. We consider
two inertial frames S and S’, which have a relative velocity v between them along the
x-axis.
2 2 2
2 2 2 2 2
2 2 2
2 2
)
( )
( initial leg of the patct L ut
L c t u t
c u t
L
t
c u
h
2 2
2 2
2
2 /
1
L
t
c u
L c
t
u c
1
21
2 2
|| 2 2
2 2
2 3
2
1 1
2
2
L u u
t t t
c c c
A fter a binom ial expansi
L u L u
t
c c c
on
 Now suppose that there is a single flash at the origin of S and S’ at time , when the
two inertial frames happen to coincide. The outgoing light wave will be spherical in
shape moving outward with a velocity c in both S and S’ by Einstein’s Second
Postulate.
 We expect that the orthogonal coordinates will not be affected by the horizontal
velocity:
 But the x coordinates will be affected. We assume it will be a linear transformation:
 But in Relativity the transformation equations should have the same form (the laws of
physics must be the same). Only the relative velocity matters. So,
 Consider the outgoing light wave along the x-axis (y = z = 0).
 Now plug these into the transformation equations:
 Plug these two equations into the light wave equation:
x
y
z
S
x'
y'
z'
S'
v
2 2 2 2 2
2 2 2 2 2
x y z c t
x y z c t
y y
z z
x k x vt
x k x vt
k k
x ct in fram e S'
x ct in fram e S
x k x vt k ct vt kct 1 v / c and
x k x vt k ct vt kct 1 v / c
ct x k ct 1 v / c
ct x k ct 1 v / c
t k t 1 v / c
t k t 1 v / c
o Plug t’ into the equation for t:
o So the modified transformation equations for the spatial coordinates are:
o Now what about time?
o Solve for t’:
o So the correct transformation (and inverse transformation) equations are:
2
2 2 2
2 2
t k t 1 v / c 1 v / c
1 k 1 v / c
1
k
1 v / c
x x vt
y y
z z
x x vt
x x vt inverse transformation
Plug one into the other:
x x vt vt
2 2
2 2
2 2
2
2 2
2 2 2 2
2 2 2 2
2
x x vt vt
x 1 vt vt
1 v / c 1
x vt vt
1 v / c
xv / c vt vt
1
t xv / c vt
v
t t vx / c
2 2
x x vt x x vt
y y y y
z z z z
t t vx / c t t vx / c
The Lorentz
Transformation
 Application of Lorentz Transformation
 Time Dilation
 We explore the rate of time in different inertial frames by considering a special kind
of clock – a light clock – which is just one arm of an interferometer. Consider a light
pulse bouncing vertically between two mirrors. We analyze the time it takes for the
light pulse to complete a round trip both in the rest frame of the clock (labeled S’),
and in an inertial frame where the clock is observed to move horizontally at a velocity
v (labeled S).
 In the rest frame S’
 Now put the light clock on a spaceship, but measure the roundtrip time of the light
pulse from the Earth frame S:
 So the time it takes the light pulse to make a roundtrip in the clock when it is moving
by us is appears longer than when it is at rest. We say that time is dilated. It also
doesn’t matter which frame is the Earth and which is the clock. Any object that
moves by with a significant velocity appears to have a clock running slow. We
summarize this effect in the following relation:
m irror
m irror
L
L
c t / 2
v t / 2
1
2
1 2
L
t = time up
c
L
t = time down
c
2L
=t t
c
1
2
2 2 2 2 2
2 2 2 2
2
2
2 2
2 2 2 2
t
t time up
2
t
t time down
2
The speed of light is still c in this frame, so
L v t / 4 c t / 4
L c v t / 4
4L
t
c v
2L 1
t
c 1 v / c 1 v / c
2 2
1
t , 1
1 v / c
 Length Contraction
o Now consider using a light clock to measure the length of an interferometer arm. In
particular, let’s measure the length along the direction of motion.
o In the rest frame S’:
o Now put the light clock on a spaceship, but measure the roundtrip time of the light
pulse from the Earth frame S:
o In other words, the length of the interferometer arm appears contracted when it moves by us.
This is known as the Lorentz-Fitzgerald contraction. It is closely related to time dilation. In
fact, one implies the other, since we used time dilation to derive length contraction.
A A’ C C’
vt1L
1
2
1 2
1 1 1
2 2 2
1 2 2 2 2 2
2 2
2 2
1 2 2 2 2 2
2 2
t tim e out
t tim e back
t t t
L
L vt ct t
c v
L
L vt ct t
c v
2Lc 2L 1
t t t
c v c 1 v / c
ct
L 1 v / c
2
But, t from tim e dilation
1 v / c
2Lc 2L 1
t t t
c v c 1 v / c
ct
L 1 v / c
2
But, t
1 v
2 2
0
2 2
from tim e dilation
/ c
L 1
L 1
1 v / c
Superconductivity
 Introduction of superconductivity
Superconductivity is a phenomenon of exactly zero electrical resistance and expulsion of
magnetic fields occurring in certain materials when cooled below a characteristic critical
temperature. It was discovered by Dutch physicist Heike Kamerlingh Onnes on April 8,
1911 in Hg, which has critical temperature of 4.2 K.
 Properties of Superconductors
(1)Electrical Resistance
Zero Electrical Resistance
Defining Property
Critical Temperature
Quickest test
10-5
Ωcm
(2)Effect of Magnetic Field
Critical magnetic field (HC) – Minimum magnetic field required to destroy
the superconducting property at any temperature.
2
0
1C
C
T
H H
T
H0 - Critical field at 0K
T - Temperature below TC
TC - Transition Temperature
Element HC at 0K
(mT)
Nb 198
Pb 80.3
Sn 30.9
(3)Effect of Electric Current
 Large electric current – induces magnetic field – destroys superconductivity
 Induced Critical Current iC = 2πrHC
Persistent Current
 Steady current which flows through a superconducting ring without any
decrease in strength even after the removal of the field.
 Diamagnetic property.
 Meissner effect
When Superconducting material cooled bellow its Tc it becomes resistenceless
& perfect diamagnetic.
When superconductor placed inside a magnetic field in Tc all magnetic flux is
expelled out of it the effect is called Meissner effect.
Perfect diamagnetism arises from some special magnetic property of
Superconductor.
If there is no magnetic field inside the superconductor relative permeability
or diamagnetic constant μr =0.
Total magnetic induction B is,
If magnetic induction B=0 then,
 Magnetic Flux Quantization
Magnetic flux enclosed in a superconducting ring = integral multiples of fluxon
Φ = nh/2e = n Φ0 ; (Φ0 = 2x10-15
Wb)
 Effect of Pressure
Pressure ↑, TC ↑
High TC superconductors – High pressure
0
( )B H M 
0
0 ( )H M 
M H  
1 m
M
H
   
 Thermal Properties
Entropy & Specific heat ↓ at TC
Disappearance of thermo electric effect at TC
Thermal conductivity ↓ at TC – Type I superconductors
 Stress
 Stress ↑, dimension ↑, TC ↑, HC affected
 Frequency
 Frequency ↑, Zero resistance – modified, TC not affected
 Impurities
 Magnetic properties affected
 Size
 Size < 10-4
cm – superconducting state modified
 General Properties
 No change in crystal structure
 No change in elastic & photo-electric properties
 No change in volume at TC in the absence of magnetic field
 Isotope Effect
Maxwell
TC = Constant / Mα
TC Mα
= Constant (α – Isotope Effect coefficient)
α = 0.15 – 0.5
α = 0 (No isotope effect)
TC√M = constant
 Classification & characterization of superconductor
Type - I or soft superconductor
o Exhibit complete Meissner effect.
o Bellow Hc super conductor above Hc Normal
o Value of Hc is order of 0.1 T.
o Aluminum, lead & Indium are type - I super conductor
o Not used as strong electromagnets
Type - II or Hard superconductor
o Exhibit complete Meissner effect bellow a certain critical field Hc1 at
this point diamagnetism & superconductivity ↓. This state is mix state
called vortex state.
o At certain critical field Hc2 superconductivity disappears.
o Niobium, Aluminum, Silicon, Ceramic are type - II superconductors.
o Pb is type I superconductor ac Hc = 600 gauss at 4º K when a small
impurity of In is added it becomes type II superconductor with Hc1 =
400 gauss & Hc2 = 1000 gauss.
 London equation
According to London’s theory there are two type of
electrons in SC.
o Super electrons
o Normal electrons
o At 0º K there are only Super electrons.
o With increasing temp. Super electrons ↓ Normal electrons ↑ .
o Let nn, un & ns, us are no. density & drift velocity of normal electrons
& super electrons respectively.
Equation of motion of Super electrons under electric field is,
Now current & drift velocity are related as,
s
du
m eE
dt
 

 

 
s s s
s s s
s
s
s
I n eAu
J n eu
J
u
n e
2
( )

  
 
s
s
s s
J
d
n e
e E
dt
n e Ed J
dt m
This is London's first equation.
- London's first equation gives absence of resistance. If E = 0 then,
- Now from Maxwell's eqns.
0s
dJ
dt

( )
d B
E
dt
B A
d A
E
dt
d A
E
dt
d A
E
dt
   
  
 
   
    
 
2
2
2
2
2
2
( )
( )
s s
s
s
s
s
s
s
s
s
s
s
n e Ed J
dt m
d J m
E
dt n e
d J m d A
dt n e dt
d m d A
J
dt n e dt
m
J A
n e
n e
J A
m
 

  
  
  
  
This is London's Second equation
- Again from ampere Law,
- Take curl on both sides
λ is called London penetration depth.
 BCS Theory of Superconductivity
 The properties of Type I superconductors were modeled successfully by the
efforts of John Bardeen, Leon Cooper, and Robert Schrieffer in what is
commonly called the BCS theory.
 A key conceptual element in this theory is the pairing of electrons close to
the Fermi level into Cooper pairs through interaction with the crystal lattice.
0
2
0
( )
s
s
B J
n e
B A
m


  
   
2
0
2
2
2
0
( )
&
( )
s
s
n e
B A
m
Now
B B B A B
n e
B B B
m
A B


       
             
        
  
 This pairing results form a slight attraction between the electrons related to lattice
vibrations; the coupling to the lattice is called a phonon interaction.
 Pairs of electrons can behave very differently from single electrons which are
fermions and must obey the Pauli exclusion principle.
 Cooper Pairs:
 The transition of a metal from the normal to the superconducting state has the
nature of a condensation of the electrons into a state which leaves a band gap
above them.
 This kind of condensation is seen with super fluid helium, but helium is made up
of bosons -- multiple electrons can't collect into a single state because of the Pauli
exclusion principle.
 Froehlich was first to suggest that the electrons act as pairs coupled by lattice
vibrations in the material.
 This coupling is viewed as an exchange of phonons, phonons being the quanta of
lattice vibration energy.
 Experimental corroboration of an interaction with the lattice was provided by the
isotope effect on the superconducting transition temperature.
 The boson-like behavior of such electron pairs was further investigated by
Cooper and they are called "Cooper pairs".
 The condensation of Cooper pairs is the foundation of the BCS theory of
superconductivity.
s
 In the normal state of a metal, electrons move independently, whereas in the BCS
state, they are bound into "Cooper pairs" by the attractive interaction. The BCS
formalism is based on the "reduced" potential for the electrons attraction.
 You have to provide energy equal to the 'energy gap' to break a pair, to break one pair
you have to change energies of all other pairs.
 This is unlike the normal metal, in which the state of an electron can be changed by
adding a arbitrary small amount of energy.
 The energy gap is highest at low temperatures but does not exist at temperatures
higher than the transition temperature.
 The BCS theory gives an expression of how the gap grows with the strength of
attractive interaction and density of states.
 The BCS theory gives the expression of the energy gap that depends on the
Temperature T and the Critical Temperature Tc and is independent of the material:
 Applications of Superconductors
Engineering:
 Transmission of power
 Switching devices
 Sensitive electrical instruments
 Memory (or) storage element in computers.
 Manufacture of electrical generators and transformers
Medical:
 Nuclear Magnetic Resonance (NMR)
 Diagnosis of brain tumor
 Magneto – hydrodynamic power generation
 Josephson effect or Devices
Principle: persistent current in d.c. voltage.
Josephson junctions
 A type of electronic circuit capable of switching at very high speeds when
operated at temperatures approaching absolute zero.
 Named for the British physicist who designed it,
 A Josephson junction exploits the phenomenon of superconductivity.
Construction
 A Josephson junction is made up of two superconductors, separated by a non-
superconducting layer so thin that electrons can cross through the insulating barrier.
 The flow of current between the superconductors in the absence of an applied voltage is
called a Josephson current,
 The movement of electrons across the barrier is known as Josephson tunneling.
 Two or more junctions joined by superconducting paths form what is called a Josephson
interferometer.
 Consists of superconducting ring having magnetic fields of quantum values (1,2,3..)
 Placed in between the two Josephson junctions.
Explanation:
 Consists of thin layer of insulating material placed between two
superconducting materials.
 Insulator acts as a barrier to the flow of electrons.
 When voltage applied current flowing between super conductors by tunneling
effect.
 Quantum tunneling occurs when a particle moves through a space in a manner
forbidden by classical physics, due to the potential barrier involved
Components of current
 In relation to the BCS theory (Bardeen Cooper Schrieffer) mentioned earlier,
pairs of electrons move through this barrier continuing the superconducting
current. This is known as the dc current.
 Current component persists only till the external voltage application. This is ac
current.
Uses of Josephson devices
 Magnetic Sensors
 Gradiometers
 Oscilloscopes
 Decoders
 Analogue to Digital converters
 Oscillators
 Microwave amplifiers
 Sensors for biomedical, scientific and defence purposes
 Digital circuit development for Integrated circuits
 Microprocessors
 Random Access Memories (RAMs)
Super conducting Quantum Interference Devices
Discovery:
The DC SQUID was invented in 1964 by Robert Jaklevic, John Lambe, Arnold Silver,
and James Mercereau of Ford Research Labs
Principle:
Small change in magnetic field, produces variation in the flux quantum.
Construction:
The superconducting quantum interference device (SQUID) consists of two
superconductors separated by thin insulating layers to form two parallel Josephson
junctions.
Type:
Two main types of SQUID:
1) RF SQUIDs have only one Josephson junction
2) DC SQUIDs have two or more junctions.
Thereby,
 More difficult and expensive to produce.
 Much more sensitive.
Fabrication:
 Lead or pure niobium, the lead is usually in the form of an alloy with 10% gold or
indium, as pure lead is unstable when its temperature is repeatedly changed.
 The base electrode of the SQUID is made of a very thin niobium layer.
 The tunnel barrier is oxidized onto this niobium surface.
 The top electrode is a layer of lead alloy deposited on top of the other two, forming a
sandwich arrangement.
 To achieve the necessary superconducting characteristics, the entire device is then
cooled to within a few degrees of absolute zero with liquid helium.
Uses:
 Storage device for magnetic flux.
 Study of earthquakes.
 Removing paramagnetic impurities.
 Detection of magnetic signals from brain, heart etc.
 Cryotron:
 The cryotron is a switch that operates using superconductivity.
 The cryotron works on the principle that magnetic fields destroy superconductivity.
 The cryotron is a piece of tantalum wrapped with a coil of niobium placed in a liquid
helium bath.
 When the current flows through the tantalum wire it is superconducting, but when a
current flows through the niobium a magnetic field is produced.
 This destroys the superconductivity which makes the current slow down or stop.
 Magnetic Levitated Train:
Principle: Electro-magnetic induction
Introduction:
 Magnetic levitation transport, or maglev, is a form of transportation that suspends
guides and propels vehicles via electromagnetic force.
 This method can be faster than wheeled mass transit systems, potentially reaching
velocities comparable to turboprop and jet aircraft (500 to 580 km/h).
 Why superconductor?
 Superconductors may be considered perfect diamagnets (μr = 0), completely expelling
magnetic fields due to the Meissner effect. The levitation of the magnet is stabilized
due to flux pinning within the superconductor. This principle is exploited by EDS
(Electrodynamics suspension) magnetic levitation trains.
 In trains where the weight of the large electromagnet is a major design issue (a very
strong magnetic field is required to levitate a massive train) superconductors are used
for the electromagnet, since they can produce a stronger magnetic field for the same
weight.
 How to use a Super conductor?
Electrodynamics suspension
 In Electrodynamic suspension (EDS), both the rail and the train exert a magnetic
field, and the train is levitated by the repulsive force between these magnetic fields.
 The magnetic field in the train is produced by either electromagnets or by an array of
permanent magnets.
 The repulsive force in the track is created by an induced magnetic field in wires or
other conducting strips in the track.
 At slow speeds, the current induced in these coils and the resultant magnetic flux is
not large enough to support the weight of the train.
 For this reason the train must have wheels or some other form of landing gear to
support the train until it reaches a speed that can sustain levitation.
 Propulsion coils on the guide way are used to exert a force on the magnets in the train
and make the train move forwards.
 The propulsion coils that exert a force on the train are effectively a linear motor: An
alternating current flowing through the coils generates a continuously varying
magnetic field that moves forward along the track.
 The frequency of the alternating current is synchronized to match the speed of the
train.
 The offset between the field exerted by magnets on the train and the applied field
create a force moving the train forward.
Advantages:
 No need of initial energy in case of magnets for low speeds
 One liter of Liquid nitrogen costs less than one liter of mineral water
 Onboard magnets and large margin between rail and train enable highest recorded
train speeds (581 km/h) and heavy load capacity. Successful operations using high
temperature superconductors in its onboard magnets, cooled with inexpensive liquid
nitrogen
 Magnetic fields inside and outside the vehicle are insignificant; proven, commercially
available technology that can attain very high speeds (500 km/h); no wheels or
secondary propulsion system needed
 Free of friction as it is “Levitating”
Atomic Physics
“Classical Physics”:
developed in 15th
to 20th
century,provides very successful description of “every day, ordinary
objects”
motion of trains, cars, bullets,….
orbit of moon, planets
how an engine works,..
subfields: mechanics, thermodynamics, electrodynamics,
Quantum Physics:
developed early 20th
century, in response to shortcomings of classical physics in describing
certain phenomena (blackbody radiation, photoelectric effect, emission and absorption
spectra…)describes “small” objects (e.g. atoms )
QP is “weird and counterintuitive”
“Those who are not shocked when they first come across quantum theory cannot possibly
have understood it” (Niles Bohr)
“Nobody feels perfectly comfortable with it “ (Murray Gell-Mann)
“I can safely say that nobody understands quantum mechanics” (Richard Feynman)
BUT…
QM is the most successful theory ever developed by humanity underlies our
understanding of atoms, molecules, condensed matter, nuclei, elementary particles
Crucial ingredient in understanding of stars, …
Quantum physics is basically the recognition that there is less difference between waves
and particles than was thought before
key insights:
light can behave like a particle
particles (e.g. electrons) are indistinguishable
particles can behave like waves (or wave packets)
waves gain or lose energy only in "quantized amounts“
detection (measurement) of a particle wave will change suddenly into a new wave
quantum mechanical interference – amplitudes add
QP is intrinsically probabilistic
what you can measure is what you can know
WAVE-PICTURE OF RADIATION—ENERGY FLOW I S CONTI N UOUS
• Radio waves, microwaves, heat waves, light waves, UV-rays, x-rays and y-rays belong to
the family of electromagnetic waves. All of them are known as radiation.
• Electromagnetic waves consist of varying electric and magnetic fields traveling at the
velocity of 'c'. The proMaxwell's theory treated the emission of radiation by a source as a
continuous process.
• A heated body may be assumed to be capable of giving out energy that travels in the form
of waves of all possible wavelengths.
• In the same way, the radiation incident on a body was thought to be absorbed at all
possible wavelengths.
• The intensity of radiation is given by,
I = 1E12
• where E is the amplitude of the electromagnetic wave.
• pagation of electromagnetic waves and their interaction with matter can be explained
with the help of Maxwell's electromagnetic theory.
• The phenomena of interference, diffraction and polarization of electromagnetic radiation
proved the wave nature of radiation.
• Therefore, it is expected that it would explain the experimental observations made on
thermal (heat) radiation emitted by a blackbody.
Blackbody radiation and Planck hypothesis
• Two patches of clouds in physics sky at the beginning of 20th
century.
• The speed of light  Relativity
• The blackbody radiation  foundation of Quantum theory
• Convection is transfer of heat by actual motion of. The hot-air furnace, the hot-water
heating system, and the flow of blood in the body are examples.
• Radiation The heat reaching the earth from the sun cannot be transferred either by
conduction or convection since the space between the earth and the sun has no material
medium. The energy is carried by electromagnetic waves that do not require a material
medium for propagation. The kind of heat transfer is called thermal radiation.
• Blackbody is defined as the body which can absorb all energies that fall on it. It is
something like a black hole. No lights or material can get away from it as long as it is
trapped. A large cavity with a small hole on its wall can be taken as a blackbody.
LAWS OF BLACK BODY RADIATION
1. Stefan and Boltzmann’s law: it is found that the radiation energy is proportional to the fourth
power of the associated temperature. 4
M (T) T
2. Wien’s displacement law: the peak of the curve shifts towards longer
wavelength as the temperature falls and it satisfies
where b is called the Wien's constant. b=2.89X10-3
4
M (T ) T
peak
T b
This law is quite useful for measuring the temperature of a blackbody with a very high
temperature. You can see the example for how to measure the temperature on the surface of the
sun.
• The above laws describes the blackbody radiation very well.
• The problem exists in the relation between the radiation power Mλ(T) and the
wavelength λ.
• Blackbody radiation has nothing to do with both the material used in the blackbody
concave wall and the shape of the concave wall.
• Two typical theoretical formulas for blackbody radiation : One is given by Rayleigh and
Jeans and the other by Wein.
3.Rayleigh and Jeans
• In 1890, Rayleigh and Jeans obtained a formula using the classical electromagnetic
(Maxwell) theory and the classical equipartition theorem of energy in thermotics. The
formula is given by
2
3
8 kT
E( )
c
Rayleigh-Jeans formula was correct for very long wavelength in the far infrared but hopelessly
wrong in the visible light and ultraviolet region. Maxwell‟s electromagnetic theory and
thermodynamics are known as correct theory. The failure in explaining blackbody radiation
puzzled physicists! It was regarded as ultraviolet Catastrophe (disaster).
4. Planck Radiation Law:
Where,
E=Quantum energy
h= Planck constant
v= frequency
PLANCK'S QUANTUM HYPOTHESIS — Energy is quantized
• Max Planck empirical formula explained the experimental observations.
• In the process of formulation of the formula, he assumed that the atoms of the walls of
the blackbody behave like small harmonic oscillators, each having a characteristic
frequency of vibration, lie further made two radical assumptions about the atomic
oscillators.
• An oscillating atom can absorb or mends energy in discrete units. The indivisible discrete
unit of energy hs, is the smallest amount of energy which can be absorbed or emitted by
the atom and is called an energy quantum. A quantum of energy has the magnitude given
by
E = hv
4
M (T) T
hc
E h
where v is the frequency of radiation and „h' is a constant now known as the Planck's
constant.
• The energy of the oscillator is quantized. It can have only certain discrete amounts of
energy En.
En= nhv n=1,2,3……
• The hypothesis that radiant energy is emitted or absorbed basically in a discontinuous
summer and in the form of quanta is known as the Planck's quantum hypothesis.
• Planck's hypothesis states that radiant energy Is quantized and implies that an atom exists
in certain discrete energy states. Such states arc called quantum stales and n is called the
quantum number.
• The atom emits or absorbs energy by jumping from one quantum state to another
quantum state. The assumption of discrete energy states for an atomic oscillator (Fig.a)
was a departure from the classical physics and our everyday exper
• If we take a mass-spring harmonic oscillator, it can receive any amount of energy form
zero to some maximum value (Fig.b). Thus, in the realm of classical physics energy
always appears to occur with continuous values and energy exchange between bodies
involves any arbitrary amounts of energy.
PARTICLE PICTURE OF RADIATION —Radiation is a stream of photons
Max Planck introduced the concept of discontinuous emission and absorption of radiation
by bodies but he treated the propagation through space as occurring in the form of
continuous waves as demanded by electromagnetic theory.
• Einstein refined the Planck's hypothesis and invested the quantum with a clear and
distinct identity.
• He successfully explained the experimental results of the photoelectric effect in 1905 and
the temperature dependence of specific heats of solids in 1907 basing on Planck's
hypothesis.
• The photoelectric effect conclusively established that light behaves as a swam of
particles. Einstein extended Planck's hypothesis as follows:
1 Einstein assumed that the light energy is not distributed evenly over the whole
expanding wave front but rather remains concentrated in discrete quanta. He
named the energy quanta as photons. Accordingly, a light beam is regarded as a
stream of photons travelling with a velocity ' c' .
2 An electromagnetic wave having a frequency f contains identical photons, each
having an energy hƒ. The higher the frequency of the electromagnetic wave, the
higher is the energy content of each photon.
3. An electromagnetic wave would have energy hƒ if it contains only one photon.
2hv if it contains 2 photons and so on. Therefore, the intensity of a
monochromatic light beam I. is related to the concentration of photons. N. present
in the beam. Thus,
I = N hƒ
Note that according to electromagnetic theory, the intensity of a light beam is given by
I = 1E12
4. When photons encounter matter, they impart all their energy to the panicles of matter and
vanish. That is why absorption of radiation is discontinuous. The number of photons
emitted by even a weak light source is enormously large and the human eye cannot
register the photons separately and therefore light appears as a continuous stream. Thus,
the discreteness of light is not readily apparent.
The Photon
• As the radiant energy is viewed as made up of spatially localized photons. we may
attribute particle properties to photons.
1. Energy: The energy of a photon is determined by its frequency v and is given by E = hƒ.
Using the relation ω= 2π and writing h/2π = ħ. we may express E= ħω
2. Velocity: Photons always travel with the velocity of light „c'.
3. Rest Mass: The rest mass of photon is zero since a photon can never be at rest. Thus, m0=
0
4. Relativistic mass: As photon travels with the velocity of light, it has relativistic mass.
given by m= E/c2
= hv/c2
5. Linear Momentum: The linear momentum associated with a photon may be expressed as
p=E/c=hv/c= h/λ
As the wave vector k= 2π/λ , p = hk/ 2π = ħk.
6. Angular Momentum: Angular momentum is also known as spin which is the intrinsic
property of all microparticles. Photon has a spin of one unit. Thus. s = lħ.
7. Electrical Charge: Photons are electrically neutral and cannot be influenced by electric or
magnetic fields. They cannot ionize matter.
Example: 1
Calculate the photon energies for the following types of electromagnetic radiation:
(a) a 600kHz radio wave; (b) the 500nm (wavelength of) green light; (c) a 0.1 nm
(wavelength of) X-rays.
Solution:
(a) for the radio wave, we can use the Planck-Einstein law directly
15 3
9
E h 4.136 10 eV s 600 10 Hz
2.48 10 eV
(b) The light wave is specified by wavelength, we can use the law explained in wavelength:
6
9
hc 1.241 10 eV m
E 2.26eV
550 10 m
(c). For X-rays, we have
6
4
9
hc 1.241 10 eV m
E 1.24 10 eV 12.4keV
0.1 10 m
Photoelectric Effect:-
The quantum nature of light had its origin in the theory of thermal radiation and was
strongly reinforced by the discovery of the photoelectric effect.
Fig. Apparatus to investigate the photoelectric effect that was first found in 1887 by Hertz.
In figure , a glass tube contains two electrodes of the same material, one of which is irradiated by
light. The electrodes are connected to a battery and a sensitive current detector measures the
current flow between them.
The current flow is a direct measure of the rate of emission of electrons from the irradiated
electrode.
The electrons in the electrodes can be ejected by light and have a certain amount of kinetic
energy. Now we change:
(1) the frequency and intensity of light,
(2) the electromotive force (e.m.f. or voltage),
(3) the nature of electrode surface.
It is found that:
(1). For a given electrode material, no photoemission exists at all below a certain frequency of
the incident light. When the frequency increases, the emission begins at a certain frequency. The
frequency is called threshold frequency of the material. The threshold frequency has to be
measured in the existence of e.m.f. (electromotive force) as at such a case the photoelectrons
have no kinetic energy to move from the cathode to anode . Different electrode material has
different threshold frequency.
(2). The rate of electron emission is directly proportional to the intensity of the incident light.
Photoelectric current ∝ The intensity of light
(3). Increasing the intensity of the incident light does not increase the kinetic energy of the
photoelectrons.
Intensity of light ∝ kinetic energy of photoelectron
However increasing the frequency of light does increase the kinetic energy of photoelectrons
even for very low intensity levels.
Frequency of light ∝ kinetic energy of photoelectron
(4). There is no measurable time delay between irradiating the electrode and the emission of
photoelectrons, even when the light is of very low intensity. As soon as the electrode is
irradiated, photoelectrons are ejected.
(5) The photoelectric current is deeply affected by the nature of the electrodes and chemical
contamination of their surface.
In 1905, Einstein solved the photoelectric effect problem by applying the Planck‟s hypothesis.
He pointed out that Planck‟s quantization hypothesis applied not only to the emission of
radiation by a material object but also to its transmission and its absorption by another material
object. The light is not only electromagnetic waves but also a quantum. All the effects of
photoelectric emission can be readily explained from the following assumptions:
Therefore we have the equation of photoelectric effect:
21
2
h A mv
Using this equation and Einstein‟s assumption, you could readily explain all the results in the
photoelectric effect: why does threshold frequency exist (problem)? why is the number of
photoelectrons proportional to the light intensity? why does high intensity not mean high
photoelectron energy (problem)? why is there no time delay (problem)?
Example: Ultraviolet light of wavelength 150nm falls on a chromium electrode. Calculate
the maximum kinetic energy and the corresponding velocity of the photoelectrons (the
work function of chromium is 4.37eV).
Solution: using the equation of the photoelectric effect, it is convenient to express the energy in
electron volts. The photon energy is
6
9
1.241 10
8.27
150 10
hc eV m
E h eV
m
2
2
1
2
1
(8.27 4.37) 3.90
2
h A mv
mv eV eV
19 19 19 2 2
1 1.602 10 1.602 10 1.602 10eV J N m kg m s
2 19 2 21
3.90 3.90 1.602 10
2
mv eV kg m s
19
6
31
2 3.90 12.496 10
1.17 10 /
9.11 10
eV
v m s
m
EXERCISE:-
1. The wavelength of yellow light is 5890 A. What is the energy of the photons in the
beam? Empress in electron volts.
2. 77w light sensitive compound on most photographic films is silver bromide, Aglin A film
is exposed when the light energy absorbed dissociates this molecule into its atoms. The
energy of dissociation of Agllr is 23.9 k.catitnot Find the energy in electron volts, the
wavelength and the frequency of the photon that is just able to dissociate a molecule of
silver bromide.
3. Calculate the energy of a photon of blue light with a frequency of 6.67 x 1014
Hz. (State
in eV) [2.76eV]
4. Calculate the energy of a photon of red light with a wavelength of 630 nm. [1.97eV]
5. Barium has a work function of 2.48 eV. What is the maximum kinetic energy of the
ejected electron if the metal is illuminated by light of wavelength 450 nm? [0.28 eV]
6. When a 350nm light ray falls on a metal, the maximum kinetic energy of the
photoelectron is 1.20eV. What is the work function of the metal? [2.3 eV]
7. A photon has 3.3 x 10-19
J of energy. What is the wavelength of this photon?
8. What is the energy of one quantum of 5.0 x 1014
Hz light?
4
M (T) T
X-Rays
Objectives:
 Introduction and production of X-Rays
 Properties of X-Rays
 Diffraction of X-Rays
 The Bragg’s X-Ray spectrometer
 Continuous spectra
 Characteristics Radiation
 Moseley’s law
 Absorption of X-Ray
 Compton effect
 Applications of X-Rays
Introduction and production of X-Rays
Introduction of X- Rays
Wilhelm Rontgen discovered X-rays in 1985 during the course of some
experiments with a discharge tube. He noticed that a screen coated with barium
platinocyanide present at a distance from the discharge tube. Rontgen called these
invisible radiations X-rays. Finally he concluded that X-rays are produced due to the
bombardment of cathode rays on the walls of the discharge tube.
It is well known that X-rays are produced when the fast moving electrons, and
that metals or high atomic weight are most effective for this purpose.
X-rays are electromagnetic waves with very short wavelengths. X-rays are highly
penetrating and it can pass through many solids. They occur beyond the UV region in the
electromagnetic spectrum. Their wavelengths range from 0.01 to 10 Å.
Production or Generation of X-rays
X-rays are produced by an X-ray tube. The schematic of the modern type of X-ray
tube designed by Coolidge is shown in above figure.
 It is an evacuated glass bulb enclosing two electrodes, a cathode and an anode.
The cathode consists of a tungsten filament which emits electrons when it
heated. The electrons are focused into a narrow beam with the help of a metal
cup S.
The anode consists of a target material, made of tungsten or molybdenum,
which is embedded in a copper bar.
Water circulating through a jacket surrounding the anode and cools the anode. Further
large cooling fins conduct the heat away to the atmosphere.
The face of the target is kept at an angle relative to the oncoming electron beam.
A very high potential difference of the order of 50 kV is applied across the electrodes.
The electrons emitted by the cathode are accelerated by the anode and acquire high
energies of order of 105
eV. When the target suddenly stops these electrons, X-rays are
emitted.
The magnetic field associated with the electron beam undergoes a change when
the electrons are stopped and electromagnetic waves in the form of X-rays are generated.
The grater of the speed of the electron beam, the shorter will be the wavelength of
the radiated X-rays. Only about 0.2 % of the electron beam energy is converted in to X-
rays and the rest of the energy transforms into heat. It is for the reason that the anode is
intensively cooled during the operation of X-ray tube.
The intensity of the electron beam depends on the number of electron leaving the
cathode. The hardness of the X-rays emitted depends on the energy of the electron beam
striking the target. It can be adjusted by varying the potential difference applied between
the cathode and anode. Therefore, the larger potential difference, the more penetrating or
harder X-rays.
Properties of X-Ray
 They have relatively high penetrating power.
 They are classified into Hard X-rays & Soft X-rays.
The X-rays which have high energy and short wavelength is known as Hard X-
rays.
The X-rays which have low energy and longer wavelength is known as Soft X-
rays.
 X-rays causes the phenomenon of flouroscence.
 On passing through a gas X-rays ionize the gas.
 They are absorbed by the materials through which they traverse.
 X-rays travel in straight line. Their speed in vacuum is equal to speed of light.
 X-rays can affect a photographic film.
 X-rays are undeflected by electric field or magnetic field.
Diffraction of X-Rays – Bragg’s law
Consider a crystal as made out of parallel planes of ions, spaced a distance d
apart. The conditions for a sharp peak in the intensity of the scattered radiation are:
1. That the X-rays should be secularly reflected by the ions in any one plane.
2. That the reflected rays from successive planes should interfere constructively.
Path difference between two rays reflected from adjoining planes:
2dsinθ, for the rays to interfere constructively, this path difference must be an integral
number of wavelength λ,
Suppose that a single monochromatic wave (of any type) is incident on aligned
planes of lattice points, with separation , at angle . Points A and C are on one plane,
and B is on the plane below. Points ABCC' form a quadrilateral.
There will be a path difference between the ray that gets reflected along AC' and
the ray that gets transmitted, and then reflected, along AB and BC respectively. This path
difference is:
The two separate waves will arrive at a point with the same phase, and hence
undergo constructive interference, if and only if this path difference is equal to any
integer value of the wavelength, i.e.
Where, the same definition of and apply as above.
Therefore,
from which it follows that,
Putting everything together,
Which simplifies to
Which is Bragg's law.
Bragg angle is just the half of the total angle by which the incident beam is deflected.
The Bragg’s X-Ray spectrometer
An X-ray diffraction experiment requires,
(1) X-ray source
(2) The sample
(3) The detector
Depending on method there can be variations in these requirements. The X-ray
radiation may either monochromatic or may have variable wave length.
Structures of polycrystalline sample and single crystals can be studied. The
detectors used in these experiments are photographic film.
The schematic diagram of Bragg’s X-ray spectrometer is given in above.
X-ray from an X-ray tube is collimated by passing team through slits S1 and S2. This
beam is then allowed to fall on a single crystal mounted on a table which can be rotated
about an axis perpendicular to the plane of incident of X-rays. The crystal behaves as a
reflected grating and reflects X-rays. By rotating the table, the glancing angle θ at which
the X-ray is incident on the crystal can be changed. The angle for which the intensity of
the reflected beam is maximum gives the value of θ. The experiment is repeated for each
plane of the crystal. For first order reflection n = 1 so that, λ = 2d sinθ; for n = 2, 2λ = 2d
sinθ; ……., and so on.
A photographic plate or an ionization chamber is used to detect the rays reflected by
the crystal.
Continuous X-rays or Bremsstrahlung X-rays
"Bremsstrahlung" means "braking radiation" and is retained from the original
German to describe the radiation which is emitted when electrons are decelerated or
"braked" when they are fired at a metal target. Accelerated charges give off
electromagnetic radiation, and when the energy of the bombarding electrons is high
enough, that radiation is in the x-ray region of the electromagnetic spectrum. It is
characterized by a continuous distribution of radiation which becomes more intense and
shifts toward higher frequencies when the energy of the bombarding electrons is
increased. The curves above are who bombarded tungsten targets with electrons of four
different energies.
The continuous distribution of x-rays which forms the base for the two sharp
peaks at left is called "Bremsstrahlung" radiation.
The bombarding electrons can also eject electrons from the inner shells of the
atoms of the metal target, and the quick filling of those vacancies by electrons dropping
down from higher levels gives rise to sharply defined characteristic x-rays.
Characteristic X-rays
Characteristic x-rays are emitted from heavy elements when their electrons make
transitions between the lower atomic energy levels. The characteristic x-rays emission
which shown as two sharp peaks in the illustration at left occur when vacancies are
produced in the n=1 or K-shell of the atom and electrons drop down from above to fill the
gap. The X-rays produced by transitions from the n=2 to n=1 levels are called Kα X-rays,
and those for the n=3->1 transition are called Kβ X-rays.
Transitions to the n=2 or L-shell are designated as L x-rays (n=3->2 is L-alpha,
n=4->2 is L-beta, etc.
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Ep notes

  • 1. OPTICAL FIBER Introduction Fiber optics deals with the light propagation through thin glass fibers. Fiber optics plays an important role in the field of communication to transmit voice, television and digital data signals fro one place to another. The transmission of light along the thin cylindrical glass fiber by total internal reflection was first demonstrated by John Tyndall in 1870 and the application of this phenomenon in the field of communication is tried only from 1927. Today the applications of fiber optics are also extended to medical field in the form of endoscopes and to instrumentation engineering in the form of optical sensors. The Basic principle of optical fiber Principle: The basic principle of optical fiber in the transmission of optical signal is total internal reflection. Total internal reflection:- When the light ray travels from denser medium to rarer medium the refracted ray bends away from the normal. When the angle of incidence is greater than the critical angle, the refracted ray again reflects into the same medium. This phenomenon is called total internal reflection. The refracted ray bends towards the normal as the ray travels from rarer medium to denser medium. The refracted ray bends away from the normal as it travels from denser medium to rarer medium. Conditions for Total Internal Reflection (a) the refractive index n1 of the core must always be greater than the refractive index n2 of the cladding. (b) The angle of incidence i must be greater than critical angle C it can be define as when light travels from a more optically dense material [larger index of refraction] to a less dense material the angle of refraction is larger than the incident angle.
  • 2. Because the refracted angle is always larger than the incident angle, it is possible for the refracted angle to reach 90° before the incident angle reaches 90°. If the light were to refract out of the denser medium, it would then run along the surface. Larger angles would then yield situations which would force the sine function to be larger than 1.00, which is mathematically impossible. When the incident angle reaches the condition whereby the refracted ray would bend to an angle of 90°, it is called the CRITICAL ANGLE. The critical angle obeys the following equation: This reflected ray changes in intensity as we vary the angle of incidence. At small incident angles (almost perpendicular to the surface) the reflected ray is weak and the refracted ray is strong. Construction of optical fiber:- The optical fiber mainly consists the following six parts as shown in figure Core: A typical glass fiber consists of a central core material. Generally core diameter is 50 . The core is surrounded by cladding. The core medium refractive is always greater than the cladding refractive index. Cladding Cladding refractive index is lesser than the cores refractive index. The over all diameter of cladding is 125 to 200 . Silicon Coating Silicon coating is provided between buffer jacket and cladding. It improves the quality of transmission of light.
  • 3. Buffer Jacket Silicon coating is surrounded by buffer jacket. Buffer jacket is made of plastic and protects the fiber cable from moisture. Strength Member Buffer jacket is surrounded by strength member. It provides strength to the fiber cable. Outer Jacket Finally the fiber cable is covered by polyurethane outer jacket. Because of this arrangement fiber cable will not be damaged during pulling, bending, stretching and rolling through the fiber cable is made up of glasses. NA & ACCEPTANCE ANGLE DERIVATION “In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light.” optical fiber will only propagate light that enters the fiber within a certain cone, known as the acceptance cone of the fiber. The half-angle of this cone is called the acceptance angle, θmax. on where n1 is the refractive index of the fiber core, and n2 is the refractive index of the cladding. When a light ray is incident from a medium of refractive index n to the core of index n1, Snell's law at medium-core interface gives From the above figure and using trigonometry, we get : Where is the critical angle for total internal reflection, since Substituting for sin θr in Snell's law we get:
  • 4. By squaring both sides Thus, from where the formula given above follows. θmax = This has the same form as the numerical aperture in other optical systems, so it has become common to define the NA of any type of fiber. Definition:- Acceptance angle:- Acceptance angle is defined as the maximum angle of incidence at the interface of air medium and core medium for which the light ray enters into the core and travels along the interface of core and cladding. Acceptance Cone:- There is an imaginary cone of acceptance with an angle .The light that enters the fiber at angles within the acceptance cone are guided down the fiber core Numerical aperture:- Numerical aperture is defined as the light gathering capacity of an optical fiber and it is directly proportional to the acceptance angle. Numerically it is equal to the sin of the acceptance angle Classification of fibers:- Based on the refractive index of core medium, optical fibers are classified into two categories. i. Step index fiber ii. Graded index fiber Based on the number of modes of transmission, optical fibers are classified into two categories i. Single mode fiber ii. Multimode fiber Based on the material used, optical fibers are may broadly classified into four categories i. All glass fibers
  • 5. ii. All plastic fibers iii. Glass core with plastic cladding fibers iv. Polymer clad silica fibers. Step index fiber:- In step index fibers the refractive index of the core medium is uniform and undergoes an abrupt change at the interface of core and cladding as shown in figure. The diameter of core is about 10micrometers in case of single mode fiber and 50 to 200 micrometers in multi mode fiber. Attenuation is more for step index multi mode fibers but less in step index single mode fibers Numerical aperture is more for step index multi mode fibers but it is less in step index single mode fibers Graded index fiber:- In graded index fibers, the refractive index of the core medium is varying in the parabolic manner such that the maximum refractive index is present at the center of the core. The diameter of the core is about 50 micro meters. Attenuation is very less in graded index fibers Numerical aperture is less in graded index fibers Graded index Figure Two types of fiber: (Top) step index fiber; (Bottom) Graded index fiber Single mode optical fiber In single mode optical fibers only one mode of propagation is possible.In case of single mode fiber the diameter of core is about 10micrometers.The difference between the refractive indices of core and cladding is very small. In single mode fibers there is no dispersion, so these are more suitable for
  • 6. Communication. The single mode optical fibers are costly, because the fabrication is difficult.The process of launching of light into single mode fibers is very difficult. Multi mode optical fiber In multi mode optical fibers many mummer of modes of propagation are possible. In case of in multi mode fiber the diameter of core is 50 to 200 micrometers. The difference between the refractive indices of core and cladding is also large compared to the single mode fibers. Due to multi mode transmission, the dispersion is large, so these fibers are not used for communication purposes. The multi mode optical fibers are cheap than single mode fibers, because the fabrication is easy. The process of launching of light into single mode fibers is very easy. Based on the material:- Three common type of fiber in terms of the material used: Glass core with glass cladding –all glass or silica fiber Glass core with plastic cladding –plastic cladded/coated silica (PCS) Plastic core with plastic cladding – all plastic or polymer fib Attenuation:- Definition: a loss of signal strength in a lightwave, electrical or radio signal usually related to the distance the signal must travel. Attenuation is caused by: Absorption Scattering Radiative loss
  • 7. Losses:- Losses in optical fiber result from attenuation in the material itself and from scattering, which causes some light to strike the cladding at less than the critical angle Bending the optical fiber too sharply can also cause losses by causing some of the light to meet the cladding at less than the critical angle Losses vary greatly depending upon the type of fiber Plastic fiber may have losses of several hundred dB per kilometer Graded-index multimode glass fiber has a loss of about 2–4 dB per kilometer Single-mode fiber has a loss of 0.4 dB/km or less Macrobending Loss: The curvature of the bend is much larger than fiber diameter. Lightwave suffers sever loss due to radiation of the evanescent field in the cladding region. As the radius of the curvature decreases, the loss increases exponentially until it reaches at a certain critical radius. For any radius a bit smaller than this point, the losses suddenly becomes extremely large. Higher order modes radiate away faster than lower order modes. Microbending Loss: microscopic bends of the fiber axis that can arise when the fibers are incorporated into cables. The power is dissipated through the microbended fiber, because of the repetitive coupling of energy between guided modes & the leaky or radiation modes in the fiber. Dispersion:- The phenomenon in an optical fibre whereby light photons arrive at a distant point in different phase than they entered the fibre. Dispersion causes receive signal distortion that ultimately limits the bandwidth and usable length of the fiBer cable The two main causes of dispersion are: Material (Chromatic) dispersion Waveguide dispersion Intermodal delay (in multimode fibres) Dispersion in fiber optics results from the fact that in multimode propagation, the signal travels faster in some modes than it would in others.Single-mode fibers are relatively free from dispersion except for intramodal dispersion .Graded-index fibers reduce dispersion by taking advantage of higher-order modes.One form of intramodal dispersion is called material
  • 8. dispersion because it depends upon the material of the core.Another form of dispersion is called waveguide dispersion .Dispersion increases with the bandwidth of the light source The advantage of fiber optic cable over metallic cable:- 1. Extremely wide (large) bandwidth. The bandwidth available with a single glass fibre is more than 100GHZ. With such a large bandwidth, it is possible to transmit thousands of voice conversations or dozens of video signals over the same fibre simultaneously. Irrespective of whether the information is voice, data or video or a combination of these, it can be transmitted easily over the optical fibre. Less no of independent signals alone can be sent through metallic cables. 2. Immunity to electrostatic interference. As optical fibres are being made of either glass or plastic external electric noise and lightning do not affect the energy in a cable. The result is noise free transmission. While this is not true for metallic cables made up of metals, as they are good conductors of electricity. 3. Elimination of cross Talk. Fibre systems are immune to cross talk between cables caused by magnetic induction. Whereas in a metallic cable cross talk results from the electromagnetic coupling between two adjacent wires. 4. Lighter weight and smaller size. Fibres are very smaller in size. This size reduction makes fibre the ideal transmission medium for ships, aircraft and high rise buildings where bulky copper cables occupy to much space. Reduction in size so reduction in weight also. 5. Lower cost. The material used in fibres is silica glass or silicon dioxide which is one of the most abundant materials on earth. So available in lower cost. 6. Security. Fibre cables are more secure than metallic cables. Due to its immunity to electromagnetic coupling and radiation, optical fibre can be used in most secure environment. Although it can be intercepted or tapped, it is very difficult to do so because, at the receiving users end an alarm would be sounded.
  • 9. 7. Greater safety. In many wired system the potential hazard of short circuits requires precautionary designs. Whereas, the dielectric nature of optical fibres eliminates the spark hazard. 8. Corrosion Fibre cables are more resistive to environmental extremes. They operate over large temperature variation than their metallic counter parts, and are less affected by corrosive liquids and gases. 9. Longer life span and ease of maintenance. A longer life span of 20 to 30 years is predicted for the fibre optic cables as compare to 12to 15 years of metallic cables. Differences between step index fibers and graded index fibers:- Step index fiber Graded index fiber 1. In step index fibers the refractive index of the core medium is uniform through and undergoes an abrupt change at the interface of core and cladding. 1. In graded index fibers, the refractive index of the core medium is varying in the parabolic manner such that the maximum refractive index is present at the center of the core. 2. The diameter of core is about 10micrometers in case of single mode fiber and 50 to 200 micrometers in multi mode fiber. 2. The diameter of the core is about 50 micro meters. 3. The transmitted optical signal will cross the fiber axis during every reflection at the core cladding boundary. 3. The transmitted optical signal will never cross the fiber axis at any time. 4. The shape of propagation of the optical signal is in zigzag manner. 4. The shape of propagation of the optical signal appears in the helical or spiral manner 5. Attenuation is more for multi mode step index fibers but Attenuation is less in single mode step index fibers 5. Attenuation is very less in graded index fibers 6. Numerical aperture is more for multi mode step index fibers but it is less in single mode step index fibers 6. Numerical aperture is less in graded index fibers
  • 10. Differences between single mode fibers and Multy mode fibers:- Single mode fiber Multimode fiber Single Mode cable is a single strand (most applications use 2 fibers) of glass fiber with a diameter of 8.3 to 10 microns that has one mode of transmission. Multi-Mode cable has a little bit bigger diameter, with a common diameters in the 50-to-100 micron range for the light carry component Single Modem fiber is used in many applications where data is sent at multi-frequency (WDM Wave-Division-Multiplexing) so only one cable is needed Most applications in which Multi-mode fiber is used, 2 fibers are used (WDM is not normally used on multi-mode fiber). Example:- step index fiber Example:- multimode step index fiber The small core and single light-wave virtually eliminate any distortion that could result from overlapping light pulses, providing the least signal attenuation and the highest transmission speeds of any fiber cable type. multiple paths of light can cause signal distortion at the receiving end, resulting in an unclear and incomplete data transmission Applications of optical fibers 1. Optical fibers are extensively used in communication system. 2. Optical fibers are in exchange of information between different computers 3. Optical fibers are used for exchange of information in cable televisions, space vehicles, submarines etc. 4. Optical fibers are used in industry in security alarm systems, process control and industrial auto machine. 5. Optical fibers are used in pressure sensors in biomedical and engine control. 6. Optical fibers are used in medicine, in the fabrication in endoscopy for the visualization of internal parts of the human body. 7. Sensing applications of optical fibers are Displacement sensor Fluid level detector Liquid Temperature and pressure sensor Chemical sensors 8. Medical applications of optical fibers are Gastroscope Orthoscope Couldo
  • 11. EXAMPLE:- 1. A silica optical fiber has a core of refractive index 1.55 and a cladding of refractive index 1.47. Determine (i) the critical angle at the core-cladding interface (ii) the numerical aperture for the fiber and (iii) the acceptance angle in the air for the fiber. Given, n1=1.55, n2=1.47 Øin(max)=? NA=? Øc=? Acceptance angle Øin(max)= sin-1 (n1 2 – n2 2 )1/2 Øin(max)= sin-1 (1.552 –1.472 )1/2 = sin-1 (2.41-2.16)1/2 = sin-1 (0.25)1/2 = sin-1 (0.316) Øin(max) =30°00’ Numerical aperture NA= (n1 2 – n2 2 )1/2 = 1.552 –1.472 )1/2 = (2.41-2.16)1/2 = (0.25)1/2 = 0.316 critical angle Øc = sin-1 (n2 / n1) = sin-1 (1.47 / 1.55) = sin-1 (0.9483) = 71°.55’ 2. An optical fiber has refractive index of core and cladding is 1.514 and 1.48 Respectively. Calculate the acceptance angle and the fractional index Change Given ,n1=1.514, n2=1.48 Øin(max)=? ∆=? Acceptance angle Øin(max ) = sin-1 (n1 2 – n2 2 )1/2 Øin(max) = sin-1 (1.5142 –1.482 )1/2 = sin-1 (2.29-2.19)1/2 = sin-1 (0.1)1/2 = sin-1 (0.316) Øin(max)=18°42’
  • 12. Numerical aperture NA= (n1 2 – n2 2 )1/2 =(1.5142 –1.482 )1/2 =(2.29-2.19)1/2 =(0.1)1/2 =0.316 NA=n1√2∆ 0.316/1.514=√2∆ (0.2087)2 =2∆ ∆=0.0435/2 ∆=0.0217
  • 13. Dielectrics  Introduction Dielectrics are the materials having electric dipole moment permanently. Dipole: A dipole is an entity in which equal positive and negative charges are separated by a small distance.. DIPOLE moment (µEle ):The product of magnitude of either of the charges and separation distance b/w them is called Dipole moment. µe = q . x  coulmb.m All dielectrics are electrical insulators and they are mainly used to store electrical energy. Ex: Mica, glass, plastic, water & polar molecules…  Dielectric const. of medium The relative permittivity(εr) is often known as dielectric const. of medium it can given by, εr=ε/ε0 Dielectric constant is ratio of permittivity of medium to permittivity of free space. The value of capacitance of capacitor is given by, C0=εrε0A/d By this eqn we can say that high εr increases capacity of capacitor.  Polar and Nonpolarized Molecules Non-polar Molecules : The Dielectric material in which there is no permanent dipole existence in absence of an external field is ….. 2 – Compounds made of molecules which are symmetrically shaped Polar Molecules :The Dielectric material in which there is permanent dipole existence even in absence of an external field is …..
  • 14. Polarization of Dielectrics As shown in fig. when an electric field is applied to dielectric material their negative & positive charges tend to align in equilibrium position.
  • 15.  Gauss’s Law In Dielectrics In absence of dielectric In presence of dielectric 0 0 d 0 0 0 0 0 0 0 0 0 E V k E V E q E k kA q q ' E A A q q q ' S o, kA A A 1 then , q ' q (1 ) k S o, E.ds V E d S q q ' 1 q q (1 ) k q k k E.ds q o, N ow This relation true is for parallel plate capacitor Which is Gauss’s law for dielectrics. 0 0 0 0 0 E.ds q q E A q E A 0 0 0 0 0 E.ds q q ' q q ' EA q q ' E A A
  • 16.  Three Electric vectors The resultant dielectric field is given by, Where, E=Electric field D=Flux Density or Displacement vector P=Polarization  Electric susceptibility: The polarization vector P is proportional to the total electric flux density and direction of electric field. Therefore the polarization vector can be written as:  Relation between εr & Displacement vector,  Types of polarization 1. Electron polarization 2. Ionic polarization 3. Orientation polarization 4. Space charge polarization 0 0 0 0 0 0 ' ' , , , D p q q E A A q now P A q P E A q E P A q now D A So E P 0 0 0 0 ( 1) 1 e e r e r P E P E E E 0 0 0 r 0 0 0 D E P Now,P= ( - ) E P (or) ( . - ) E P ( 1) . P W here,( 1) r r E E
  • 17. 1. Electronic polarization When no external field is applied nucleus of atom is like in fig. (a) When external field is applied, displacement in opposite direction is observed between nucleus & electrons due to this dipole moment is induced. This type of polarization is called Electronic polarization. Ex. Germanium, Silicon, Diamond etc… 2. Ionic polarization Some materials like ionic crystal does not possess permanent dipole moment. Fig. (a) shows natural arrangement of ionic crystal. When Ele. Field is applied on this type of material displacement of ions is observed. Due to an external electric field a positive & negative ion displaces in the direction opposite to each other due to which distance between them is reduced & ionic polarization is generated. Ionic polarization is observed in materials like NaCl, KBr, KCl etc… Let us consider simple example of NaCl crystal. As shown in fig. when crystal is placed in an external electric field Na+ ion displaces in one direction & Cl- ion goes in opposite direction. 3. Orientation polarization Some molecules like H2O, HCl having permanent dipole moment p0. In the absence of a field, individual dipoles are arranged in random way, so net average dipole moment in a unit volume is zero as shown in fig. (b). A dipole such as HCl placed in a field experiences a torque that tries to rotate it to align p0 with the field E.
  • 18. In the presence of an applied field, the dipoles try to rotate to align parallel to each other in direction of electric field fig (d). This type of polarization is Orientation polarization. This type of polarization occurs only in polar substances like H2O, CH3Cl when they are placed in external field. 4. Space charge polarization (Interfacial polarization) A crystal with equal number of mobile positive ions and fixed negative ions. In the absence of a field, there is no net separation between all the positive charges and all the negative charges. In the presence of an applied field, the mobile positive ions migrate toward the negative charges and positive charges in the dielectric. The dielectric therefore exhibits Space charge or interfacial polarization.  Energy stored in dielectric field Work done is, . ? . . dW F dr F dW qE dr dW E dp p p P lA V 0 0 0 2 0 2 0 ( 1) . . .( 1) . . .( 1) . 1 ( 1) E 2 1 ( 1) E 2 ? r r r r r p PV dW EVdP P E dW E V dE dW E V dE W V W V U
  • 19. Band Theory of Solid  Objectives • Effective Mass of electron • Concept of Holes • Energy Band Structure of Solids:  Conductors, Insulators and Semiconductors • Semiconductors  Intrinsic and Extrinsic Semiconductors • Type of diodes  Simple Diode  Zener Diode  Effective Mass of electron  An electron moving in the solid under the influence of the crystal potential is subjected to an electric field.  We expect an external field to accelerate the electron, increasing E and k and change the electron’s state. ------ (1) But, dx/dt = vg ------ (2) ------ (3) dk d gv   1  gv dx dV e dt dk dk d  
  • 20. ----- (4) ------ (5) ------ (6) ------ (7) ----- (8)  Concept of Holes Consider a semiconductor with a small number of electrons excited from the valence band into the conduction band.  If an electric field is applied, • The conduction band electrons will participate in the electrical current • The valence band electrons can “move into” the empty states, and thus can also contribute to the current.  If we describe such changes via “movement” of the “empty” states – the picture will be significantly simplified. This “empty space” is called a Hole.  “Deficiency” of negative charge can be treated as a positive charge. dx dV ek dt d gv dx dV e dt dk gv     eEk dt d  dt dk dk d dk d dk d dt d dt dv a g                11                     k dt d dk d dt dk dk d   2 2 22 2 11 
  • 21.  Holes act as charge carriers in the sense that electrons from nearby sites can “move” into the hole.  Holes are usually heavier than electrons since they depict collective behavior of many electrons.  To understand hole motion, one requires another view of the holes, which represent them as electrons with negative effective mass m*.  For example the movement of the hole think of a row of chairs occupied by people with one chair empty, and to move all people rise all together and move in one direction, so the empty spot moves in the same direction.  Energy Band Structure of Solids Conductor, Semiconductor and Insulator  In isolated atoms the electrons are arranged in energy levels.  Energy Band in Solid The following are the important energy band in solids:  Valence band  Conduction band  Forbidden energy gap or Forbidden band
  • 22.  Valance band The band of energy occupied by the valance electrons is called valence band. The electrons in the outermost orbit of an atom are known as valance electrons. This band may be completely or partial filled. Electron can be move from one valance band to the conduction band by the application of external energy.  Conduction band The band of energy occupied by the conduction electrons is called conduction band. This is the uppermost band and all electrons in the conduction band are free electrons. The conduction band is empty for insulator and partially filled for conductors.  Forbidden Energy Gap or Forbidden band The gap between the valance band and conduction band on energy level diagram known as forbidden band or energy gap. Electrons are never found in the gap. Electrons may jump from back and forth from the bottom of valance band to the top of the conduction band. But they never come to rest in the forbidden band.  According to the classical free electron theory, materials are classified in to three types:  Conductors  Semiconductors  Insulators  Conductors There is no forbidden gap and the conduction band and valence band are overlapping each other between and hence electrons are free to move about. Examples are Ag, Cu, Fe, Al, Pb ….  Conductor are highly electrical conductivity  So, in general electrical resistivity of conductor is very low and it is of the order of 10-6 Ω cm.  Due to the absence of the forbidden gap, there is no structure for holes.  The total current in conductor is simply a flow of electrons.  For conductors, the energy gap is of the order of 0.01 eV.
  • 23.  Semiconductors: Semiconductors are materials whose electrical resistivity lies between insulator and conductor. Examples are silicon (Si), germanium (Ge) ….  The resistivity of semiconductors lies between 10-4 Ω cm to 103 Ω cm at room temperature.  At low temperature, the valence band is all most full and conduction band is almost empty. The forbidden gap is very small equal to 1 eV.  Semiconductor behaves like an insulator at low temperature. The most commonly used semiconductor is silicon and its band gap is 1.21 eV and germanium band gap is 0.785 eV. When a conductor is heated its resistance increases; the atoms vibrate more and the electrons find it more difficult to move through the conductor but, in a semiconductor the resistance decreases with an increase in temperature. Electrons can be excited up to the conduction band and Conductivity increases.  Insulators  Here the valence band is full but the conduction band is totally empty. So, a free electron from conduction band is not available.  In insulator the energy gap between the valence and conduction band is very large and it’s approximately equal to 5 eV or more.  Hence electrons cannot jump from valence band to the conduction band. So, a very high energy is required to push the electrons to the conduction band.  Therefore the electrical conductivity is extremely small.  The resistivity of insulator lie between 103 to 1017 Ωm, at the room temperature  Examples are plastics, paper …..
  • 24.  Types of semiconductors  Intrinsic Semiconductor The intrinsic semiconductors are pure semiconductor materials. These semiconductors possess poor conductivity. The elemental and compound semiconductor can be intrinsic type. The energy gap in semiconductor is very small. So, even at the room temperature, some of electrons from valance band can jump to the conduction band by thermal energy. The jump of electron in conduction band adds one conduction electron in conduction band and creates a hole in the valence band. The process is called as “generation of an electron–hole pair”. In pure semiconductor the no. of electrons in conduction band and holes in holes in valence bands are equal.  Extrinsic Semiconductor Extrinsic semiconductor is an impure semiconductor formed from an intrinsic semiconductor by adding a small quantity of impurity atoms called dopants. The process of adding impurities to the semiconductor crystal is known as doping. This added impurity is very small of the order of one atom per million atoms of pure semiconductor. Depending upon the type of impurity added the extrinsic semiconductors are classified as: • p – type semiconductor • n – type semiconductor
  • 25. p – type semiconductor The addition of trivalent impurities such as boron, aluminum or gallium to an intrinsic semiconductor creates deficiencies of valence electrons, called "holes". It is typical to use B2H6 di-borane gas to diffuse boron into the silicon material. n – type semiconductor The addition of pentavalent impurities such as antimony, arsenic or phosphorous contributes free electrons, greatly increasing the conductivity of the intrinsic semiconductor. Phosphorous may be added by diffusion of phosphine gas (PH3).  Simple Diode The two terminals are called Anode and Cathode. At the instant the two materials are “joined”, electrons and holes near the junction cross over and combine with each other. Holes cross from P-side to N-side and free electrons cross from N-side to P-side.
  • 26. At P-side of junction, negative ions are formed. At N-side of junction, positive ions are formed. Depletion region is the region having no free carriers. Further movement of electrons and holes across the junction stops due to formation of depletion region. Depletion region acts as barrier opposing further diffusion of charge carriers. So diffusion stops within no time. Current through the diode under no-bias condition is zero. Reverse bias Positive of battery connected to n-type material (cathode). Negative of battery connected to p-type material (anode). Free electrons in n-region are drawn towards positive of battery; Holes in p-region are drawn towards negative of battery. Depletion region widens, barrier increases for the flow of majority carriers. Majority charge carrier flow reduces to zero.
  • 27. Minority charge carriers generated thermally can cross the junction – results in a current called “reverse saturation current” Is , Is is in micro or nano amperes or less. Is does not increase “significantly” with increase in the reverse bias voltage  Zener Diode A diode which is heavily doped and which operates in the reverse breakdown region with a sharp breakdown voltage is called a Zener diode. This is similar to the normal diode except that the line (bar) representing the cathode is bent at both side ends like the letter Z for Zener diode. In simple diode the doping is light; as a
  • 28. result, the breakdown voltage is high and not sharp. But if doping is made heavy, then the depletion layers becomes very narrow and even the breakdown voltage gets reduced to a sharp value.  Working Principle The reverse breakdown of a Zener diode may occur either due to Zener effect or avalanche effect. But the Zener diode is primarily depends on Zener effect for its working. When the electrical field across the junction is high due to the applied voltage, the Zener breakdown occurs because of breaking of covalent bonds. This produces a large number of electrons and holes which constitute a steep rise in the reverse saturation current (Zener current IZ). This effect is called as Zener effect. Zener current IZ is independent of the applied voltage and depends only on the external resistance. The I-V characteristic of a Zener diode is shown in this figure. The forward characteristic is simply that of an ordinary forward biased junction diode. Under the reverse bias condition, the breakdown of a junction occurs. Its depends upon amount of doping. It can be seen from above figure as the reverse voltage is increased the reverse current remains negligibly small up to the knee point (K) of the curve.
  • 29. At point K, the effect of breakdown process beings. The voltage corresponding to the point K in figure is called the Zener breakdown voltage or simply Zener voltage (VZ), which is very sharp compared to a simple p-n junction diode. Beyond this voltage the reverse current (IZ) increases sharply to a high value. The Zener diode is not immediately burnt just because it has entered the breakdown region. The Zener voltage VZ remains constant even when Zener current IZ increases greatly. This ability of a diode is called regulating ability and it enables us to use Zener diode for voltage regulation. The maximum value of current is denoted by IZ max and the minimum current to sustain breakdown is denoted by IZ min. By two points A and B on the reverse VI characteristic, the Zener resistance is given by the relation rz = ( Δ VZ / Δ IZ). ------- (1)  Zener diode Applications: 1) Zener diodes are used as a voltage regulator. 2) They are used in shaping circuits as peak limiters or clippers. 3) They are used as a fixed reference voltage in transistor biasing and for comparison purpose. 4) They are used for meter protection against damage from accidental application of excessive voltage.
  • 30. LASER Light Amplification by Stimulated Emission of Radiation  Introduction The full form of LASER is Light Amplification by Stimulated Emission of Radiation. Laser light is highly powerful and it is capable of propagating over long distances and it is not easily absorbed by water.  Light having following Properties: • Wavelength • Frequency • Amplitude • Phase • Coherence/Incoherence • Velocity • Direction The characteristics or properties of Laser Light are: • Coherence • High Intensity • High directionality • High monochromaticity  Absorption According to Bohr’s law atomic system is characterized by discrete energy level. When atoms absorb or release energy it transit upward or downward. Here lower level is E1 and excited level is E2, the photon energy hƒ = E2 – E1. The atom absorbed an incident photon. As the result of absorption atom absorbed energy and the atom jumped to excited state E2. This transition is called absorption. It is also referred to as induced absorption. We may express the process as, A + hν = A*
  • 31. Where A is an atom in lower state and A* is an excited atom. The rate of absorption depends on no. of atoms N1 present in E1 and spectral energy density u(ƒ) of radiation. P12 α N1 u(ƒ) -----(1) So, P12 = B12N1 u(ƒ) -----(2) In each absorption transition event, an atom in the medium is excited and one photon is subtracted from the incident beam, which result in attenuation of light in the medium.  Spontaneous Emission An atom cannot stay in the excited state for a longer time. Ina time of 10-8 sec, the atom come back to the ground state by releasing a photon of energy hν, and hν = E = E2 – E1. Where E1 = Ground State and E2 = Excited State. The emission of photon by an atom without any external impetus is called spontaneous emission. We may write the process as, A* → hν + A Here system having atoms in excited state. Atom goes to downward transition with emitting photons, hƒ = E1 – E2. Emission is random, so if not in same phase becomes incoherent. The transition depends on atoms in excited state N2. P12 (spont) α N2 = A21 N2 ------- (1) Where, A21 = Einstein coefficient for spontaneous Emission. We get Incoherent radiation forms heat by light amplification of radiation by spontaneous emission.  Stimulated Emission
  • 32. An atom in the excited state need not wait for spontaneous emission of photon. Well before the atom can make a spontaneous transition, it may interacts with a photon with energy hν = E2 – E1, and make a downward transition. The photon is said to stimulated of induced the excited atom to emit a photon of energy hν = E2 – E1. The passing photon does not disappear and in addition to it there is a second photon which is emitted by the excited atom. The phenomenon of forced photon emission by an excited atom due to the action of an external energy is called stimulated emission or induced emission. The process may be expressed as, A* + hν → A + 2hν Here system having atoms in excited state. The atom goes to downward transition with emitting photons. 2hƒ = E1 – E2. After applying photon energy hƒ. Emission is depends on energy density u(ƒ) & No. of atoms in excited state N2 P12 (stimul) α u(ƒ) N2 - -------- (1) = B21 N2 u(ƒ) -------- (2) Where, B21 = Einstein coefficient for Stimulated Emission. Thus one photon of energy hƒ stimulates two photons of energy hƒ in same phase & directions. So, we get coherent light amplification of radiation by stimulated emission.  Population Inversion It is the process of increasing exited electrons in higher energy levels. Due to this process the production of laser is possible. The energy level between the ground state E1 (1st level) and exited state E3 (3rd level) is known as metastable state E2 (2nd level). By the optical pumping electrons from ground state jumps to excited state by absorbing photons. The electrons remain only for 10-8 sec in exited state E3, so most of them jump back to the ground state E1 by emitting photons. But some of them jump to the metastable state E2.
  • 33. They (electron) stay in metastable state for more then 10-3 sec. So electron density increases in metastable state. Thus the transitions are possible it takes more no. of electrons together and ν – (knew) 12 photon beam is produced which constitute laser beam.  Optical Pumping There are no of techniques for pumping a collection of atoms to an inverted state. •Optical pumping • Electrical discharge • Direct conversion When photon of blue green light incident on Ruby crystal, electrons from ground state absorbs and exited and jumps on higher energy state levels and comes back to metastable state. They increase population of electrons in metastable state. This process is called “optical pumping” which is done by flash tube.  Relation between Einstein’s ‘A’ and ‘B’ coefficients Einstein obtained a mathematical expression for the existence of two different kinds of processes, (1) Spontaneous emission (2) Stimulated emission Consider all atoms r in thermal equilibrium at T and radiation of frequency (ƒ) and energy density u(ƒ). Here N1 and N2 r atoms in E1 and E2 respectively. In equilibrium absorption rates and emission rates must be same. i.e. B12 N1 u(ƒ) = A21 N2+ B21 N2 u(ƒ) → A21 N2= u(ƒ) [B12N1 – B21N2] → u(f) = [A21 N2 / (B12 N1 – B21 N2)] --------- (1) ---------- (2) So Boltzmann distribution law is, ---------- (3) 21 21 12 1 21 2 ( ) [ ] ƒ 1 A B u B N B N 1 2 / 1 0 / 2 0 E kT E kT N N e N N e
  • 34. And ----------- (4) But, E2 – E1 = hf ----------- (5) So, ----------- (6) ------------ (7) According to plank’s radiation formula, ------------ (8) Where, B12 = B21 & A21 / B21 = 8∏hf3 /c3 ------------ (9) So, Ratio of spontaneous to stimulated emission: ----------- (10) So, ------------ (11) ------------ (12) R = e hf/KT - 1 -------------- (13) So, • If hƒ << kT, in thermal equilibrium, Then R = ehf/KT - 1 << 1 • hƒ<<kT – Stimulated emission – Valid in microwave region (MASER) • hƒ>>kT – Spontaneous emission – Valid in visible region, incoherent Valid 2 1( )/1 2 E E kTN e N h /1 2 ƒ kTN e N 21 21 ƒ12 21 h / ƒ 1 ( ) [ ] kT e A B u B B 3 3 ƒh / 8 1 ( ) ( ) [ ] ƒ ƒ 1 kT u c h e 2 21 21 2 21 21 3 3 8 ( ) ( ) ( ) ƒ ƒ ƒ ƒ N A A h R B u B u ucN 3 3 / 3 3 ƒh 8 ( ) 8 ƒ ƒ & ƒ ƒ 1 1 ( ) ( ) [ ] kT h u c u R h e c
  • 35.  Types of LASER There are three types of lasers 1. Solid Laser (Ruby Laser) 2. Liquid Laser 3. Gas Laser ( He – Ne Laser, CO2 Laser) Ruby Laser To produce laser from solid, Ruby crystal is used. Ruby is an aluminum oxide crystal (Al 2 O 3 ) in which some of the aluminum atoms have been replaced with Cr +3 chromium atoms (0.05% by weight). It was the first type of laser invented, and was first operated by Maiman in research laboratories on 1960. Chromium gives ruby its characteristic pink or red color by absorbing green and blue light. For a ruby laser, a crystal of ruby is formed into a cylinder. The ruby laser is used as a pulsed laser, producing red light at 6943 Å. Ruby crystal is surrounded by xenon tube. Ruby crystal is fully silvered at one side and partially silvered at the other end. A strong beam of blue green light is made to fall up on crystal from xenon tube and this light is absorbed by the crystal.
  • 36. Because of this, many electrons from ground state or normal state are raised to the excited state or higher state and electron falls to metastable state. During this transition photon is not emitted but excess energy of the electrons absorbed in crystal lattice. As electron drops to metastable state they remain there for certain time ~ 10-6 sec. Thus, the incident blue green light from tube increases the number of electron in metastable state and then the population inversion can be achieved. If a light of different frequency is allowed to fall on this material, the electrons move back and forth between silvered ends of the crystal. While moving through they get stimulated and exited electrons radiate energy. Thus readia photon has the same frequency as that of incident photon and is also in exactly same phase. When the intensity of light beam is increased the same process is repeated. Finally extremely intensified beam of light energies from the semi silvered side of the crystal. This way it is possible to get extremely intensified and coherent beam of light from the crystal. This beam is nothing but higher energetic beam – ie. LASER beam. Applications of Ruby Laser Ruby lasers have declined in use with the discovery of better lasing media. They are still used in a number of applications where short pulses of red light are required. Holography's around the world produce holographic portraits with ruby lasers, in sizes up to a meter squared.
  • 37. Many non-destructive testing labs use ruby lasers to create holograms of large objects such as aircraft tires to look for weaknesses in the lining. Ruby lasers were used extensively in tattoo and hair removal. Drawbacks of Ruby Laser The laser requires high pumping power because the laser transition terminates at the ground state and more than half of ground state atoms must be pumped to higher state to achieve population inversion. The efficiency of ruby laser is very low because only green component of the pumping light is used while the rest of components are left unused. The laser output is not continues but occurs in the form of pulses of microseconds duration. The defects due to crystalline imperfections are also present in this laser. Gaseous Laser (He – Ne Laser) Helium - neon laser, usually called a He-Ne laser, is a type of small gas laser. He-Ne lasers have many industrial and scientific uses, and are often used in laboratory demonstrations of optics. He-Ne laser is an atomic laser which employs a four-level pumping scheme. The active medium is a mixture of 10 parts of helium to 1 part of neon. Neon atoms are centers and have energy levels suitable for laser transitions while helium atoms help efficient excitation of neon atoms. The most common wavelength is 6328 Å. These lasers produced powers in the range 0.5 to 50 mW in the red portion of the visible spectrum. They have long operating life of the order of 50,000 hrs.
  • 38. Construction It consists of a glass discharge tube of about typically 30 cm long and 1.5 cm diameter. The tube is filled with a mixture of helium and neon gases in the 10:1. Electrodes are provided in the tube to produce a discharge in the gas. They are connected to a high voltage power supply. The tube is hermetically sealed with glass windows oriented at Brewster angle to the tube. The cavity mirrors are arranged externally. Working When the power is switched on, a high voltage of about 10 kV is applied across the gas. It is sufficient to ionize the gas. The electrons and ions are produced in the process of discharge are accelerated toward the anode and cathode respectively. The electron have a smaller mass, they acquire a higher velocity. They transfer their kinetic energy to helium atoms through inelastic collisions. The initial excitation effects only the helium atoms. They are in metastable state and cannot return in ground state by the spontaneous emission. The excited helium atoms can return to the ground state by transforming their energy to neon atoms through collision. These transformations take place when two colliding atoms have initial energy state. It is called resonant transfer of energy. So, the pumping mechanism of He-Ne Laser is when the helium atom in the metastable state collides with neon atom in the ground state the neon atom is excited and the helium atom drops back to the ground state. The role of helium atom is thus to excite neon atom and cause, population inversion. The probability of energy transfer from helium atoms to neon atoms is more as there are 10 atoms of helium per 1 neon atom in gas mixture.
  • 39. Without the Brewster windows, the light output is unpolarized; because of it laser output to be linearly polarized. When the excited Ne atom passes from metastable state (3s) to lower level (2p), it emits photon of wavelength 632 nm. This photon travels through the gas mixture parallel to the axis of tube; it is reflected back and forth by the mirror ends until it stimulates an excited Ne atom and causes it to emit a photon of 632 nm with the stimulating photon. The stimulated transition from (3s) level to (2p) level is laser transition. Although 6328 Å is standard wavelength of He-Ne Laser, other visible wavelengths 5430 Å (Green) 5940 Å (yellow-orange), 6120 Å (red-orange) can also produce. Overall gain is very low and is typically about 0.010 % to 0.1 %. The laser is simple practical and less expensive. The Laser beam is highly collimated, coherent and monochromatic. Applications of He-Ne Laser The Narrow red beam of He-Ne laser is used in supermarkets to read bar codes. The He-Ne Laser is used in Holography in producing the 3D images of objects. He-Ne lasers have many industrial and scientific uses, and are often used in laboratory demonstrations of optics.  Semiconductor Laser (Diode Laser) A semiconductor laser is a laser in which a semiconductor serves as a photon source. The most common semiconductor material that has been used in lasers is gallium arsenide.
  • 40. Einstein’s Photoelectric theory states that light should be understood as discrete lumps of energy (photons) and it takes only a single photon with high enough energy to knock an electron loose from the atom it's bound to. Stimulated, organized photon emission occurs when two electrons with the same energy and phase meet. The two photons leave with the same frequency and direction.  P-type Semiconductors In the compound GaAs, each Ga atom has three electrons in its outermost shell of electrons and each As atom has five. When a trace of an impurity element with two outer electrons, such as Zn (zinc), is added to the crystal. The result is the shortage of one electron from one of the pairs, causing an imbalance in which there is a “hole” for an electron but there is no electron available. This forms a p-type semiconductor.  N-type Semiconductors When a trace of an impurity element with six outer electrons, such as Se (selenium), is added to a crystal of GaAs, it provides on additional electron which is not needed for the bonding. This electron can be free to move through the crystal. Thus, it provides a mechanism for electrical conductivity. This type is called an n-type semiconductor. Under forward bias (the p-type side is made positive) the majority carriers, electrons in the n-side, holes in the p-side, are injected across the depletion region in both directions to create
  • 41. a population inversion in a narrow active region. The light produced by radioactive recombination across the band gap is confined in this active region.  Application of Lasers 1. Laser beam is used to measure distances of sun, moon, stars and satellites very accurately. 2. It can be used for measuring velocity of light, to study spectrum of matters, to study Raman effect. 3. It can be is used for increasing speed and efficiency of computer. 4. It is used for welding. 5. It is used in biomedical science. 6. It is used in 3D photography. 7. It is used for communication, T. V. transmission, to search the objects under sea. 8. It can be used to predict earthquake. 9. Laser tools are used in surgery. 10. It is used for detection and treatment of cancer. 11. It is used to aline straight line for construction of dam, tunnels etc. 12. It is used in holography. 13. It is used in fiber optic communication. 14. It is also used in military, like LIDAR. 15. It is used to accelerate some chemical reactions.
  • 42. Special Theory of Relativity  Introduction to Relativity o The dependence of various physical phenomena on relative motion of the observer and the observed objects, especially regarding the nature and behaviour of light, space, time, and gravity is called relativity. o When we have two things and if we want to find out the relation between their physical property i.e.velocity,accleration then we need relation between them that which is higher and which is lower.In general way we reffered it to as a relativity. o The famous scientist Einstein has firstly found out the theory of relativity and he has given very useful theories in relativity. o In 1905, Albert Einstein determined that the laws of physics are the same for all non- accelerating observers, and that the speed of light in a vacuum was independent of the motion of all observers. This was the theory of special relativity.  FRAMES OF REFERENCE o A Reference Frame is the point of View, from which we Observe an Object. o A Reference Frame is the Observer it self, as the Velocity and acceleration are common in Both. o Co-ordinate system is known as FRAMES OF REFERENCE o Two types: 1. Inertial Frames Of Reference. 2. non-inertial frame of reference. o We have already come across idea of frames of reference that move with constant velocity. In such frames, Newton’s law’s (esp. N1) hold. These are called inertial frames of reference. o Suppose you are in an accelerating car looking at a freely moving object (I.e., one with no forces acting on it). You will see its velocity changing because you are accelerating! In accelerating frames of reference, N1 doesn’t hold – this is a non- inertial frame of reference.
  • 43.  Galilean Transforms o Parallel axes (for convenience) o K’ has a constant relative velocity in the x-direction with respect to K o Time (t) for all observers is a Fundamental invariant, i.e., the same for all inertial observers o Galilean Transformation Inverse Relations o Step 1. Replace with . o Step 2. Replace “primed” quantities with “unprimed” and “unprimed” with “primed.” o General Galilean Transformations o Newton’s Eqn of Motion is same at face-value in both reference frames
  • 44.  Einstein’s postulates of special theory of relativity o The First Postulate of Special Relativity  The first postulate of special relativity states that all the laws of nature are the same in all uniformly moving frames of reference. o The Second Postulate of Special Relativity  The second postulate of special relativity states that the speed of light in empty space will always have the same value regardless of the motion of the source or the motion of the observer.  The speed of a light flash emitted by either the spaceship or the space station is measured as c by observers on the ship or the space station. Everyone who measures the speed of light will get the same value, c.  The Ether o Light is a wave. o Waves require a medium through which to propagate. o Medium as called the “ether.” (from the Greek aither, meaning upper air) o Maxwell’s equations assume that light obeys the Newtonian-Galilean transformation.  The Ether: Since mechanical waves require a medium to propagate, it was generally accepted that light also require a medium. This medium, called the ether, was assumed to pervade all mater and space in the universe.  The Michelson-Morley Experiment o Experiment designed to measure small changes in the speed of light was performed by Albert A. Michelson (1852 – 1931, Nobel ) and Edward W. Morley (1838 – 1923). o Used an optical instrument called an interferometer that Michelson invented. o Device was to detect the presence of the ether. o Outcome of the experiment was negative, thus contradicting the ether hypothesis. o Michelson developed a device called an inferometer. o Device sensitive enough to detect the ether. o Apparatus at rest wrt the ether. o Light from a source is split by a half silvered mirror (M)
  • 45. o The two rays move in mutually perpendicular directions o The rays are reflected by two mirrors (M1 and M2) back to M where they recombine. o The combined rays are observed at T. o The path distance for each ray is the same (l1=l2). o Therefore no interference will be observed o Apparatus at moving through the ether. o First consider the time required for the parallel ray o Distance moved during the first part of the path is o Similarly the time for the return trip is o The total time o For the perpendicular ray ,we can write, from fig. || L t (c u ) ct L ut L t (c u ) || 2 2 2 2 ( ) ( ) 2 ( ) 2 / 1 L L t c u c u Lc c u L c u c
  • 46. o The return path is the same as the initial leg therefore the total time is o The time difference between the two rays is, o The expected time difference is too small to be measured directly! o Instead of measuring time, Michelson and Morley looked for a fringe change. o as the mirror (M) was rotated there should be a shift in the interference fringes.  Results of the Experiment  A NULL RESULT o No time difference was found! o Hence no shift in the interference patterns  Conclusion from Michelson-Morley Experiment o the ether didn’t exist.  The Lorentz Transformation  We are now ready to derive the correct transformation equations between two inertial frames in Special Relativity, which modify the Galilean Transformation. We consider two inertial frames S and S’, which have a relative velocity v between them along the x-axis. 2 2 2 2 2 2 2 2 2 2 2 2 2 ) ( ) ( initial leg of the patct L ut L c t u t c u t L t c u h 2 2 2 2 2 2 / 1 L t c u L c t u c 1 21 2 2 || 2 2 2 2 2 3 2 1 1 2 2 L u u t t t c c c A fter a binom ial expansi L u L u t c c c on
  • 47.  Now suppose that there is a single flash at the origin of S and S’ at time , when the two inertial frames happen to coincide. The outgoing light wave will be spherical in shape moving outward with a velocity c in both S and S’ by Einstein’s Second Postulate.  We expect that the orthogonal coordinates will not be affected by the horizontal velocity:  But the x coordinates will be affected. We assume it will be a linear transformation:  But in Relativity the transformation equations should have the same form (the laws of physics must be the same). Only the relative velocity matters. So,  Consider the outgoing light wave along the x-axis (y = z = 0).  Now plug these into the transformation equations:  Plug these two equations into the light wave equation: x y z S x' y' z' S' v 2 2 2 2 2 2 2 2 2 2 x y z c t x y z c t y y z z x k x vt x k x vt k k x ct in fram e S' x ct in fram e S x k x vt k ct vt kct 1 v / c and x k x vt k ct vt kct 1 v / c ct x k ct 1 v / c ct x k ct 1 v / c t k t 1 v / c t k t 1 v / c
  • 48. o Plug t’ into the equation for t: o So the modified transformation equations for the spatial coordinates are: o Now what about time? o Solve for t’: o So the correct transformation (and inverse transformation) equations are: 2 2 2 2 2 2 t k t 1 v / c 1 v / c 1 k 1 v / c 1 k 1 v / c x x vt y y z z x x vt x x vt inverse transformation Plug one into the other: x x vt vt 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 x x vt vt x 1 vt vt 1 v / c 1 x vt vt 1 v / c xv / c vt vt 1 t xv / c vt v t t vx / c 2 2 x x vt x x vt y y y y z z z z t t vx / c t t vx / c The Lorentz Transformation
  • 49.  Application of Lorentz Transformation  Time Dilation  We explore the rate of time in different inertial frames by considering a special kind of clock – a light clock – which is just one arm of an interferometer. Consider a light pulse bouncing vertically between two mirrors. We analyze the time it takes for the light pulse to complete a round trip both in the rest frame of the clock (labeled S’), and in an inertial frame where the clock is observed to move horizontally at a velocity v (labeled S).  In the rest frame S’  Now put the light clock on a spaceship, but measure the roundtrip time of the light pulse from the Earth frame S:  So the time it takes the light pulse to make a roundtrip in the clock when it is moving by us is appears longer than when it is at rest. We say that time is dilated. It also doesn’t matter which frame is the Earth and which is the clock. Any object that moves by with a significant velocity appears to have a clock running slow. We summarize this effect in the following relation: m irror m irror L L c t / 2 v t / 2 1 2 1 2 L t = time up c L t = time down c 2L =t t c 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 t t time up 2 t t time down 2 The speed of light is still c in this frame, so L v t / 4 c t / 4 L c v t / 4 4L t c v 2L 1 t c 1 v / c 1 v / c 2 2 1 t , 1 1 v / c
  • 50.  Length Contraction o Now consider using a light clock to measure the length of an interferometer arm. In particular, let’s measure the length along the direction of motion. o In the rest frame S’: o Now put the light clock on a spaceship, but measure the roundtrip time of the light pulse from the Earth frame S: o In other words, the length of the interferometer arm appears contracted when it moves by us. This is known as the Lorentz-Fitzgerald contraction. It is closely related to time dilation. In fact, one implies the other, since we used time dilation to derive length contraction. A A’ C C’ vt1L 1 2 1 2 1 1 1 2 2 2 1 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 t tim e out t tim e back t t t L L vt ct t c v L L vt ct t c v 2Lc 2L 1 t t t c v c 1 v / c ct L 1 v / c 2 But, t from tim e dilation 1 v / c 2Lc 2L 1 t t t c v c 1 v / c ct L 1 v / c 2 But, t 1 v 2 2 0 2 2 from tim e dilation / c L 1 L 1 1 v / c
  • 51. Superconductivity  Introduction of superconductivity Superconductivity is a phenomenon of exactly zero electrical resistance and expulsion of magnetic fields occurring in certain materials when cooled below a characteristic critical temperature. It was discovered by Dutch physicist Heike Kamerlingh Onnes on April 8, 1911 in Hg, which has critical temperature of 4.2 K.  Properties of Superconductors (1)Electrical Resistance Zero Electrical Resistance Defining Property Critical Temperature Quickest test 10-5 Ωcm (2)Effect of Magnetic Field Critical magnetic field (HC) – Minimum magnetic field required to destroy the superconducting property at any temperature. 2 0 1C C T H H T
  • 52. H0 - Critical field at 0K T - Temperature below TC TC - Transition Temperature Element HC at 0K (mT) Nb 198 Pb 80.3 Sn 30.9 (3)Effect of Electric Current  Large electric current – induces magnetic field – destroys superconductivity  Induced Critical Current iC = 2πrHC Persistent Current  Steady current which flows through a superconducting ring without any decrease in strength even after the removal of the field.  Diamagnetic property.
  • 53.  Meissner effect When Superconducting material cooled bellow its Tc it becomes resistenceless & perfect diamagnetic. When superconductor placed inside a magnetic field in Tc all magnetic flux is expelled out of it the effect is called Meissner effect. Perfect diamagnetism arises from some special magnetic property of Superconductor. If there is no magnetic field inside the superconductor relative permeability or diamagnetic constant μr =0. Total magnetic induction B is, If magnetic induction B=0 then,  Magnetic Flux Quantization Magnetic flux enclosed in a superconducting ring = integral multiples of fluxon Φ = nh/2e = n Φ0 ; (Φ0 = 2x10-15 Wb)  Effect of Pressure Pressure ↑, TC ↑ High TC superconductors – High pressure 0 ( )B H M  0 0 ( )H M  M H   1 m M H    
  • 54.  Thermal Properties Entropy & Specific heat ↓ at TC Disappearance of thermo electric effect at TC Thermal conductivity ↓ at TC – Type I superconductors  Stress  Stress ↑, dimension ↑, TC ↑, HC affected  Frequency  Frequency ↑, Zero resistance – modified, TC not affected  Impurities  Magnetic properties affected  Size  Size < 10-4 cm – superconducting state modified  General Properties  No change in crystal structure  No change in elastic & photo-electric properties  No change in volume at TC in the absence of magnetic field  Isotope Effect Maxwell TC = Constant / Mα TC Mα = Constant (α – Isotope Effect coefficient) α = 0.15 – 0.5 α = 0 (No isotope effect) TC√M = constant  Classification & characterization of superconductor Type - I or soft superconductor o Exhibit complete Meissner effect.
  • 55. o Bellow Hc super conductor above Hc Normal o Value of Hc is order of 0.1 T. o Aluminum, lead & Indium are type - I super conductor o Not used as strong electromagnets Type - II or Hard superconductor o Exhibit complete Meissner effect bellow a certain critical field Hc1 at this point diamagnetism & superconductivity ↓. This state is mix state called vortex state. o At certain critical field Hc2 superconductivity disappears. o Niobium, Aluminum, Silicon, Ceramic are type - II superconductors. o Pb is type I superconductor ac Hc = 600 gauss at 4º K when a small impurity of In is added it becomes type II superconductor with Hc1 = 400 gauss & Hc2 = 1000 gauss.  London equation According to London’s theory there are two type of electrons in SC. o Super electrons o Normal electrons o At 0º K there are only Super electrons. o With increasing temp. Super electrons ↓ Normal electrons ↑ . o Let nn, un & ns, us are no. density & drift velocity of normal electrons & super electrons respectively. Equation of motion of Super electrons under electric field is, Now current & drift velocity are related as, s du m eE dt         s s s s s s s s s I n eAu J n eu J u n e
  • 56. 2 ( )       s s s s J d n e e E dt n e Ed J dt m This is London's first equation. - London's first equation gives absence of resistance. If E = 0 then, - Now from Maxwell's eqns. 0s dJ dt  ( ) d B E dt B A d A E dt d A E dt d A E dt                     2 2 2 2 2 2 ( ) ( ) s s s s s s s s s s s s n e Ed J dt m d J m E dt n e d J m d A dt n e dt d m d A J dt n e dt m J A n e n e J A m               
  • 57. This is London's Second equation - Again from ampere Law, - Take curl on both sides λ is called London penetration depth.  BCS Theory of Superconductivity  The properties of Type I superconductors were modeled successfully by the efforts of John Bardeen, Leon Cooper, and Robert Schrieffer in what is commonly called the BCS theory.  A key conceptual element in this theory is the pairing of electrons close to the Fermi level into Cooper pairs through interaction with the crystal lattice. 0 2 0 ( ) s s B J n e B A m          2 0 2 2 2 0 ( ) & ( ) s s n e B A m Now B B B A B n e B B B m A B                                    
  • 58.  This pairing results form a slight attraction between the electrons related to lattice vibrations; the coupling to the lattice is called a phonon interaction.  Pairs of electrons can behave very differently from single electrons which are fermions and must obey the Pauli exclusion principle.  Cooper Pairs:  The transition of a metal from the normal to the superconducting state has the nature of a condensation of the electrons into a state which leaves a band gap above them.  This kind of condensation is seen with super fluid helium, but helium is made up of bosons -- multiple electrons can't collect into a single state because of the Pauli exclusion principle.  Froehlich was first to suggest that the electrons act as pairs coupled by lattice vibrations in the material.  This coupling is viewed as an exchange of phonons, phonons being the quanta of lattice vibration energy.  Experimental corroboration of an interaction with the lattice was provided by the isotope effect on the superconducting transition temperature.  The boson-like behavior of such electron pairs was further investigated by Cooper and they are called "Cooper pairs".  The condensation of Cooper pairs is the foundation of the BCS theory of superconductivity.
  • 59. s  In the normal state of a metal, electrons move independently, whereas in the BCS state, they are bound into "Cooper pairs" by the attractive interaction. The BCS formalism is based on the "reduced" potential for the electrons attraction.  You have to provide energy equal to the 'energy gap' to break a pair, to break one pair you have to change energies of all other pairs.  This is unlike the normal metal, in which the state of an electron can be changed by adding a arbitrary small amount of energy.  The energy gap is highest at low temperatures but does not exist at temperatures higher than the transition temperature.  The BCS theory gives an expression of how the gap grows with the strength of attractive interaction and density of states.  The BCS theory gives the expression of the energy gap that depends on the Temperature T and the Critical Temperature Tc and is independent of the material:  Applications of Superconductors Engineering:  Transmission of power  Switching devices  Sensitive electrical instruments
  • 60.  Memory (or) storage element in computers.  Manufacture of electrical generators and transformers Medical:  Nuclear Magnetic Resonance (NMR)  Diagnosis of brain tumor  Magneto – hydrodynamic power generation  Josephson effect or Devices Principle: persistent current in d.c. voltage. Josephson junctions  A type of electronic circuit capable of switching at very high speeds when operated at temperatures approaching absolute zero.  Named for the British physicist who designed it,  A Josephson junction exploits the phenomenon of superconductivity.
  • 61. Construction  A Josephson junction is made up of two superconductors, separated by a non- superconducting layer so thin that electrons can cross through the insulating barrier.  The flow of current between the superconductors in the absence of an applied voltage is called a Josephson current,  The movement of electrons across the barrier is known as Josephson tunneling.  Two or more junctions joined by superconducting paths form what is called a Josephson interferometer.  Consists of superconducting ring having magnetic fields of quantum values (1,2,3..)  Placed in between the two Josephson junctions.
  • 62. Explanation:  Consists of thin layer of insulating material placed between two superconducting materials.  Insulator acts as a barrier to the flow of electrons.  When voltage applied current flowing between super conductors by tunneling effect.  Quantum tunneling occurs when a particle moves through a space in a manner forbidden by classical physics, due to the potential barrier involved
  • 63. Components of current  In relation to the BCS theory (Bardeen Cooper Schrieffer) mentioned earlier, pairs of electrons move through this barrier continuing the superconducting current. This is known as the dc current.  Current component persists only till the external voltage application. This is ac current. Uses of Josephson devices  Magnetic Sensors  Gradiometers  Oscilloscopes  Decoders  Analogue to Digital converters  Oscillators  Microwave amplifiers  Sensors for biomedical, scientific and defence purposes  Digital circuit development for Integrated circuits  Microprocessors  Random Access Memories (RAMs) Super conducting Quantum Interference Devices
  • 64. Discovery: The DC SQUID was invented in 1964 by Robert Jaklevic, John Lambe, Arnold Silver, and James Mercereau of Ford Research Labs Principle: Small change in magnetic field, produces variation in the flux quantum. Construction: The superconducting quantum interference device (SQUID) consists of two superconductors separated by thin insulating layers to form two parallel Josephson junctions. Type: Two main types of SQUID: 1) RF SQUIDs have only one Josephson junction 2) DC SQUIDs have two or more junctions. Thereby,  More difficult and expensive to produce.  Much more sensitive. Fabrication:  Lead or pure niobium, the lead is usually in the form of an alloy with 10% gold or indium, as pure lead is unstable when its temperature is repeatedly changed.  The base electrode of the SQUID is made of a very thin niobium layer.  The tunnel barrier is oxidized onto this niobium surface.  The top electrode is a layer of lead alloy deposited on top of the other two, forming a sandwich arrangement.  To achieve the necessary superconducting characteristics, the entire device is then cooled to within a few degrees of absolute zero with liquid helium. Uses:  Storage device for magnetic flux.
  • 65.  Study of earthquakes.  Removing paramagnetic impurities.  Detection of magnetic signals from brain, heart etc.  Cryotron:  The cryotron is a switch that operates using superconductivity.  The cryotron works on the principle that magnetic fields destroy superconductivity.  The cryotron is a piece of tantalum wrapped with a coil of niobium placed in a liquid helium bath.  When the current flows through the tantalum wire it is superconducting, but when a current flows through the niobium a magnetic field is produced.  This destroys the superconductivity which makes the current slow down or stop.  Magnetic Levitated Train: Principle: Electro-magnetic induction Introduction:  Magnetic levitation transport, or maglev, is a form of transportation that suspends guides and propels vehicles via electromagnetic force.  This method can be faster than wheeled mass transit systems, potentially reaching velocities comparable to turboprop and jet aircraft (500 to 580 km/h).  Why superconductor?  Superconductors may be considered perfect diamagnets (μr = 0), completely expelling magnetic fields due to the Meissner effect. The levitation of the magnet is stabilized due to flux pinning within the superconductor. This principle is exploited by EDS (Electrodynamics suspension) magnetic levitation trains.  In trains where the weight of the large electromagnet is a major design issue (a very strong magnetic field is required to levitate a massive train) superconductors are used for the electromagnet, since they can produce a stronger magnetic field for the same weight.  How to use a Super conductor? Electrodynamics suspension
  • 66.  In Electrodynamic suspension (EDS), both the rail and the train exert a magnetic field, and the train is levitated by the repulsive force between these magnetic fields.  The magnetic field in the train is produced by either electromagnets or by an array of permanent magnets.  The repulsive force in the track is created by an induced magnetic field in wires or other conducting strips in the track.  At slow speeds, the current induced in these coils and the resultant magnetic flux is not large enough to support the weight of the train.  For this reason the train must have wheels or some other form of landing gear to support the train until it reaches a speed that can sustain levitation.  Propulsion coils on the guide way are used to exert a force on the magnets in the train and make the train move forwards.  The propulsion coils that exert a force on the train are effectively a linear motor: An alternating current flowing through the coils generates a continuously varying magnetic field that moves forward along the track.  The frequency of the alternating current is synchronized to match the speed of the train.  The offset between the field exerted by magnets on the train and the applied field create a force moving the train forward. Advantages:  No need of initial energy in case of magnets for low speeds  One liter of Liquid nitrogen costs less than one liter of mineral water  Onboard magnets and large margin between rail and train enable highest recorded train speeds (581 km/h) and heavy load capacity. Successful operations using high temperature superconductors in its onboard magnets, cooled with inexpensive liquid nitrogen  Magnetic fields inside and outside the vehicle are insignificant; proven, commercially available technology that can attain very high speeds (500 km/h); no wheels or secondary propulsion system needed  Free of friction as it is “Levitating”
  • 67. Atomic Physics “Classical Physics”: developed in 15th to 20th century,provides very successful description of “every day, ordinary objects” motion of trains, cars, bullets,…. orbit of moon, planets how an engine works,.. subfields: mechanics, thermodynamics, electrodynamics, Quantum Physics: developed early 20th century, in response to shortcomings of classical physics in describing certain phenomena (blackbody radiation, photoelectric effect, emission and absorption spectra…)describes “small” objects (e.g. atoms ) QP is “weird and counterintuitive” “Those who are not shocked when they first come across quantum theory cannot possibly have understood it” (Niles Bohr) “Nobody feels perfectly comfortable with it “ (Murray Gell-Mann) “I can safely say that nobody understands quantum mechanics” (Richard Feynman) BUT… QM is the most successful theory ever developed by humanity underlies our understanding of atoms, molecules, condensed matter, nuclei, elementary particles Crucial ingredient in understanding of stars, … Quantum physics is basically the recognition that there is less difference between waves and particles than was thought before key insights: light can behave like a particle particles (e.g. electrons) are indistinguishable particles can behave like waves (or wave packets) waves gain or lose energy only in "quantized amounts“ detection (measurement) of a particle wave will change suddenly into a new wave quantum mechanical interference – amplitudes add QP is intrinsically probabilistic what you can measure is what you can know WAVE-PICTURE OF RADIATION—ENERGY FLOW I S CONTI N UOUS • Radio waves, microwaves, heat waves, light waves, UV-rays, x-rays and y-rays belong to the family of electromagnetic waves. All of them are known as radiation.
  • 68. • Electromagnetic waves consist of varying electric and magnetic fields traveling at the velocity of 'c'. The proMaxwell's theory treated the emission of radiation by a source as a continuous process. • A heated body may be assumed to be capable of giving out energy that travels in the form of waves of all possible wavelengths. • In the same way, the radiation incident on a body was thought to be absorbed at all possible wavelengths. • The intensity of radiation is given by, I = 1E12 • where E is the amplitude of the electromagnetic wave. • pagation of electromagnetic waves and their interaction with matter can be explained with the help of Maxwell's electromagnetic theory. • The phenomena of interference, diffraction and polarization of electromagnetic radiation proved the wave nature of radiation. • Therefore, it is expected that it would explain the experimental observations made on thermal (heat) radiation emitted by a blackbody. Blackbody radiation and Planck hypothesis • Two patches of clouds in physics sky at the beginning of 20th century. • The speed of light  Relativity • The blackbody radiation  foundation of Quantum theory • Convection is transfer of heat by actual motion of. The hot-air furnace, the hot-water heating system, and the flow of blood in the body are examples. • Radiation The heat reaching the earth from the sun cannot be transferred either by conduction or convection since the space between the earth and the sun has no material medium. The energy is carried by electromagnetic waves that do not require a material medium for propagation. The kind of heat transfer is called thermal radiation. • Blackbody is defined as the body which can absorb all energies that fall on it. It is something like a black hole. No lights or material can get away from it as long as it is trapped. A large cavity with a small hole on its wall can be taken as a blackbody. LAWS OF BLACK BODY RADIATION 1. Stefan and Boltzmann’s law: it is found that the radiation energy is proportional to the fourth power of the associated temperature. 4 M (T) T 2. Wien’s displacement law: the peak of the curve shifts towards longer wavelength as the temperature falls and it satisfies where b is called the Wien's constant. b=2.89X10-3 4 M (T ) T peak T b
  • 69. This law is quite useful for measuring the temperature of a blackbody with a very high temperature. You can see the example for how to measure the temperature on the surface of the sun. • The above laws describes the blackbody radiation very well. • The problem exists in the relation between the radiation power Mλ(T) and the wavelength λ. • Blackbody radiation has nothing to do with both the material used in the blackbody concave wall and the shape of the concave wall. • Two typical theoretical formulas for blackbody radiation : One is given by Rayleigh and Jeans and the other by Wein. 3.Rayleigh and Jeans • In 1890, Rayleigh and Jeans obtained a formula using the classical electromagnetic (Maxwell) theory and the classical equipartition theorem of energy in thermotics. The formula is given by 2 3 8 kT E( ) c Rayleigh-Jeans formula was correct for very long wavelength in the far infrared but hopelessly wrong in the visible light and ultraviolet region. Maxwell‟s electromagnetic theory and thermodynamics are known as correct theory. The failure in explaining blackbody radiation puzzled physicists! It was regarded as ultraviolet Catastrophe (disaster). 4. Planck Radiation Law: Where, E=Quantum energy h= Planck constant v= frequency PLANCK'S QUANTUM HYPOTHESIS — Energy is quantized • Max Planck empirical formula explained the experimental observations. • In the process of formulation of the formula, he assumed that the atoms of the walls of the blackbody behave like small harmonic oscillators, each having a characteristic frequency of vibration, lie further made two radical assumptions about the atomic oscillators. • An oscillating atom can absorb or mends energy in discrete units. The indivisible discrete unit of energy hs, is the smallest amount of energy which can be absorbed or emitted by the atom and is called an energy quantum. A quantum of energy has the magnitude given by E = hv 4 M (T) T hc E h
  • 70. where v is the frequency of radiation and „h' is a constant now known as the Planck's constant. • The energy of the oscillator is quantized. It can have only certain discrete amounts of energy En. En= nhv n=1,2,3…… • The hypothesis that radiant energy is emitted or absorbed basically in a discontinuous summer and in the form of quanta is known as the Planck's quantum hypothesis. • Planck's hypothesis states that radiant energy Is quantized and implies that an atom exists in certain discrete energy states. Such states arc called quantum stales and n is called the quantum number. • The atom emits or absorbs energy by jumping from one quantum state to another quantum state. The assumption of discrete energy states for an atomic oscillator (Fig.a) was a departure from the classical physics and our everyday exper • If we take a mass-spring harmonic oscillator, it can receive any amount of energy form zero to some maximum value (Fig.b). Thus, in the realm of classical physics energy always appears to occur with continuous values and energy exchange between bodies involves any arbitrary amounts of energy. PARTICLE PICTURE OF RADIATION —Radiation is a stream of photons Max Planck introduced the concept of discontinuous emission and absorption of radiation by bodies but he treated the propagation through space as occurring in the form of continuous waves as demanded by electromagnetic theory.
  • 71. • Einstein refined the Planck's hypothesis and invested the quantum with a clear and distinct identity. • He successfully explained the experimental results of the photoelectric effect in 1905 and the temperature dependence of specific heats of solids in 1907 basing on Planck's hypothesis. • The photoelectric effect conclusively established that light behaves as a swam of particles. Einstein extended Planck's hypothesis as follows: 1 Einstein assumed that the light energy is not distributed evenly over the whole expanding wave front but rather remains concentrated in discrete quanta. He named the energy quanta as photons. Accordingly, a light beam is regarded as a stream of photons travelling with a velocity ' c' . 2 An electromagnetic wave having a frequency f contains identical photons, each having an energy hƒ. The higher the frequency of the electromagnetic wave, the higher is the energy content of each photon. 3. An electromagnetic wave would have energy hƒ if it contains only one photon. 2hv if it contains 2 photons and so on. Therefore, the intensity of a monochromatic light beam I. is related to the concentration of photons. N. present in the beam. Thus, I = N hƒ Note that according to electromagnetic theory, the intensity of a light beam is given by I = 1E12 4. When photons encounter matter, they impart all their energy to the panicles of matter and vanish. That is why absorption of radiation is discontinuous. The number of photons emitted by even a weak light source is enormously large and the human eye cannot register the photons separately and therefore light appears as a continuous stream. Thus, the discreteness of light is not readily apparent. The Photon • As the radiant energy is viewed as made up of spatially localized photons. we may attribute particle properties to photons. 1. Energy: The energy of a photon is determined by its frequency v and is given by E = hƒ. Using the relation ω= 2π and writing h/2π = ħ. we may express E= ħω 2. Velocity: Photons always travel with the velocity of light „c'. 3. Rest Mass: The rest mass of photon is zero since a photon can never be at rest. Thus, m0= 0
  • 72. 4. Relativistic mass: As photon travels with the velocity of light, it has relativistic mass. given by m= E/c2 = hv/c2 5. Linear Momentum: The linear momentum associated with a photon may be expressed as p=E/c=hv/c= h/λ As the wave vector k= 2π/λ , p = hk/ 2π = ħk. 6. Angular Momentum: Angular momentum is also known as spin which is the intrinsic property of all microparticles. Photon has a spin of one unit. Thus. s = lħ. 7. Electrical Charge: Photons are electrically neutral and cannot be influenced by electric or magnetic fields. They cannot ionize matter. Example: 1 Calculate the photon energies for the following types of electromagnetic radiation: (a) a 600kHz radio wave; (b) the 500nm (wavelength of) green light; (c) a 0.1 nm (wavelength of) X-rays. Solution: (a) for the radio wave, we can use the Planck-Einstein law directly 15 3 9 E h 4.136 10 eV s 600 10 Hz 2.48 10 eV (b) The light wave is specified by wavelength, we can use the law explained in wavelength: 6 9 hc 1.241 10 eV m E 2.26eV 550 10 m (c). For X-rays, we have 6 4 9 hc 1.241 10 eV m E 1.24 10 eV 12.4keV 0.1 10 m Photoelectric Effect:- The quantum nature of light had its origin in the theory of thermal radiation and was strongly reinforced by the discovery of the photoelectric effect.
  • 73. Fig. Apparatus to investigate the photoelectric effect that was first found in 1887 by Hertz. In figure , a glass tube contains two electrodes of the same material, one of which is irradiated by light. The electrodes are connected to a battery and a sensitive current detector measures the current flow between them. The current flow is a direct measure of the rate of emission of electrons from the irradiated electrode. The electrons in the electrodes can be ejected by light and have a certain amount of kinetic energy. Now we change: (1) the frequency and intensity of light, (2) the electromotive force (e.m.f. or voltage), (3) the nature of electrode surface. It is found that: (1). For a given electrode material, no photoemission exists at all below a certain frequency of the incident light. When the frequency increases, the emission begins at a certain frequency. The frequency is called threshold frequency of the material. The threshold frequency has to be measured in the existence of e.m.f. (electromotive force) as at such a case the photoelectrons have no kinetic energy to move from the cathode to anode . Different electrode material has different threshold frequency. (2). The rate of electron emission is directly proportional to the intensity of the incident light. Photoelectric current ∝ The intensity of light (3). Increasing the intensity of the incident light does not increase the kinetic energy of the photoelectrons. Intensity of light ∝ kinetic energy of photoelectron However increasing the frequency of light does increase the kinetic energy of photoelectrons even for very low intensity levels. Frequency of light ∝ kinetic energy of photoelectron (4). There is no measurable time delay between irradiating the electrode and the emission of photoelectrons, even when the light is of very low intensity. As soon as the electrode is irradiated, photoelectrons are ejected.
  • 74. (5) The photoelectric current is deeply affected by the nature of the electrodes and chemical contamination of their surface. In 1905, Einstein solved the photoelectric effect problem by applying the Planck‟s hypothesis. He pointed out that Planck‟s quantization hypothesis applied not only to the emission of radiation by a material object but also to its transmission and its absorption by another material object. The light is not only electromagnetic waves but also a quantum. All the effects of photoelectric emission can be readily explained from the following assumptions: Therefore we have the equation of photoelectric effect: 21 2 h A mv Using this equation and Einstein‟s assumption, you could readily explain all the results in the photoelectric effect: why does threshold frequency exist (problem)? why is the number of photoelectrons proportional to the light intensity? why does high intensity not mean high photoelectron energy (problem)? why is there no time delay (problem)? Example: Ultraviolet light of wavelength 150nm falls on a chromium electrode. Calculate the maximum kinetic energy and the corresponding velocity of the photoelectrons (the work function of chromium is 4.37eV). Solution: using the equation of the photoelectric effect, it is convenient to express the energy in electron volts. The photon energy is 6 9 1.241 10 8.27 150 10 hc eV m E h eV m 2 2 1 2 1 (8.27 4.37) 3.90 2 h A mv mv eV eV 19 19 19 2 2 1 1.602 10 1.602 10 1.602 10eV J N m kg m s 2 19 2 21 3.90 3.90 1.602 10 2 mv eV kg m s 19 6 31 2 3.90 12.496 10 1.17 10 / 9.11 10 eV v m s m
  • 75. EXERCISE:- 1. The wavelength of yellow light is 5890 A. What is the energy of the photons in the beam? Empress in electron volts. 2. 77w light sensitive compound on most photographic films is silver bromide, Aglin A film is exposed when the light energy absorbed dissociates this molecule into its atoms. The energy of dissociation of Agllr is 23.9 k.catitnot Find the energy in electron volts, the wavelength and the frequency of the photon that is just able to dissociate a molecule of silver bromide. 3. Calculate the energy of a photon of blue light with a frequency of 6.67 x 1014 Hz. (State in eV) [2.76eV] 4. Calculate the energy of a photon of red light with a wavelength of 630 nm. [1.97eV] 5. Barium has a work function of 2.48 eV. What is the maximum kinetic energy of the ejected electron if the metal is illuminated by light of wavelength 450 nm? [0.28 eV] 6. When a 350nm light ray falls on a metal, the maximum kinetic energy of the photoelectron is 1.20eV. What is the work function of the metal? [2.3 eV] 7. A photon has 3.3 x 10-19 J of energy. What is the wavelength of this photon? 8. What is the energy of one quantum of 5.0 x 1014 Hz light? 4 M (T) T
  • 76. X-Rays Objectives:  Introduction and production of X-Rays  Properties of X-Rays  Diffraction of X-Rays  The Bragg’s X-Ray spectrometer  Continuous spectra  Characteristics Radiation  Moseley’s law  Absorption of X-Ray  Compton effect  Applications of X-Rays Introduction and production of X-Rays Introduction of X- Rays Wilhelm Rontgen discovered X-rays in 1985 during the course of some experiments with a discharge tube. He noticed that a screen coated with barium platinocyanide present at a distance from the discharge tube. Rontgen called these invisible radiations X-rays. Finally he concluded that X-rays are produced due to the bombardment of cathode rays on the walls of the discharge tube. It is well known that X-rays are produced when the fast moving electrons, and that metals or high atomic weight are most effective for this purpose. X-rays are electromagnetic waves with very short wavelengths. X-rays are highly penetrating and it can pass through many solids. They occur beyond the UV region in the electromagnetic spectrum. Their wavelengths range from 0.01 to 10 Å. Production or Generation of X-rays X-rays are produced by an X-ray tube. The schematic of the modern type of X-ray tube designed by Coolidge is shown in above figure.
  • 77.  It is an evacuated glass bulb enclosing two electrodes, a cathode and an anode. The cathode consists of a tungsten filament which emits electrons when it heated. The electrons are focused into a narrow beam with the help of a metal cup S. The anode consists of a target material, made of tungsten or molybdenum, which is embedded in a copper bar. Water circulating through a jacket surrounding the anode and cools the anode. Further large cooling fins conduct the heat away to the atmosphere. The face of the target is kept at an angle relative to the oncoming electron beam. A very high potential difference of the order of 50 kV is applied across the electrodes. The electrons emitted by the cathode are accelerated by the anode and acquire high energies of order of 105 eV. When the target suddenly stops these electrons, X-rays are emitted. The magnetic field associated with the electron beam undergoes a change when the electrons are stopped and electromagnetic waves in the form of X-rays are generated. The grater of the speed of the electron beam, the shorter will be the wavelength of the radiated X-rays. Only about 0.2 % of the electron beam energy is converted in to X- rays and the rest of the energy transforms into heat. It is for the reason that the anode is intensively cooled during the operation of X-ray tube. The intensity of the electron beam depends on the number of electron leaving the cathode. The hardness of the X-rays emitted depends on the energy of the electron beam striking the target. It can be adjusted by varying the potential difference applied between the cathode and anode. Therefore, the larger potential difference, the more penetrating or harder X-rays. Properties of X-Ray  They have relatively high penetrating power.  They are classified into Hard X-rays & Soft X-rays.
  • 78. The X-rays which have high energy and short wavelength is known as Hard X- rays. The X-rays which have low energy and longer wavelength is known as Soft X- rays.  X-rays causes the phenomenon of flouroscence.  On passing through a gas X-rays ionize the gas.  They are absorbed by the materials through which they traverse.  X-rays travel in straight line. Their speed in vacuum is equal to speed of light.  X-rays can affect a photographic film.  X-rays are undeflected by electric field or magnetic field. Diffraction of X-Rays – Bragg’s law Consider a crystal as made out of parallel planes of ions, spaced a distance d apart. The conditions for a sharp peak in the intensity of the scattered radiation are: 1. That the X-rays should be secularly reflected by the ions in any one plane. 2. That the reflected rays from successive planes should interfere constructively. Path difference between two rays reflected from adjoining planes: 2dsinθ, for the rays to interfere constructively, this path difference must be an integral number of wavelength λ, Suppose that a single monochromatic wave (of any type) is incident on aligned planes of lattice points, with separation , at angle . Points A and C are on one plane, and B is on the plane below. Points ABCC' form a quadrilateral. There will be a path difference between the ray that gets reflected along AC' and the ray that gets transmitted, and then reflected, along AB and BC respectively. This path difference is:
  • 79. The two separate waves will arrive at a point with the same phase, and hence undergo constructive interference, if and only if this path difference is equal to any integer value of the wavelength, i.e. Where, the same definition of and apply as above. Therefore, from which it follows that, Putting everything together, Which simplifies to Which is Bragg's law. Bragg angle is just the half of the total angle by which the incident beam is deflected. The Bragg’s X-Ray spectrometer An X-ray diffraction experiment requires, (1) X-ray source (2) The sample (3) The detector Depending on method there can be variations in these requirements. The X-ray radiation may either monochromatic or may have variable wave length.
  • 80. Structures of polycrystalline sample and single crystals can be studied. The detectors used in these experiments are photographic film. The schematic diagram of Bragg’s X-ray spectrometer is given in above. X-ray from an X-ray tube is collimated by passing team through slits S1 and S2. This beam is then allowed to fall on a single crystal mounted on a table which can be rotated about an axis perpendicular to the plane of incident of X-rays. The crystal behaves as a reflected grating and reflects X-rays. By rotating the table, the glancing angle θ at which the X-ray is incident on the crystal can be changed. The angle for which the intensity of the reflected beam is maximum gives the value of θ. The experiment is repeated for each plane of the crystal. For first order reflection n = 1 so that, λ = 2d sinθ; for n = 2, 2λ = 2d sinθ; ……., and so on. A photographic plate or an ionization chamber is used to detect the rays reflected by the crystal. Continuous X-rays or Bremsstrahlung X-rays
  • 81. "Bremsstrahlung" means "braking radiation" and is retained from the original German to describe the radiation which is emitted when electrons are decelerated or "braked" when they are fired at a metal target. Accelerated charges give off electromagnetic radiation, and when the energy of the bombarding electrons is high enough, that radiation is in the x-ray region of the electromagnetic spectrum. It is characterized by a continuous distribution of radiation which becomes more intense and shifts toward higher frequencies when the energy of the bombarding electrons is increased. The curves above are who bombarded tungsten targets with electrons of four different energies. The continuous distribution of x-rays which forms the base for the two sharp peaks at left is called "Bremsstrahlung" radiation. The bombarding electrons can also eject electrons from the inner shells of the atoms of the metal target, and the quick filling of those vacancies by electrons dropping down from higher levels gives rise to sharply defined characteristic x-rays. Characteristic X-rays Characteristic x-rays are emitted from heavy elements when their electrons make transitions between the lower atomic energy levels. The characteristic x-rays emission which shown as two sharp peaks in the illustration at left occur when vacancies are produced in the n=1 or K-shell of the atom and electrons drop down from above to fill the gap. The X-rays produced by transitions from the n=2 to n=1 levels are called Kα X-rays, and those for the n=3->1 transition are called Kβ X-rays. Transitions to the n=2 or L-shell are designated as L x-rays (n=3->2 is L-alpha, n=4->2 is L-beta, etc.