Optical fibers Theory and applications

Engineering physics: Author: Praveen N Vaidya, SDM College of Engg. and Tech. Dharwad.
OPTICAL FIBERS
Fiber optics:
This is a branch of physics which deals with the study of transmission of light through long
strands of transparent material with a high refractive index. If light it admitted at one end of the
fiber, it can travel through the fiber extremely fast, with a very low loss, even if the fiber is curved.
The process is extremely quick as light travels at a speed of about 300000km per second; therefore a
torch could be used to flash a signal right around the world in next to no time, hence the light is most
suitable way to transmit the information. This is also become the safest way of transmission as cannot be
tapped or leakage of signal.
Fiber Optics includes the production and usage of glass or plastic fibers like transparent mediums to
guide the information in the form of electromagnetic waves.
Optical Fibers:
Optical fibers are hair-thin strands of ultra pure transparent dielectrics like plastic or glass,
designed to guide the light wave along its length. A single pair of optical fibers can carry hundreds
of thousands of two-way conversations at once.
For the first time guiding of light through the transparent material is shown by the John Tyndall
in 1870. He showed that the transmission of light through the curved water stream.
In 1960 the light guided through the glass fibers for the first time. But there is heavy loss of energy or
large attenuation, because of large absorption of light by the glass. Later it is shown that the absorption
is due to impurities present in the glass. In 1970 – The glass fiber obtained with attenuation 20dB/km
and in 1979 – the fibers are manufactured those reduced the loss to 4dB/km. Now the loss is less than
0.2dB/km.
The optical fiber is working on the principle of total internal reflection.
Before heading towards the construction of optical fiber one should understand geometry of total internal
reflection.
Reflection: P P’
N
Q
N’
R
In case reflection angle of incident = angle of reflection,
1
A light ray, traveling in one medium is incident on the surface of
another medium; part of light sent back to original medium is
called as reflection.
Another part of light propagates through second medium, but it
deviates from it’s original path this phenomenon is called as
refraction.
In fig PQ – incident Ray, QR – Refracted ray , RS – emergent
ray, QP’ – Reflected ray, NQN’ is normal to surface

In case of refraction we have, S
i) Angle of refraction (r) is varies directly as angle of incidence (i)
ii) == 2
1
n
Sinr
Sini
Refractive index of second medium w.r.t. first medium,
iii) == 2
1
n
Sinr
Sini
1
2
n
n
, therefore n1sini=n2sinr is called snell’s law, where n1 and v1 – R.I. of first
medium w.r.t. air, n 2- R.I. of second medium w.r.t. air
iv)
1
2
n
n
2
1
v
v
= , Where v1 velocity of first medium, v2 velocity of second medium, if first medium is air
then we have n1=1 and n2=n, v1 = c, therefore, refractive index n = c/v
v) When light travels from rarer medium to denser medium refracted ray bends towards the
normal and bends away from the normal when it travels from denser to rarer medium.
vi) The total internal reflection takes place when light travels from denser medium to rarer medium
with incident angle above critical angle.
Total Internal Reflection:
Total internal reflection takes place whenever light travels from denser medium to rarer medium.
A O B
R S
Therefore, when i = C, r = 90o
then from snell’s law we have
n1sinC=n2sin90 => Sin C =
1
2
n
n
,
If second medium is air then, n2 = 1 and n1= n
Sin C = n
1
, or C = sin-1
(1/n)
If the angle of incidence exceeds the critical angle, the ray reflects totally internally instead of getting
refraction, this phenomenon is called as Total Internal Reflection.
In figure, the incident ray RO incident on the surface at an angle of incidence i > C, reflects
totally internally in the direction OS. Here angle of incidence = angle of reflection.
2
Consider a ray of light travel from denser medium
of R.I. n1 to rarer medium of R.I. n2, whenever the
angle of incidence (i) go on increases the angle of
refraction (r) also increase as shown in figure. At
a particular angle of incidence the refracted ray
(OF) grazes on the surface of separating two
media, i.e., angle of refraction is 90o
.
Therefore the angle of incidence (i=C) at which
at which the angle of refraction is 90o
is called
as Critical Angle (C).

Therefore, when light travels from denser medium to rarer medium at an angle of
incidence greater than critical angle, it reflects totally internally, this phenomenon is known as
Total Internal Reflection (TIR).
The principle of TIR is used instead of reflection to guide light through fibers because there is
energy loss is minimum in case of TIR, that takes place in the form absorption, dispersion or
scattering etc. The reflection of light is not suitable for guiding the light, this is because highly polished
materials also absorb the large amount of incident energy and cause the decay of the signal.
Construction of Optical Fiber:
The purest form of Silica (SiO2) which is nothing but as glass is used to manufacture the optical fiber.
Optical fiber is a thin solid cylinder whose diameter is negligible compared to its length. The light
travels through such fibers by the method of total internal reflection.
The optical fiber mainly contains three parts.
1. Core. 2. Cladding. 3. Sheath.
1. Core: This is central part of the optical fiber made of transparent material, namely pure glass or
plastic, through which light propagates by the method of TIR. Thickness of the core varies from
10μm to 100 μm depending upon the type of the optical fiber.
2. Cladding: The core is surrounded by a coaxial middle region known as cladding. The cladding is
fused with the core such that there is no material discontinuity between two. It is also made of glass
or plastic, whose R.I. is slightly less than R.I. of Core that helps to achieve TIR. Thickness of
the cladding varies from 25 μm to 50 μm depends upon the type of optical fibers.
3. Sheath: Sheath is outermost region of the optical fiber. It is an opaque material covers the
cladding and protects the optical fiber from any sort of damage. Thickness of the sheath over
cladding is about 25 μm
Numerical Aperture
The light ray incident on a face of optical fiber along any direction will not undergo total internal
reflection. But the light ray sent within certain circular area around a point on optical axis at one face
under go TIR.
The line angle made by the line joining between circumference of circle to mid point on an end
of optical fiber is angle of acceptance. The light ray incident at an angle above the angle of acceptance
will not undergo TIR.
3
Core Cladding Sheath10μm to 100 μm
50to125μm
60t0150μm

Hence the largest angle of incidence made by the light ray at one face of the fiber to
undergo TIR, at the interface between core and cladding is called as angle of acceptance (θ0),
Consider a ray of light AO traveling in a medium of R.I. no, incident at point O on the axis of the core of
R.I. n1 at an angle θ0, which refracts along OB in the core at an angle θ1.
From Snell’s law we have, n0 sin θ0 = n1 sin θ1 --------------------- 1
Where, n1 is R.I. of Core.
Consider, refracted ray strikes the interface between core and cladding at an angle of equals to critical
angle,
Hence at critical angle we have n1 sin C = n2 sin 90 Where n2 – R.I. of Cladding
Or Sin C =
1
2
n
n
-------------- 2
Also θ1 = 90 – C, Eqn. 1 takes the form
n0 sin θ0 = n1 sin (90 - C)
n0 sin θ0 = n1 cos C
n0 sin θ0 = n1 [1 - sin2
C]1/2
-------------- 3,
Substitute eqn. 2 in in eqn. 3, n0 sin θ0 = n1 2
1
2
2
1
n
n
−
n0 sin θ0 =








− 2
1
2
22
1 1
n
n
n
n0 sin θ0 = 2
2
2
1 nn −
0
2
2
2
1
0
n
nn
Sin
−
=θ
4
C
90 – C
θ0
A
O
B C

If the incident medium is air then n0 =1, 2
2
2
10 nnSin −=θ
This equation is called as numerical aperture.
Therefore N.A. = 2
2
2
1 nn −
The Numerical aperture is always positive as n1 > n2
The angle of acceptance 



 −= − 2
2
2
1
1
nnSinoθ
But the to get total internal reflection angle of incidence (θi) < θ0
Numerical aperture of the fiber depends only on the indices of the core and cladding of
the fiber, provided the surrounding medium is air.
Numerical aperture is always positive as n1 is always greater than n2.
Fraction change of Refractive Index (Δ):
Fractional index change is defined as the ratio of difference between the R.I. of core and cladding to the
R.I. of Core.
1
21
n
nn −
=∆ or 211 nnn −=∆
Relation between N.A. and Δ:
N.A. = 2
2
2
1 nn −
= ( )( )2121 nnnn −+ = ( ) ∆+ 121 nnn
= ( ) ∆112 nn
Therefore, N.A. = ∆21n
Modes of light Propagation:
Modes of propagation of light of an optical fiber corresponds to those light waves, continue to
propagate in the optical fiber, among number of waves incident on it, within the angle of acceptance.
Modes result from the fact that light can propagate in the fiber core at discrete angles within the cone of
acceptance, i.e. the incident rays at the cone of acceptance that should have the value of angle of
incidence in integral multiples are considered, such rays are in phase and interfere constructively and
continues the transmission.
5

The light waves on other angles will suffer destructive interference because of interfere out of phase are
not considered as modes.
V-number:
The number of modes supported for propagation in the fiber is determined by a parameter called
as V-number. It is dependent on diameter (d) Numerical aperture (in air)( 2
2
2
1 nn − ) of fiber,
wavelength of light guided and RI of surrounding medium.
It is given by,
2
2
2
10 nnn
d
V −=
λ
π
Modes of communication: section of radiations those enter optical fiber are guided through it, these are
in phase and produce constructing interference, the modes of communication is determined by equation,
2
2
V
N ≅
Types of Optical Fibers:
The optical fibers divided into three categories depending on the number of modes of
electromagnetic waves pass through an optical fiber simultaneously.
Single Mode Optical Fiber:
It is a single stand of glass fiber with core diameter of 8 to 10 microns and that of including cladding it
will become 60 to 70μm.
The refractive index of the core and cladding are uniform through out. As this fiber guides only one
mode of light wave hence it is called as single mode optical fiber.
Single Mode Fiber with a relatively narrow diameter, through which only one mode of wave length
1310 or 1550nm will propagate. Carries higher bandwidth than multimode fiber, but requires a light
source with a narrow spectral width like laser.
Single Modem fiber is used in many applications where data is sent at multi-frequency (Wave-Division-
Multiplexing) so only one cable is needed
Single-mode fiber gives you a higher transmission rate and up to 50 times more distance than
multimode, 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.
6

Single-mode fiber is best designed for longer transmission distances, making it suitable for long-
distance telephony and multi channel television broadcast systems. They give lower signal loss and
a higher information capacity (bandwidth) than multimode fibers
Single-mode fiber has disadvantages. The smaller core diameter makes coupling light into the core is
more difficult. It is also difficult to splice (connect the ends of optical fiber) the optical fibers with one
another.
Single mode fibers are capable of transferring higher amounts of data due to low fiber dispersion. Single
mode fibers lose more power at fiber bends. They lose power because light radiates into the cladding,
Multimode Fibers:
As their name implies, multimode fibers can guide the lights more than one mode. Multimode fibers can
propagate over 100 modes. The number of modes propagated depends on the core size and numerical
aperture (NA).
As the core size and NA increase, the number of modes increases.
The multimode step index fiber
It has the core of diameter about 50 μm to 100 μm and Numerical Aperture is about 0.20 to 0.29. It is
surrounded by the cladding of thickness about 25 μm, which is covered by the sheath.
A large core size and a higher NA have several advantages. Light is launched into a multimode fiber
with more ease. The higher NA and the larger core size make it easier to make fiber connections. During
fiber splicing, core-to-core alignment becomes less critical. Another advantage is that multimode fibers
permit the use of light-emitting diodes (LEDs).
The multimode step index optical fibers are used for the short distance communication like, Local Area
Network (LAN), sending codes and massages in the defence area. Multimode fibers also have some
disadvantages. As the number of modes increases, the effect of modal dispersion increases. Fiber
manufacturers adjust the core diameter, NA, and index profile properties of multimode fibers to
maximize system bandwidth.
Graded-index fiber. Graded Index multimode fibers can also propagate over 100 modes like step index
fiber. The number of modes propagated depends on the core size and numerical aperture (NA). As the
core size and NA increase, the number of modes increases. Typical values of fiber core size and NA are
50 to 100 and 0.20 to 0.29 respectively.
7

In this type of fiber, the core has a refractive index that gradually decreases as the distance from the
centre of the fiber increases and equates to the cladding at the interface. The R.I. of cladding remains
constant.
The Grin has also similar applications as that of the Step index multimode optical fibers. But has more
advantageous over the Step Index fiber.
Because of the continuously varying refractive index across the core, the light rays are bent smoothly
and converge repeatedly at points along the cable. The rays near edge of the core take a longer path but
travel faster since R.I. is lower. the dispersion and scattering of rays is avoided considerably. All other
characteristics of GRIN are similar to Step index multimode fibers.
Attenuation
Attenuation the decrease in magnitude of power of a signal in transmission between points; a
term used for expressing the total loss of an optical system, normally measured in decibels (dB) at
a specific wavelength.
Signal attenuation is defined as the ratio of optical input power (Pi) to the optical output power (Po).
Attenuation reduces the amount of optical power transmitted by the fiber.
Attenuation controls the distance an optical signal (pulse) can travel. Once the power of an optical pulse
is reduced to a point where the receiver is unable to detect the pulse, an error occurs.
Optical input power is the power injected into the fiber from an optical source. Optical output power is
the power received at the fiber end or optical detector.
Attenuation Coefficient
The rate of optical power loss with respect to distance along the fiber, usually measured in decibels per
kilometer (dB/km) at a specific wavelength; lower the number, better the fiber's attenuation.






=
o
i
P
P
L
nAttenuatio 10log
10
Signal attenuation is a log relationship. Length (L) is expressed in kilometers. Therefore, the unit of
attenuation is decibels/kilometer (dB/km).
Attenuation is mainly a result of light absorption, scattering, Dispersion and bending losses.
Absorption:
Absorption is a major cause of signal loss in an optical fiber. Absorption is defined as the portion of
attenuation resulting from the conversion of optical power into another energy form, such as heat.
Absorption in optical fibers is explained by three factors:
• Imperfections in the atomic structure of the fiber material
• The intrinsic or basic fiber-material properties
8

• The extrinsic (presence of impurities) fiber-material properties
Imperfections in the atomic structure induce absorption by the presence of missing molecules or oxygen
defects. Absorption is also induced by the diffusion of impurities like hydrogen, traces of metals like
iron, cobalt, chromium or presence of hydroxyl ions into the glass fiber.
If the amount of impurities in a fiber is reduced, then fiber attenuation is reduced.
Dispersion spreads the optical pulse as it travels along the fiber. This spreading of the signal pulse
reduces the system bandwidth or the information-carrying capacity of the fiber. Dispersion limits how
fast information is transferred. The effects of attenuation and dispersion increase as the pulse travels the
length of the fiber.
Scattering
Scattering is the loss of signal power (light) from the fiber core caused by impurities or changes in the
index of refraction of the fiber.
Rayleigh scattering accounts for the majority (about 96%) of attenuation in optical fiber. Light travels in
the core and interacts with the atoms in the glass. The light waves elastically collide with the atoms, and
light is scattered as a result.
Rayleigh scattering is the result of these elastic collisions between the light wave and the atoms in the
fiber. If the scattered light maintains an angle that supports forward travel within the core, no attenuation
occurs. If the light is scattered at an angle that does not support continued forward travel, the light is
diverted out of the core and attenuation occurs.
Some scattered light is reflected back toward the light source (input end).
Macrobending
If a bend is imposed on an optical fiber, strain is placed on the fiber along the region that is bent. The
bending strain will affect the refractive index and the critical angle of the light ray in that specific area.
As a result, light traveling in the core can refract out, and loss occurs.
This is a restriction on how much bend a fiber can withstand before experiencing problems in optical
performance or mechanical reliability. The rule of thumb for minimum bend radius is 1 1/2" for bare,
9
A macro bend is a large-scale bend that is visible; for example,
a fiber wrapped around a person's finger. This loss is generally
reversible once bends are corrected.
To prevent macro bends, all optical fiber (and optical fiber
cable) has a minimum bend radius specification that should not
be exceeded.

single-mode fiber; 10 times the cable's outside diameter (O.D.) for non-armored cable; and 15 times the
cable's O.D. for armored cable.
Microbending
This is a small-scale distortion, generally indicative of pressure on the fiber. Micro bending may be
related to temperature, tensile stress, or crushing force. Like macro bending, micro bending will cause a
reduction of optical power in the glass.
Micro bending is much localized, and the bend may not be clearly visible upon inspection. With bare
fiber, micro bending may be reversible; in the cabling process, it may not.
Dispersion
Dispersion is the "spreading" of a light pulse as it travels down a fiber. As the pulses spread, or broaden,
they tend to overlap, and are no longer distinguishable by the receiver as 0s and 1s. Light pulses
launched close together (high data rates) that spread too much (high dispersion) result in errors and loss
of information.
Light from lasers and LEDs consists of a range of wavelengths. Each of these wavelengths travels at a
slightly different speed. Over distance, the varying wavelength speeds cause the light pulse to spread in
time. This is of most importance in single-mode applications.
Modal dispersion is significant in multimode applications, where the various modes of light traveling
down the fiber arrive at the receiver at different times, causing a spreading effect.
Dispersion limits how fast, or how much, information can be sent over an optical fiber.
Bandwidth:
In simplest terms, bandwidth is the amount of information a fiber can carry so that every pulse is
distinguishable by the receiver at the end. (Figure)
Dispersion causes light pulses to spread. The
spreading of these light pulses causes them to
merge together. At a certain distance and
frequency, the pulses become unreadable by the
receiver. The multiple pathways of a multimode
fiber cause this overlap to be much greater than
for single-mode fiber. These different paths have
different lengths, which cause each mode of light
to arrive at a different time.
10

Applications of Optical fiber in Communication:
Nowadays the optical fibers find applications in all fields including, Industries, medicals, science and
Engineering institutions and entertainments (decorative).
Among all the maximum and efficient usage of optical fiber is in communications, namely,
Telephone cables, Local area networks, intermediate range communications like intercoms and TV
cables etc.
The network of the Optical Fiber communication is explained as follows,
BLOCK DIAGRAM:
•
The Input signal in the form of sound is convert into electrical signal (analog signal). Using Analog to
Digital Converter (DAL) or coder the analog signal is converted into digital signal.
The laser or LED is converting the digital electrical signal to the electromagnetic beam of light which is
coupled to optical fiber.
11
System bandwidth is measured in megahertz (MHz) at one km. In general, when a system's
bandwidth is 200 MHz·km, it means that 200 million pulses of light per second will travel down/ km
(1000 meters) of fiber, and each pulse will be distinguishable by the receiver.
This is how the basic structure of optical fiber was first created. At the same time, efforts continued
to make glass without impurities so as not to hinder the movement of the light, and to perfect other
technologies to prevent light from escaping to the outside.
Glass without impurities means glass with a high degree of transparency. In order to carry out
communications over long distances using glass fiber, the glass has to become highly transparent.
Because the glass we typically use in windows turns dark green if it is about 2 m thick, it doesn't
allow light to pass through. This is why an ordinary glass pane looks green when you see it from the
side. Glass used for optical fiber must be able to allow light to pass through for distances of some
20,000 m. This means that impurities have to be reduced to one-millionth or one-billionth those in
ordinary glass. After many struggles to eliminate impurities, today's optical fiber using quartz glass
was finally created.
In 1988, an optical fiber cable was laid under the Atlantic Ocean for the first time in the world. This
has made it possible to transmit 40,000 telephone calls between Europe and the US at the same time.
And it was the beginning of the era of optical communications.
Sound
waves
Analog
(electrical)
Signal
ADL –
Analog to
digital
converter
LED or
LASER
diodes
Amplifier
DAL –
Digital to
analog
coverter
Photo
Detector
Digital
Signal
Sound
OF CABLE
OF CABLE

During its path in the optical fiber light suffers various losses due to absorption, dispersion, scattering
etc., so the intensity may fall below the threshold in such cases it must be amplified.
To amplify the light is again converted to analog signal and is amplified to optimum level and further it
is converted to light signal.
The amplified light signal again made to transmit through optical fiber. Between two destinations
numbers of such amplifiers are installed depending upon the distance through which signal traverse.
At receiving station a Photo detector used to converts light pulses into Digital signal and is converted
into analog signal using Decoder. The analog or electrical signal further converted into sound at
telephone receiver.
In case of LAN the information in the form of digital signal directly fed into the computer.
Fiber optic gyroscope
(FOG) is a gyroscope that uses the interference of light to detect mechanical rotation. The sensor is a
coil of as much as 5 km of optical fiber. Two light beams travel along the fiber in opposite directions.
Due to the Sagnac effect, the beam traveling against the rotation experiences a slightly shorter path than
the other beam. The resulting phase shift affects how the beams interfere with each other when they are
combined. The intensity of the combined beam then depends on the rotation rate of the device.
The development of low loss single mode optical fiber in the early 1970s for the telecommunications
industry enabled Sagnac effect fiber optic gyros to be developed. These use an external laser diode
source together with beam splitting objects to launch the laser light so that photons travel simultaneously
in clockwise and anticlockwise directions through a cylindrical coil comprised of many turns of optical
fibre. The effective area of the closed optical path is thus multiplied by the number of turns in the coil.
Path lengths of hundreds of metres are achievable. The first FOG was demonstrated in the US by Vali
and Shorthill in 1976. Development of both the passive interferometer type of FOG, or IFOG, and the
passive ring resonator type of FOG, or RFOG, is proceeding in many companies and establishments
world-wide.
A FOG provides extremely precise rotational rate information, in part because of its lack of cross-axis
sensitivity to vibration, acceleration, and shock. Unlike the classic spinning-mass gyroscope, the FOG
has virtually no moving parts and no inertial resistance to movement. The FOG typically shows a higher
resolution than a ring laser gyroscope but also a higher drift and worse scale factor performance. It is
used in surveying, stabilization and inertial navigation tasks. FOGs are designed in both open-loop and
closed-loop configurations.
12

Other applications & Advantages of optical fibers
Fibre Optic Sensors
When an optical fibre is subjected to perturbations of different kind, it experiences geometrical (size,
shape) and optical (refractive index, mode conversion) changes to a larger or lesser extent depending
upon the nature and the magnitude of the perturbation. In fibre optic sensing, this response to external
influence is deliberately enhanced so that the resulting change in optical radiation can be used as a
measure of the external perturbation. So the optical fibre serves as a transducer and converts measurands
like temperature, stress, strain, rotation or electric and magnetic currents into a corresponding change in
the optical radiation. Since light is characterized by intensity, phase, frequency and polarization, any one
or more of these parameters may undergo a change. The usefulness of the fibre optic sensor therefore
depends upon the magnitude of this change and our ability to measure and quantify the same reliably
and accurately.
Fibre optic sensors can also be classified on the basis of their application.
• Physical sensors : used to measure physical proparties like temperature, stress, etc.
• Chemical sensors : used for pH measurement, gas analysis, spectroscopic studies, etc.
• Bio-medical sensors : used in bio-medical applications like measurement of blood flow , glucose
content etc.
Fibre optic sensors can again be classified as extrinsic or intrinsic sensors. In the former, sensing takes
place in a region outside of the fibre and the fibre essentially serves as a conduit for the to-and-fro
transmission of light to the sensing region .On the other hand, in an intrinsic sensor one or more of the
physical properties of the fibre undergo a change and this change is measure of the external perturbation.
13

2. The simplest & the most important use of optical fibers is their use as flexible light pipes. It can
transmit light to otherwise inaccessible areas & even provide information about such regions by
returning images. The fiberscope, a bundle of fibers end-equipped with objective lens & eye piece is
used by doctors to examine regions of the stomach, lungs and duodenum.
3. The rods & the cones of the human eye function as light pipes transmitting light as in optical fibers.
4. Voice or video communication & data transmission.
5. Optical fibers are smaller in size & light in weight compared to conventional metallic cables. Since
optical frequencies are much higher than the conventional electrical signals, replacement of copper
coaxial cables by fiber optic cables offers greater communication capacity in smaller space. Their
maintenance cost is much lower.
6. In contrast with the metallic conduction techniques, communication by light through optical fibers
offers complete electrical isolation, immunity to electromagnetic interference, radio frequency
interference & voltage surge. Optical fibers are free from signal leakage, electric sparks & fire hazards.
They are useful in laying cables near electronic hardware in industrial equipment.
6. Communication through optical fibers is especially important & advantageous where security of
information is vital.
1. A step index optical fiber has a core of R.I 1.46 and the cladding of R.I. 1.409. If the core diameter is
80μm and wavelength of the light source is 1.2 μm, determine the number of modes present in the fiber.
n1= 1.46, n1= 1.409, Radius of the fiber, d = 80 μm, λ =1.2 x10-6
m, n0 = 1
Let ‘V’ number is given by equation, 2
2
2
10 nnn
d
V −=
λ
π
And Number of modes, N =
2
2
V
= ( )2
2
2
1
2
0
2
1
nnn
d
−





λ
π
)409.146.1(
102.1
1040
2
1 22
2
6
6
−








×
××
= −
−
π
N
N = 21932.45 x 0.146319
N = 3202 modes
2. A single mode step index optical fiber used in communication has a core with R.I. 1.45, Fraction
index change (R.I. change) of 5 x 10-3, and a core diameter of 6 μm. If the operating wavelength of the
communication system is 1.2 μm, determine the V-parameter of the cable.
n1= 1.46 ∆ = 5 x 10-3, d = 6 x 10-6
m λ =1.2 x10-6
m, n0 = 1
14

2
2
2
10 nnn
d
V −=
λ
π
∆=−= 21
2
2
2
10 n
d
nnn
d
V
λ
π
λ
π
because, N. A. = ∆=− 21
2
2
2
1 n
d
nn
λ
π
= 2.28 When no = 1
3. A fiber sample 500m long has an input power of 8.6 μW, and an output power of 7.5μW. What is the
loss specification for the cable sample?






==
5.7
6.8
log
500
10
10nattenuatioα = 0.0011887 dB/m
α = 1.1887dB/km
15

Optical fibers Theory and applications

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Optical fibers Theory and applications