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Modes in Optical Fibers 
Prof. B.Mahapatra 
Assistant Professor 
Mumbai University 
Pro.Byomakesh Mahapatra
Topics:- 
Basic principle of light 
propagation 
Numerical Aperture & 
Acceptance angle 
Mode Theory 
Modes in planar waveguides 
Mode Condition 
TE Pro.Byomakesh and Mahapatra 
TM modes 
Single and Multi-mode Fibers
Basic principles light propagation 
Pro.Byomakesh Mahapatra
Pro.Byomakesh Mahapatra
r = light incidence ray position (0 to a) 
a = core radius 
Pro.Byomakesh Mahapatra
Ray optics analysis of light wave 
propagation in optical fiber 
Pro.Byomakesh Mahapatra
Pro.Byomakesh Mahapatra
Numerical Aperture 
Pro.Byomakesh Mahapatra
Pro.Byomakesh Mahapatra
Mode Theory 
The mode theory, along with the ray theory, is used to 
describe the propagation of light along an optical fiber 
The mode theory uses electromagnetic wave behavior to 
describe the propagation of light along a fiber 
Pro.Byomakesh Mahapatra
Light Propagation planer wave guide 
ᵟ 
Pro.Byomakesh Mahapatra
Then the equation for sustain propagation is depend upon the 
diameter of core (d) 
Wave length (λ) 
And angle of propagation sinӨ 
Refractive index of core (n1) 
Then the equation represent as 
Pro.Byomakesh Mahapatra
Modes in planar waveguide 
The optical wave is effectively confined within the guide 
and the electric field distribution in the x direction does 
not change as the wave propagates in z direction. 
The stable field distribution in the x direction with only 
aperiodic z dependence is known as a mode. 
A specific mode is obtained only when the angle 
between the propagation vectors or the rays and the 
interface has a particular value. 
 Hence, the light propagating within the guide is formed 
into discrete modes, each typified Pro.Byomakesh Mahapatra by a distinct value of θ.
Waveguides or fiber optics obey Maxwell equations, for 
the light propagation in an isotropic dielectric material 
with no free charges are: 
(Faraday law, Gauss law) 
(Ampere law, Gauss law) 
Green: magnetic field 
Red : electric field 
Pro.Byomakesh Mahapatra
And the relationships between field types (for simple, 
isotropic dielectric material with no free charges) are: 
And corresponding wave equation can be found by using above 
value and the vector identity method 
which is the same for the magnetic field: 
Pro.Byomakesh Mahapatra
Planer wave guide light propagation 
Pro.Byomakesh Mahapatra
Mode Condition 
The component of plane wave in the x-direction is 
reflected at the interface between the higher and lower 
refractive index media. 
The component of wave in x-direction gives constructive 
interference to form standing wave patterns across the guide 
when the following condition is met 
= m 2π ΔΦ , where m is an integer 
The next slide shows examples of such rays for m=1,2,3 
together with the electric field distributions in the x direction 
Pro.Byomakesh Mahapatra
Modes in a Planar Guide 
Pro.Byomakesh Mahapatra
Mode designation in circular cylindrical 
waveguide (Optical Fiber) 
TE modes : 
lm The electric field vector lies in transverse plane. 
TM modes : 
Hybrid HE modes : 
lm 
Hybrid EH modes : 
lm 
lm 
The magnetic field vector lies in transverse plane. 
TE component is larger than TM component. 
TM component is larger than TE component. 
f 
l= # of variation cycles or zeros in direction. 
m= # of variation cycles or zeros in r direction. 
x 
y 
r 
z 
f 
Linearly Polarized (LP) modes in weakly-guided fibers ( 1 ) 1 2 n - n << 
LP (HE ),LP (TE TM HE ) 0m 1m 1m 0m 0m 0m + + 
Fundamental Mode: LP (HE ) 01 11 
Pro.Byomakesh Mahapatra
TE and TM Modes 
 Maxwell's equations describe electromagnetic waves or modes 
as having two components. 
 The two components are the electric field, E(x, y, z), and the 
magnetic field, H(x, y, z). The electric field, E, and the magnetic 
field, H, are at right angles to each other. 
Modes traveling in an optical fiber are said to be transverse. 
The transverse modes propagate along the axis of the fiber. 
 In TE modes, the electric field is perpendicular to the 
direction of propagation. 
 In TM modes, the magnetic field is perpendicular to the 
direction of propagation. The electric field is in the direction of 
propagation 
Pro.Byomakesh Mahapatra
TE Modes 
Pro.Byomakesh Mahapatra
Pro.Byomakesh Mahapatra
High and Low order Modes 
Pro.Byomakesh Mahapatra
Two degenerate fundamental modes in 
Fibers (Horizontal & Vertical 
HE 
11 Modes) 
Pro.Byomakesh Mahapatra
End view, cylindrical modes 
Pro.Byomakesh Mahapatra
Practical end view of different fringes pattern in 
different hybrid mode from 830nm LASER source 
Multimode 
o/p 
HE pattern 
showing 
interference 
Pro.Byomakesh Mahapatra
Mode propagation constant as a 
function of frequency 
 An index value V, defined as the normalized frequency is used to 
determines how many different guided modes a fiber can 
support. 
 In order to find a mode propagation constant and cut-off frequencies of 
various modes of the optical fiber, V- number is most importance. And 
it can be given as: 
V = pa n - n = a 
2 2 2 NA 
2 
1 2 
l 
p 
l 
a: radius of the core, λ is the optical free space wavelength, 
are the refractive indices of the core & cladding. 1 2 n & n 
Pro.Byomakesh Mahapatra
Mode of fiber based on V-number and 
propagation constant:- 
Each mode has a specific 
– Propagation constant β 
(=bz) 
– Spatial field distribution 
– Polarization 
Pro.Byomakesh Mahapatra
Single Mode Fibers 
 Fiber supporting only one mode is called single-mode or 
mono-mode fiber. 
 Single-mode fiber allows for a higher capacity to 
transmit information because it can retain the fidelity of each 
light pulse over longer distances, and it exhibits no dispersion 
caused by multiple modes 
 The most common type of single-mode fiber has a core 
diameter of 4 to 10 μm. The smaller core diameter 
makes coupling light into the core more difficult. 
 Data rates of up to 10 gigabits per second are possible 
at distances of over 60 km with commercially available 
transceivers. 
Pro.Byomakesh Mahapatra
Single Mode vs Multimode 
Pro.Byomakesh Mahapatra
Light propagation in single Mode Fiber 
Cladding 
Cladding 
Core 
Core 
Pro.Byomakesh Mahapatra
Multi-mode Fiber 
 Multimode fiber is best designed for short transmission distances, 
and is suited for use in LAN systems and video surveillance 
 Modes result from the fact that light will only propagate in the 
fibercore at discrete angles within the cone of acceptance. 
 Multi-mode fibers have large core diameters and they can 
support applications from 10 Mbit/s to 10 Gbit/s over link lengths 
of up to 550meters, more than sufficient for the majority of 
premises applications. 
Pro.Byomakesh Mahapatra
Light propagation in a multimode 
Fiber 
Pro.Byomakesh Mahapatra
Modal Dispersion 
Pro.Byomakesh Mahapatra
Distortion in MI Fibers 
Pro.Byomakesh Mahapatra
Distortion in Step Index Fibers 
 Reduction in pulse spreading 
– Mode mixing 
 Due to bends and scattering 
– Attenuation of higher ordered modes 
Total pulse spreading 
Which of the material dispersion or multimode spreading is 
greater? 
– We can reduce material and waveguide dispersion using a source 
with smaller line width like laser but since modal distortion is 
much greater, it is in effective and it will be cheaper to use an LED 
Pro.Byomakesh Mahapatra
Distortion in Graded-Index Fibers 
 Much Less multi-mode distortion. Why? 
Typical pulse spread is just a few nano sec per km 
 Modal Spread in GRIN Fiber 
D2 
Δτ/L = n1 /2c 
Pulse spread decreases by a factor of 2/Δ by using 
GRIN instead of SI 
What is the pulse spread for GRIN fiber with n1 = 1.48 
and n2 = 1.46? 
Pro.Byomakesh Mahapatra
Distortion in Single Mode Fibers 
Only material and waveguide dispersion 
Pulse Spread is smaller for longer 
wavelengths and narrower line widths. Why? 
Which source is preferable in this case?? 
Can the sum of material and wave guide 
dispersion become zero? 
Pro.Byomakesh Mahapatra

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Mode ppt.bmk

  • 1. Modes in Optical Fibers Prof. B.Mahapatra Assistant Professor Mumbai University Pro.Byomakesh Mahapatra
  • 2. Topics:- Basic principle of light propagation Numerical Aperture & Acceptance angle Mode Theory Modes in planar waveguides Mode Condition TE Pro.Byomakesh and Mahapatra TM modes Single and Multi-mode Fibers
  • 3. Basic principles light propagation Pro.Byomakesh Mahapatra
  • 5. r = light incidence ray position (0 to a) a = core radius Pro.Byomakesh Mahapatra
  • 6. Ray optics analysis of light wave propagation in optical fiber Pro.Byomakesh Mahapatra
  • 10. Mode Theory The mode theory, along with the ray theory, is used to describe the propagation of light along an optical fiber The mode theory uses electromagnetic wave behavior to describe the propagation of light along a fiber Pro.Byomakesh Mahapatra
  • 11. Light Propagation planer wave guide ᵟ Pro.Byomakesh Mahapatra
  • 12. Then the equation for sustain propagation is depend upon the diameter of core (d) Wave length (λ) And angle of propagation sinӨ Refractive index of core (n1) Then the equation represent as Pro.Byomakesh Mahapatra
  • 13. Modes in planar waveguide The optical wave is effectively confined within the guide and the electric field distribution in the x direction does not change as the wave propagates in z direction. The stable field distribution in the x direction with only aperiodic z dependence is known as a mode. A specific mode is obtained only when the angle between the propagation vectors or the rays and the interface has a particular value.  Hence, the light propagating within the guide is formed into discrete modes, each typified Pro.Byomakesh Mahapatra by a distinct value of θ.
  • 14. Waveguides or fiber optics obey Maxwell equations, for the light propagation in an isotropic dielectric material with no free charges are: (Faraday law, Gauss law) (Ampere law, Gauss law) Green: magnetic field Red : electric field Pro.Byomakesh Mahapatra
  • 15. And the relationships between field types (for simple, isotropic dielectric material with no free charges) are: And corresponding wave equation can be found by using above value and the vector identity method which is the same for the magnetic field: Pro.Byomakesh Mahapatra
  • 16. Planer wave guide light propagation Pro.Byomakesh Mahapatra
  • 17. Mode Condition The component of plane wave in the x-direction is reflected at the interface between the higher and lower refractive index media. The component of wave in x-direction gives constructive interference to form standing wave patterns across the guide when the following condition is met = m 2π ΔΦ , where m is an integer The next slide shows examples of such rays for m=1,2,3 together with the electric field distributions in the x direction Pro.Byomakesh Mahapatra
  • 18. Modes in a Planar Guide Pro.Byomakesh Mahapatra
  • 19. Mode designation in circular cylindrical waveguide (Optical Fiber) TE modes : lm The electric field vector lies in transverse plane. TM modes : Hybrid HE modes : lm Hybrid EH modes : lm lm The magnetic field vector lies in transverse plane. TE component is larger than TM component. TM component is larger than TE component. f l= # of variation cycles or zeros in direction. m= # of variation cycles or zeros in r direction. x y r z f Linearly Polarized (LP) modes in weakly-guided fibers ( 1 ) 1 2 n - n << LP (HE ),LP (TE TM HE ) 0m 1m 1m 0m 0m 0m + + Fundamental Mode: LP (HE ) 01 11 Pro.Byomakesh Mahapatra
  • 20. TE and TM Modes  Maxwell's equations describe electromagnetic waves or modes as having two components.  The two components are the electric field, E(x, y, z), and the magnetic field, H(x, y, z). The electric field, E, and the magnetic field, H, are at right angles to each other. Modes traveling in an optical fiber are said to be transverse. The transverse modes propagate along the axis of the fiber.  In TE modes, the electric field is perpendicular to the direction of propagation.  In TM modes, the magnetic field is perpendicular to the direction of propagation. The electric field is in the direction of propagation Pro.Byomakesh Mahapatra
  • 23. High and Low order Modes Pro.Byomakesh Mahapatra
  • 24. Two degenerate fundamental modes in Fibers (Horizontal & Vertical HE 11 Modes) Pro.Byomakesh Mahapatra
  • 25. End view, cylindrical modes Pro.Byomakesh Mahapatra
  • 26. Practical end view of different fringes pattern in different hybrid mode from 830nm LASER source Multimode o/p HE pattern showing interference Pro.Byomakesh Mahapatra
  • 27. Mode propagation constant as a function of frequency  An index value V, defined as the normalized frequency is used to determines how many different guided modes a fiber can support.  In order to find a mode propagation constant and cut-off frequencies of various modes of the optical fiber, V- number is most importance. And it can be given as: V = pa n - n = a 2 2 2 NA 2 1 2 l p l a: radius of the core, λ is the optical free space wavelength, are the refractive indices of the core & cladding. 1 2 n & n Pro.Byomakesh Mahapatra
  • 28. Mode of fiber based on V-number and propagation constant:- Each mode has a specific – Propagation constant β (=bz) – Spatial field distribution – Polarization Pro.Byomakesh Mahapatra
  • 29. Single Mode Fibers  Fiber supporting only one mode is called single-mode or mono-mode fiber.  Single-mode fiber allows for a higher capacity to transmit information because it can retain the fidelity of each light pulse over longer distances, and it exhibits no dispersion caused by multiple modes  The most common type of single-mode fiber has a core diameter of 4 to 10 μm. The smaller core diameter makes coupling light into the core more difficult.  Data rates of up to 10 gigabits per second are possible at distances of over 60 km with commercially available transceivers. Pro.Byomakesh Mahapatra
  • 30. Single Mode vs Multimode Pro.Byomakesh Mahapatra
  • 31. Light propagation in single Mode Fiber Cladding Cladding Core Core Pro.Byomakesh Mahapatra
  • 32. Multi-mode Fiber  Multimode fiber is best designed for short transmission distances, and is suited for use in LAN systems and video surveillance  Modes result from the fact that light will only propagate in the fibercore at discrete angles within the cone of acceptance.  Multi-mode fibers have large core diameters and they can support applications from 10 Mbit/s to 10 Gbit/s over link lengths of up to 550meters, more than sufficient for the majority of premises applications. Pro.Byomakesh Mahapatra
  • 33. Light propagation in a multimode Fiber Pro.Byomakesh Mahapatra
  • 35. Distortion in MI Fibers Pro.Byomakesh Mahapatra
  • 36. Distortion in Step Index Fibers  Reduction in pulse spreading – Mode mixing  Due to bends and scattering – Attenuation of higher ordered modes Total pulse spreading Which of the material dispersion or multimode spreading is greater? – We can reduce material and waveguide dispersion using a source with smaller line width like laser but since modal distortion is much greater, it is in effective and it will be cheaper to use an LED Pro.Byomakesh Mahapatra
  • 37. Distortion in Graded-Index Fibers  Much Less multi-mode distortion. Why? Typical pulse spread is just a few nano sec per km  Modal Spread in GRIN Fiber D2 Δτ/L = n1 /2c Pulse spread decreases by a factor of 2/Δ by using GRIN instead of SI What is the pulse spread for GRIN fiber with n1 = 1.48 and n2 = 1.46? Pro.Byomakesh Mahapatra
  • 38. Distortion in Single Mode Fibers Only material and waveguide dispersion Pulse Spread is smaller for longer wavelengths and narrower line widths. Why? Which source is preferable in this case?? Can the sum of material and wave guide dispersion become zero? Pro.Byomakesh Mahapatra