1. Unit-2 Polarization and Dispersion

2. One Dimensional EM Wave
For most purposes, a travelling light wave can be presented as a
one-dimensional, scalar wave provided it has a direction of
propagation.
Such a wave is usually described in terms of the electric field E.
Wavelength  Eo
Phase z
A plane wave propagating in the direction of z is:
The propagation constant (or wave number)
Phase velocity
n = Propagation medium refractive index

3. Group Velocity
As monochromatic light wave propagates along a waveguide in the
z direction, the points of constant phase travel at a phase velocity.
Phase velocity
However, non-monochromatic waves travelling
together will have a velocity known as Group Velocity:
1.44
1.46
1.49
500
1700
1900 n ng
 (nm)
Ref. index
Where the fibre
group index is:

4. Classification of Polarization
Light in the form of a plane wave in space is said to be linearly polarized.
If light is composed of two plane waves of equal amplitude by differing in phase by 90°, then the light is said to be circularly polarized.
If two plane waves of differing amplitude are related in phase by 90°, or if the relative phase is other than 90° then the light is said to be elliptically polarized.

5. Linear Polarization
A plane electromagnetic wave is said to be linearly polarized.
The transverse electric field wave is accompanied by a magnetic field wave as illustrated.

6. Circular Polarization
Circularly polarized light consists of two perpendicular electromagnetic plane waves of equal amplitude and 90° difference in phase.
The light illustrated is right- circularly polarized.

7. Elliptical Polarization
Elliptically polarized light consists of two perpendicular waves of unequal amplitude which differ in phase by 90°.
The illustration shows right- elliptically polarized light.

8. Fiber Dispersion

9. Fibre Dispersion
Data carried in an optical fibre consists of pulses of light energy
consists of a large number of frequencies travelling at a given rate.
There is a limit to the highest data rate (frequency) that can be
sent down a fibre and be expected to emerge intact at the output.
This is because of a phenomenon known as Dispersion (pulse
spreading), which limits the "Bandwidth” of the fibre.
si(t) T
so(t)
Output
pulse  L
Many modes
Cause of Dispersion:
Chromatic (Intramodal) Dispersion
Modal (Intermodal) Dispersion

10. Effects of Dispersion and Attenuation

11. Definitions
Group velocity
Group delay
Dispersion

12. Group and Phase Velocity
The formation of a wave packet from the combination of two waves
with nearly equal frequencies. The envelope of the wave package
or group of waves travels at a group velocity vg.

13. Chromatic/Intramodal Dispersion
Intramodal dispersion arises due to the propagation delay differences between
the different spectral components of the transmitted signal.
Further it increases with the increase in spectral width of the optical source.
This spectral width is the range of
wavelengths emitted by the optical source.
For example in the case of LED,
it has a large spectral width about
40 nm since it emits wavelengths
from 830–870 nm with the peak emission wavelength at 850 nm.
In the case of laser diode which has a very narrow spectral width, the spectral width
is about 1 or 2 nm only.
Thus the Intramodal dispersion can be reduced in an optical fiber using single mode
laser diode as an optical source.
Laser
 = 1-2 nm
 = R.M.S Spectral
width
LED
(many modes)
 = 40 nm
wavelength

14. Chromatic/Intramodal Dispersion
Main causes:
Material dispersion
Waveguide dispersion

15. Material Dispersion
This dispersion arises due to the different group velocities of the various spectral
components launched into the fiber.
A material is said to exhibit material dispersion when
Pulse spreading occurs even when different wavelengths follow the same path.
Sometimes referred to as Chromatic dispersion ,
since this is the same effect by
which a prism spreads out
a spectrum.
In a prism, material dispersion (a wavelength-dependent refractive index)
causes different colors to refract at different angles, splitting white light into a rainbow

16. Material Dispersion

17. Material Dispersion RMS pulse broadening
Refractive index of silica is frequency dependent. Thus different
frequency (wavelength) components travel at different speed
RMS pulse broadening
Where material dispersion coefficient:
-100
100
175
Dmat 
2nd window
Note: Negative sign, indicates that low
wavelength components arrives before
higher wavelength components.

18. Waveguide Dispersion
This results from variation of the group velocity with wavelength for
a particular mode.
Signal in the cladding travels with a different velocity than the signal in the core
The amount of waveguide dispersion depends on the fiber design like core radius and the size of the fiber.
This can usually be ignored in multimode fibres, since it is very
small compared with material dispersion.
However it is significant in monomode fibres.

19. Waveguide Dispersion
In the case of single mode fibers, waveguide dispersion
arises when
-100
100
175
Dmat 
Waveguide dispersion
Total dispersion
Material dispersion

20. Modifying Chromatic Dispersion

21. Modal (Intermodal) Dispersion
Result of different values of the group delay for each individual mode at a single frequency.
This variation in the group velocities of the different modes results in a group delay spread of intermodal distortion.
This distortion mechanism is eliminated by single-mode operation, but it is important in multimode fibers.

22. Modal (Intermodal) Dispersion
Lower order modes travel almost parallel to the centre line of the fibre cover the shortest distance, thus reaching the end of fibre sooner.
The higher order modes (more zig-zag rays) take a longer route
as they pass along the fibre and so reach the end of the fibre later.
Mainly in multimode fibers 1 2
Cladding n2
Core n1 c  

23. Modal Dispersion - SIMMF
The time taken for ray 1 to propagate a length of fibre L gives the minimum delay time:
The time taken for the ray to propagate a length of fibre L gives the maximum delay time:
Since
The delay difference
Since relative refractive index difference
Thus

24. Modal Dispersion - SIMMF
For ,
and
Thus
For a rectangular input pulse, the RMS pulse broadening due to
modal dispersion at the output of the fibre is:
Total dispersion = chromatic dispersion + modal dispersion

25. Modal Dispersion - GIMMF
The delay difference
the RMS pulse broadening

26. Modal Dispersion - GIMMF
Intermodal dispersion in multimode fibers is minimized with the use of graded index fibers.
Hence multimode graded index fibers show substantial bandwidth improvement over multimode step index fibers.
The fiber has a parabolic index profile with a maximum at the core axis.

27. Step and Graded Index Fibers

28. Modal Dispersion - GIMMF
It may be observed that apart from the axial ray the meridional rays follow sinusoidal trajectories of different path lengths which results from the index grading.
The longer sinusoidal paths are compensated for by the higher speeds in the lower index medium away from the axis.
The ray that travels along the axial ray is exclusively in the high index region at the core axis, and at the lowest speed.
Thus there is an equalization of the transmission times of the various trajectories and the graded index profile reduces the disparity in the mode transit times.
Thus the delay difference between the fastest and slowest modes are reduced for graded index fiber.

29. Problem

30. Problem

31. Bandwidth Limitations
Maximum channel bandwidth B:
For non-return-to-zero (NRZ) data format: B = BT /2
For return-to-zero (RZ) data format: B = BT
Where the maximum bit rate BT = 1/T, and T = bit duration.
For zero pulse overlap at the output of the fibre BT <= 1/2
where  is the pulse width.
For MMSF: BT (max) = 1/2Ts
For a Gaussian shape pulse:BT  0.2/rms
where rms is the RMS pulse width.
For MMSF: BT (max) =0.2/ modal or
BT (max) =0.2/ T Total dispersion

32. Bandwidth Distance Product (BDP)
The BDP is the bandwidth of a kilometer of fibre and is a constant
for any particular type of fibre.
Bopt * L = BT * L (MHzkm)
For example, A multimode fibre has a BDP of 20 MHz.km, then:-
- 1 km of the fibre would have a bandwidth of 20 MHz
- 2 km of the fibre would have a bandwidth of 10 MHz
Typical B.D.P. for different types of fibres are:
Multimode MHz.km
Single Mode MHz.km
Graded Index MHZ.km

33. Polarization Mode Dispersion

34. Polarizations of fundamental mode

35. Birefringence in single-mode fibers
Because of asymmetries the refractive indices for the two degenerate modes (vertical & horizontal polarizations) are different. This difference is referred to as birefringence, :
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

36. Birefringence in single-mode fibers
The effects of fiber birefringence on the polarization states of an optical signal are another source of pulse broadening.
Results from intrinsic factors such as geometric irregularities of the fiber core or internal stresses on it.
External factors such as bending, twisting or pinching of the fiber can also lead to birefringence.
All these mechanisms exist to some extent in the fiber, there will be a varying birefringence along its length.

37. Polarization Mode dispersion

39. Fiber Beat Length
In general, a linearly polarized mode is a combination of both of the degenerate modes. As the modal wave travels along the fiber, the difference in the refractive indices would change the phase difference between these two components & thereby the state of the polarization of the mode. However after certain length referred to as fiber beat length, the modal wave will produce its original state of polarization. This length is simply given by:

40. Fiber Beat Length