Dispersion in optical fibers

This narrated power point presentation attempts to explain the various dispersion mechanisms that are observed in optical fibers. Some fundamental terms and concepts are also discussed. The material will be useful for KTU final year B Tech students who prepare for the subject EC 405, Optical Communications.

1. 1
Dispersion in Optical Fibers
MEC

2. 2
Contents
•Fundamental terms and definitions.
•Chromatic / Intramodal Dispersion.
-Material Dispersion.
-Waveguide Dispersion.
•Intermodal / Mode Dispersion.
•Polarisation Mode Dispersion /
Birefringence.

3. 3
Phase and Group velocity
•Points of constant phase within all
electromagnetic waves.
•For plane waves constant phase points
form a surface called wavefront.
•Points of constant phase travel at a phase
velocity
ω–angular frequency of the wave,
β–mode propagation constant.

4. 4
Phase and Group velocity
•Cannot produce perfectly monochromatic
light waves, light sources emit multiple
frequencies.
•A group of waves with closely similar
frequencies propagate, their resultant
forms a packet of waves.
•Wave packet does not travel at the phase
velocity of the individual waves, move at a
group velocity

5. 5
Phase and Group velocity
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 υ
g.
υ
g

6. 6
Phase and Group velocity
•For propagation in an infinite medium of
refractive index n
1, propagation constant
•Phase velocity

7. 7
Phase Propagation Constant
•A plane wave propagating in the guide
shown by its wave vector or equivalent ray
–wave vector resolved into components in
the z and x directions.
•Component of phase propagation constant
in the z direction
•Component of the phase propagation
constant in the x direction

8. 8
Components of Phase Propagation
Constant

9. 9
Light Penetration into Cladding

10. 10
Goos–Haenchen Shift

11. 11
Dispersion
•Dispersion mechanisms cause pulse
broadening.
•Each pulse broadens and overlaps with its
neighbours, indistinguishable at the receiver
input –Intersymbol Interference.
•Cause distortion and errors at the output, limits
the maximum attainable bandwidth.
•Error rate a function of the signal attenuation
and signal-to-noise ratio (SNR) at the receiver.

12. 12
Dispersion

13. 13
Dispersion
•For no overlapping of light pulses down on
an optical fiber link the digital bit rate B
T
must be less than the reciprocal of the
broadened (through dispersion) pulse
duration (2τ).
•Maximum bit rate that may be obtained on
an optical fiber link is 1/2τ.

14. 14
NRZ/RZ Bit Rates

15. 15
Pulse Broadening
graded index fiber

16. 16
Chromatic / Intramodal Dispersion
•Results from finite spectral line width of the
optical source.
•Optical sources emit a band of frequencies.
•Propagation delay differences between different
spectral components cause broadening.
•Delay differences due to dispersive properties of
the waveguide material (material dispersion) and
guidance effects within the fiber structure
(waveguide dispersion).

17. 17
Material dispersion
•Results from different group velocities of
various spectral components launched into
the fiber.
•Phase velocity of a plane wave
propagating in the dielectric medium
varies nonlinearly with wavelength.
•Second differential of refractive index with
respect to wavelength is not zero (d
2
n/dλ
2
≠ 0).

18. 18
Material Dispersion
•Pulse delay τ
mdue to material dispersion
in a fiber of length L
•For a source with rms spectral width σ
λ
and a mean wavelength λ, the rms pulse
broadening due to material dispersion σ
m

19. 19
Material Dispersion
•Pulse spread may be evaluated by
considering the dependence of τ
mon λ
•RMS pulse broadening due to material
dispersion

20. 20
Material Dispersion
•Material dispersion parameter M
(ps/nm/km)
•Also pulse broadening due to material
dispersion

21. 21
Material Dispersion

22. 22
Waveguide Dispersion
•Results from the variation in group velocity
with wavelength for a particular mode.
•Multimode fibers -negligible waveguide
dispersion.
•Single mode fiber exhibits waveguide
dispersion when d
2
β/dλ
2
≠ 0, (β -
propagation constant).

23. 23
Intermodal dispersion
•Results from propagation delay differences
between modes within a multimode fiber.
•Different modes travel at different group
velocities output pulse width depends on
transmission times of the slowest and fastest
modes.
•Multimode step index fibers -large amount of
intermodal dispersion, greatest pulse
broadening.

24. 24
Intermodal Dispersion
•Graded index fibers -near-parabolic
profile –intermodal dispersion reduced -
bandwidth advantage.
•Pure single-mode operation -no
intermodal dispersion -pulse broadening
solely due to the intramodal dispersion -
least pulse broadening -greatest possible
bandwidths limited by the finite spectral
width of the source.

25. 25
Intermodal Dispersion

26. 26
Intermodal Dispersion
c

27. 27
Polarisation
•Electric field orientation of light.
•Birefringent fibers -each polarisation
mode travel at a slightly different velocity.
•Difference in propagation times between
the two orthogonal polarising modes result
in pulse broadening -polarisation mode
dispersion.
•Arrival time difference between two
orthogonal polarisations

28. 28
Fiber Birefringence
•Can result from geometric irregularities of
the fiber core or internal stress on it.
•Other causes are bending, twisting or
pinching of the fiber.

29. 29
Thank You