Special Fibers and Attenuation Feb. 20, 2018

+ Chromatic dispersion away from : where is the zero dispersion slope, i.e. or () at .
Example for dispersion calculation

+ Chromatic dispersion near : E.g. dispersion shift fibers, we need to consider high order dispersion (i.e. 3rd term in Taylor series or term) and use
.

+ Dispersion compensation: use optical elements (e.g. dispersion compensated fiber or fiber grating) to negate the effect of so that on average chromatic dispersion is zero and even the dispersion slope can be reduced (see Sec 5.7.3 pp. 314-319 2nd Ed, pp. 320-325 3rd Ed.)

+ Polarization mode dispersion (PMD): the single mode is composed of 2 orthogonal polarizations. PMD introduces random delays for pulses in different polarizations. ()
A slight difference in delay for high speed (>2.5Gb/s) channel widens pulses. The dispersion parameter . If the delay is too larger than 10% of a bit period, power in the slow polarization is considered lost. (see Sec 5.7.4 pp. 320-323 2nd Ed., pp. 325-328 3rd Ed.)

+ Fiber Attenuation: nonuniform refractive index Rayleigh scattering, attenuation coef. .
Imperfection of fiber (e.g. non-circular), .
Absorption from impurities, .

+ Transmission windows: 3rd window (C band) around has the lowest absorption ()
1st window around 800 nm.
2nd window (S band) around .
4th window (L band) > .
5th window (pending on removing impurities) between 1.55 and 1.3 .

+ Definition of : In terms of power, .
In terms of field, .
In terms of decibel (dB), .
Conversion - and .
Also .

+ Power budgeting:
Note - is degradation factors from components in dB, e.g. 1dB loss in connector means 79.4% of power surviving after the connector.
Example of dB calculation

+ Cut-off wavelength : In theory for step index fiber, we can obtain from which means 2nd and higher order mode occurring if .
In experiment, the single (fundamental) mode decreases to less than 0.1 dB while the 2nd mode attenuated by 19.3dB.

+ Birefringence: Birefringence in fiber causes polarization evoluting along the fiber. A complete cycle is reached at the beat length with .
Application: Polarization maintaining fiber (PMF)