Special Fibers and Attenuation Feb. 20, 2018

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

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

+ Dispersion compensation: use optical elements (e.g. dispersion compensated fiber or fiber grating) to negate the effect of [equation] 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. [equation] ([equation])
A slight difference in delay for high speed (>2.5Gb/s) channel widens pulses. The dispersion parameter [equation]. 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 [equation] Rayleigh scattering, attenuation coef. [equation].
Imperfection of fiber (e.g. non-circular), [equation].
Absorption from impurities, [equation].

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

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

+ Power budgeting: [equation]
Note - [equation] 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 [equation]: In theory for step index fiber, we can obtain [equation] from [equation] which means 2nd and higher order mode occurring if [equation].
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 [equation] with [equation].
Application: Polarization maintaining fiber (PMF)

Last Modified: February 20, 2018
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