Fiber Nonlinearity Feb. 22, 2018

+ Fiber nonlinearity: 2nd order nonlinearity [equation] occurs only in anisotropic crystal, not in fiber.
3rd order nonlinearity [equation] occurs in fiber.

+ Effective area ([equation]) and length ([equation]) (pp. 77-79 2nd Ed., pp. 79-81 3rd Ed.): Since nonlinear effects are much dependent on power and intensity, the propagation distance [equation] and the fiber cross section [equation] where high power and high intensity are maintained.
[equation]; for [equation], [equation] where [equation] is the attenuation coefficient of the fiber.
[equation]; effective intensity [equation].

+ Stimulated Raman Scattering (SRS) (pp. 80-81, 326-329 2nd Ed., pp. 82-83, 332-334 3rd Ed.): Input high freq [equation] output low freq.
It has broadband (100's of nm) output and provide forward & backward scattering.
It requires power above a threshold [equation] where [equation] is almost equal to core area, [equation] is Raman gain coef., typical [equation].
Application: optical amplifier, laser.
Problems: Generate cross talk and limits power per channel, e.g.
considering Raman gain profile as a triangle with linewidth [equation] and W equally spaced channels [equation] with spacing [equation] & equal power P.
The fraction of power coupled from Channel 0 (with shortest wavelength) to all other channels is [equation].

Example on calculating the threshold power

+ Stimulated Brillouin Scattering (SBS) (pp. 79-80 2nd Ed., pp. 81-82 3rd Ed.): SBS causes backward scattering and down shifted by 11 GHz at 1550nm.
It requires power above a threshold [equation] where [equation] is core area, [equation] is Brillouin gain coef., typical [equation].
SBS is narrowband 100'S of MHz. As bandwidth increases, [equation] increases. (pp. 325-326 2nd Ed., pp. 331-332 3rd Ed.)

+ Four-wave mixing (FWM): Mixing 3 beams with different frequencies [equation] dominant freq. [equation], [equation] and [equation]
Mixing 2 beam with different frequencies [equation] freq. [equation], [equation]
FWM increases when a) channel spacing small and even distribution ([equation] match), b) power / channel large, c) Small chromatic dispersion, d) short fiber distance (pulses overlapping), e) very close refractive indices for channels, f) large [equation].

+ Temporal FWM: Near end, pulses overlap [equation] strong FWM
Far end, pulses overlapping decrease [equation] less FWM.

Last Modified: February 20, 2018
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