Solitons

Mar. 1, 2018

• Solitons (pp. 735-739): The effect of anomalous dispersion and positive nonlinearity cancel exactly.
Model by nonlinear Schr`sf(ddoto)`dinger equation (NSE)>

`{partial A}/{partial z} + k prime {partial A}/{partial t} -j {k prime prime}/2 {partial^2 A}/{partial t^2} = -j gamma |A|^2 A`
Note: `E = (A(t,z) e ^{j(omega t - kz}))/ sqrt {A_e/(2 eta)}` and `A` is an envelope created by modulation & `A^2 =` power. Soliton `A(t,z) = A_o sech ((t - z/v_g)/T_o) e^(jz/(2L_D))`

where dispersion length `L_D = (T_o^2)/(|k prime prime |)` & `gamma = (2 pi n_2) / (lambda_o A_e)` (rad/W-m).
Soliton condition -- `T_o A_o = sqrt {(|k prime prime|}/ gamma}`
Example on calcula ting soliton width

Soliton can be generated in a fiber system with any pulse providing that soliton condition is roughly satisfied.
The outcome will be soliton plus noise which is detrimental to the system. If a pulse with peak amplitude of `NA_o` is input to a system, an Nth order soliton will be generated.
An Nth order soliton does not have a constant envelope, instead `A` is periodically evolving.

• Recap important soliton parameters: `A_o` should be constant (enemy: attenuation)
Soliton should move steadily (enemy: timing jitter from soliton collisions)
Soliton should have constant phase and energy (enemy: soliton interaction within collision length)


Last Modified: February 26, 2018
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