• Solitons (pp. 735-739): The effect of
.
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}`
Soliton can be generated in a fiber system with
any pulse providing that
.
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
will be generated.
An ,
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 should have constant phase and energy (enemy:
within collision length)