Nonlinear pulse propagation - the Keller Group
Nonlinear pulse propagation - the Keller Group
Nonlinear pulse propagation - the Keller Group
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<strong>Nonlinear</strong> Schrödinger Equation (NSE)<br />
∂<br />
∂z A z, t′<br />
k n<br />
( ) = i ′′<br />
2<br />
∂ 2<br />
∂ t′<br />
A z, t′<br />
2<br />
( ) − ikn A( z, t′<br />
) 2 2<br />
A( z, t′<br />
) <strong>Nonlinear</strong> Schrödinger Equation (NSE)<br />
Solution: a fundamental soliton<br />
k n<br />
τ p<br />
= 1.7627 × 4 D = 1.7627 × 2 ′′<br />
δ e p<br />
kn 2<br />
e p<br />
∝ 1 e p<br />
τ p<br />
∝ 1 e p<br />
τ p<br />
∝ k n<br />
′′<br />
⎛<br />
Soliton area = ∫ A 0<br />
sech t ⎞<br />
⎝<br />
⎜<br />
τ ⎠<br />
⎟ dt = π A 0<br />
τ<br />
“Solitons have constant area”<br />
ULP, Chap. 4, p. 22
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