Modulational instability: Difference between revisions

Revision as of 18:14, 3 January 2017

Revision as of 22:00, 8 January 2017

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:<math>\beta_2^2\omega_m^2 + 2 \gamma P \beta_2 < 0,</math> {{pad|2em}} that is for {{pad|2em}} <math>\omega_m^2 < -2 \frac{\gamma P}{\beta_2}.</math>

This condition describes the requirement for anomalous dispersion (such that <math>\gamma\beta_2</math> is negative). The gain spectrum can be described by defining a gain parameter as <math>g \equiv \Im [ 2|\Im\{k_m\}| ],</math> so that the power of a perturbing signal grows with distance as <math>P\, e^{g z}.</math> The gain is therefore given by

:<math>g = \begin{cases}