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Modulation instability only happens under certain circumstances. The most important condition is ''anomalous group velocity [[dispersion relation|dispersion]]'', whereby pulses with shorter [[wavelength]]s travel with higher [[group velocity]] than pulses with longer wavelength.<ref name="agrawal" /> (This condition assumes a ''focussing'' [[Kerr nonlinearity]], whereby refractive index increases with optical intensity.) There is also a threshold power, below which no instability will be seen.<ref name="agrawal" />
The instability is strongly dependent on the frequency of the perturbation. At certain frequencies, a perturbation will have little effect, whilst at other frequencies, a perturbation will [[exponential growth|grow exponentially]]. The overall [[gain]] spectrum can be derived [[Analytical expression|analytically]], as is shown below. Random perturbations will generally contain a broad range of frequency components, and so will cause the generation of spectral sidebands which reflect the underlying gain spectrum.
The tendency of a perturbing signal to grow makes modulation instability a form of [[amplifier|amplification]]. By tuning an input signal to a peak of the gain spectrum, it is possible to create an [[optical amplifier]].
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