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In the fields of nonlinear optics and fluid dynamics, modulational instability or sideband instability is a phenomenon whereby deviations from a periodic waveform are reinforced by nonlinearity, leading to the generation of spectral-sidebands and the eventual breakup of the waveform into a train of pulses.〔 Concluded with a discussion by Klaus Hasselmann.〕 The phenomenon was first discovered − and modelled − for periodic surface gravity waves (Stokes waves) on deep water by T. Brooke Benjamin and Jim E. Feir, in 1967. Therefore, it is also known as the Benjamin−Feir instability. It is a possible mechanism for the generation of rogue waves. ==Initial instability and gain== Modulation instability only happens under certain circumstances. The most important condition is ''anomalous group velocity dispersion'', whereby pulses with shorter wavelengths travel with higher group velocity than pulses with longer wavelength.〔 (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.〔 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 grow exponentially. The overall gain spectrum can be derived 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 amplification. By tuning an input signal to a peak of the gain spectrum, it is possible to create an optical amplifier. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Modulational instability」の詳細全文を読む スポンサード リンク
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