Modulation Instability

Abstract A continuous wave with a cubic nonlinearity in an anomalous dispersion regime is known to develop instability with respect to small modulations in amplitude or in phase, called modulational instability. The phenomenon of modulational instability was discovered in fluids (Ostrovskii 1963, 1966; Whitham 1965; Benjamin and Feir 1967), in nonlinear optics (Bespalov and Talanov 1966; Karpman 1967), and in plasmas (Taniuti and Washimi 1968; Tam 1969; Hasegawa 1970, 1971). Modulational instability of a light wave in a fibre was suggested by Hasegawa and Brinkman (1980) as a means to generate a far infrared light source. Akhmediev et al. (1986, 1987) studied the modulational instability by constructing exact periodic solutions of the NLS equation. The first experimental verification of the modulational instability of a light wave in a fibre was made by Tai et al. (1986a). The modulational instability can also be induced by a mixture of a small amplitude light waves with the frequency separation (with respect to the carrier cw wave) falling into the sideband frequency range of instability (Hasegawa 1984). This induced modulational instability can be used to generate an ultra short pulse train with a desired repetition rate. The first experimental evidence of an induced modulational instability was also produced by Tai et al. (1986b). Modulational instability can also be produced by cross phase modulation (Berkhoer and Zakharov 1970; Agrawal 1987). This chapter is devoted to presenting theoretical and experimental analyses of modulational instabilities in fibres.