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Wave propagation in nonlinear media is usually accompanied by variation of their spacetime spectra (V.I. Bespalov & Talanov, 1966; Lighthill, 1965; Litvak & Talanov, 1967; Benjamin & Feir, 1967; Zakharov & Ostrovsky, 2009; Bejot et al., 2011). The character of this variation is frequently explained in terms of modulation instability which occurs, in particular, for electromagnetic waves in cubic media, where polarization is approximately equal to the cube of electric field intensity. Modulation instability manifests itself in partitioning of the originally uniform packet into separate beams and pulses. It has been studied in ample detail for the perturbations whose frequencies and propagation directions slightly differ from those of intense waves (pump waves), i.e., temporal and spatial spectra of the waves participating in the process are rather narrow (paraxial approximation) (V.I. Bespalov & Talanov, 1966; Litvak & Talanov, 1967; Agraval, 1995; Talanov & Vlasov, 1997). In this case, modulation instability is described by the nonlinear parabolic equation for a wave train envelope. The instability is quite different, if the nonlinearity is higher than the third order of magnitude. It was shown in (Talanov & Vlasov, 1994; Koposova & Vlasov, 2007) that the wave propagating in such a medium may be unstable relative to collinear perturbations at frequencies so high that not only wave packet envelope but the structure of each wave in the packet may change too. The parabolic equation does not hold for description of such phenomena; hence, the methods for solution of wave equations in a wide frequency band developed in (Talanov & Vlasov, 1995; Brabec & Krausz, 1997; V.G. Bespalov et al., 1999; Kolesic & Moloney, 2004; Ferrando et al., 2005; Koposova et al., 2006) are employed. One of such methods, namely, the technique of pseudodifferential operators (Koposova et al., 2006) is used in the current paper. The first part of the paper that is an extension of (Talanov & Vlasov, 1994) is concerned with the instability of perturbation waves at combination frequencies noncollinear to pump for the case of nonlinear polarization represented as a polynomial of arbitrary but finite degree. Further, application of the theory to air, for which dielectric permittivity may be represented in the form of a polynomial, is addressed (Loriot et al., 2009). Finally, methods of finding amplitude and phase distribution of electric field in an ultrashort wave packet by analyzing signals from intensity autocorrelator traditionally used for measuring duration of ultrashort laser pulses are considered.

Broadband Instability of Electromagnetic Waves in Nonlinear Media