Abstract
This chapter discusses the modulational instability (MI) of electromagnetic waves in inhomogeneous and in discrete media. MI exists because of the interplay between the nonlinearity and dispersion/diffraction effects. Important models for investigating MI of electromagnetic waves in nonlinear media represent the scalar and vectorial nonlinear Schrödinger (NLS) equations, the system describing evolution of the envelopes of fundamental and second harmonics waves in quadratically nonlinear media, and sine-Gordon equation. The methods such as periodic solutions of the NLS equation and the coupled-mode theory with three modes are discussed. The chapter discusses the MI of electromagnetic waves in optical media with periodic inhomogeneities. The origin of the random fluctuations of parameters in optical fibers and other nonlinear optical media is described. MI in fibers with random amplification and dispersion and MI in randomly birefringent fibers are discussed. The chapter discusses the MI of electromagnetic waves in nonlinear discrete optical systems such as an array of planar waveguides and fibers. Particular cases of MI in discrete media with cubic nonlinearity and quadratic nonlinearity are investigated.
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