Transverse modulation instability of copropagating optical beams in nonlinear Kerr media

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Abstract
Two optical beams, copropagating in a Kerr medium, interact with each other through cross-phase modulation. Such nonlinear beam coupling leads to a transverse modulation instability that is evident as spatial modulation of the beam profiles. A linear-stability analysis in the plane-wave approximation predicts the range of spatial frequencies over which modulation can occur. The case of self-defocusing media is particularly interesting, since modulation instability occurs only when both beams are present simultaneously. Numerical simulations are used to study how modulation instability can occur for finite-size beams. In particular, the mutual coupling of two copropagating Gaussian beams is studied in detail.