Coupled-mode equations for Kerr media with periodically modulated linear and nonlinear coefficients

We apply the multiple-scales formalism to derive a complete set of equations for a finite medium with periodic linear and nonlinear Kerr optical coefficients. The equations for a single-frequency field reveal three new, nonlinear terms that are related to the difference in the Kerr nonlinearity in two-component media. The nonlinear evolution of coupled forward and backward fields in a multilayered film is numerically simulated by a spectral method. We examine the linear stability of the steady-state solution for an infinite medium and extend previous discussions of modulational instabilities to the new set of equations. We find that the inhomogeneous coefficient can selectively suppress modulational instability in the longitudinal or transverse direction. (C) 2002 Optical Society of America.