Gap solitons in quadratically nonlinear gratings: Beyond the cascading limit

We consider pulse propagation in quadratically nonlinear gratings. Assuming that the phase mismatch between the fundamental and the second-harmonic fr equencies delta k is large, we present a perturbation method in delta k(-1) . In the well known cascading limit, terms to delta k(-1) are kept; here we keep terms to delta k(-2), which lends to another type of coupled mode equ ations. Numerical calculation of the full equations support our theoretical results.