Coupled-mode equations for quadratically nonlinear deep gratings

Using the method of multiple scales, we present a systematic derivation of the coupled-mode equations for the propagation of light in quadratically no nlinear deep gratings. We show that the resulting coupled-mode equations fo r deep gratings differ from those for shallow gratings in that the coeffici ents have different values, and that additional nonlinear terms appear. Our equations reduce to well known results, in the appropriate shallow grating limit. [S1063-651X(98)07512-6].