Deep gratings with a chi((2)) nonlinearity: Analysis and solutions

Using a systematic approach based on a Bloch function expansion and the met hod of multiple scales, we present a rigorous derivation of the coupled-mod e equations for light propagation through deep quadratically nonlinear grat ings. The coupled-mode equations for deep gratings differ from those derive d previously for shallow gratings in that the coefficients have different v alues and additional nonlinear terms appear. In the shallow grating limit t hese equations reduce to the standard coupled-mode equations. Our results s how that deep grating effects can be significant in GaAs-AlAs thin film sta cks, while in glass optical fibers these effects are too small to play a ro le. Using a standard shooting technique, bright soliton solutions to the ne w equations are obtained. (C) 1999 Academic Press.