Asymptotic approximation and first-order correction of coupled-mode equations

A reformulation of the asymptotic solution of the coupled-mode equations with a periodic variation of the refractive index along the propagation length is presented, A first-order correction using the asymptotic solution and Piccard's method are also determined, It is found that the first-order solution compares very well with the numerical solution throughout a wide range of coupling parameters, The key differences between the method presented here and elsewhere reside in the derivation of the asymptotic solution as well as in the carefull derivation of the higher order corrections. (C) 1997 Society of Photo-Optical Instrumentation Engineers.