EFFICIENT SHOOTING ALGORITHMS FOR SOLVING THE NONLINEAR ONE-DIMENSIONAL SCALAR HELMHOLTZ-EQUATION

We study numerically the effect of nonlinearity on the transmission of monochromatic scalar optical fields through one-dimensional stratifie d dielectric media. We implement two different efficient shooting algo rithms to solve the boundary value problem associated to the governing Helmholtz equation. One is based upon a recursive two-dimensional bis ection procedure acting on the vector space of all allowed starting fi eld phase space quadratures to solve the two-dimensional root-finding problem. This method is valid for any kind of nonlinearity. The other one makes use of a particular phase invariance of the specific equatio ns and boundary conditions considered, reducing thereby the number of independent variables for the shooting method. We compare the accuracy and the computational expenses of both algorithms. (C) 1998 Elselvier Science Inc. All rights reserved.