Complex ray-tracing algorithms with application to optical problems

We suggest a numerical algorithm for complex ray tracing. Such an algorithm is intended for the computation of a wave field in the framework of comple x geometrical optics. The main advantage of the complex method is the possi bility to take into account diffraction effects by use of only ordinary dif ferential equations of geometrical optics, thus reducing the calculation ti me. The efficiency of the suggested algorithm is illustrated by several num erical examples that allow comparison with known analytic solutions: the fi eld of a plane wave behind a caustic in a linear layer, uniform held asympt otics on a caustic in a linear layer, and a Gaussian beam held in a homogen eous medium. It is pointed out that the approach under consideration can be readily np plied to a great variety of real wave problems that have an ana lytical solution: nonplane waves, nonplane-stratified media, and the like. In particular, a numerical solution for Gaussian beam propagation through i nhomogeneities of Gaussian form is presented. (C) 2001 Optical Society of A merica.