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 complex geometrical optics. The main advantage of the complex method is the possibility to take into account diffraction effects by use of only ordinary differential equations of geometrical optics, thus reducing the calculation time. The efficiency of the suggested algorithm is illustrated by several numerical examples that allow comparison with known analytic solutions: the field of a plane wave behind a caustic in a linear layer, uniform held asymptotics on a caustic in a linear layer, and a Gaussian beam held in a homogeneous 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 analytical solution: nonplane waves, nonplane-stratified media, and the like. In particular, a numerical solution for Gaussian beam propagation through inhomogeneities of Gaussian form is presented. (C) 2001 Optical Society of America.