Using rays better. III. Error estimates and illustrative applications in smooth media

摘要

A new method for computing ray-based approximations to optical wave fields is demonstrated through simple examples involving wave propagation in free space and in a gradient-index waveguide. The analytic solutions that exist for these cases make it easy to compare the new estimates with exact results. A particularly simple RMS error estimate is developed here, and corrections to the basic field estimate are also discussed and tested. A key step for any ray-based method is the choice of a family of rays to be associated with the initial wave field. We show that, for maximal accuracy, not only must the initial field be considered in;choosing the rays, but so too must the medium that is to carry the wave. (C) 2001 Optical Society of America. [References: 5]