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.
© 2001 Optical Society of America
(000.3860) General : Mathematical methods in physics
(080.2710) Geometric optics : Inhomogeneous optical media
(080.2720) Geometric optics : Mathematical methods (general)
(350.7420) Other areas of optics : Waves
M. A. Alonso and G. W. Forbes, "Using rays better. III. Error estimates and illustrative applications in smooth media," J. Opt. Soc. Am. A 18, 1357-1370 (2001)