Abstract:

In wave propagation in complex media, phase changes along the propagation path are often approximated by a series of abrupt phase changes at discrete planes called ``phase screens.'' It is shown here how phase screens can be used in an analogous way in ray-tracing problems. The total travel time of each ray is formulated as a sum over phase screen and free space contributions. Fermat's principle is then applied to the travel time, yielding a discrete mapping. The mapping connects the ray position at one phase screen to that at each succeeding screen. Examples of the method are given for both nonchaotic and chaotic ray tracing problems. The ray-tracing solution is compared to the wave solution calculated by the parabolic equation. By letting the separation between phase screens go to zero, the connection between continuous propagation and propagation with discrete transitions at phase screens is shown. [Work supported by the Penn State Univ. Applied Res. Lab.]