Application of phase screens to ray chaos. Martin A. Mazur and
Kenneth E. Gilbert (Applied Research Laboratory and the Graduate
Program in Acoustics, The Pennsylvania State University. P.O. Box
30, State College, PA 16804.)
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." We show here how
phase screens can be used in an analogous way in ray tracing
problems. We formulate the total travel time of each ray 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 non-
chaotic and chaotic ray tracing problems. We compare the ray tracing
solution to the wave solution calculated by the parabolic equation. By
letting the separation between phase screens go to zero, we show the
connection between continuous propagation and propagation with
discrete transitions at phase screens.
[Work supported by the Pennsylvania State University Applied
Research Laboratory.]