### ASA 125th Meeting Ottawa 1993 May

## 5aSA1. Fresnel width of the coupling regions of generalized leaky Lamb
waves and Fermat's principle.

**Philip L. Marston
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*Dept. of Phys., Washington State Univ., Pullman, WA 99164-2814
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Ray methods describe guided-wave scattering contributions based on local
coupling processes. To estimate the effective width of coupling regions for
launching and radiation of sound by leaky guided waves of phase velocity c[sub
l], Fresnel volume concepts of Y. A. Kravtsov and others [see, e.g., P. L.
Marston, Physical Acoustics (Academic, New York, 1992), Vol. 21, pp. 1--234]
were generalized. First, the usual coupling condition on the angle of incidence
(theta)[sub l] for a sphere or cylinder, sin (theta)[sub l]=c/c[sub l], is
derived by Fermat's principle. Then the angular shift (Delta)(theta)[sub l] is
derived for a (pi) radian phase deviation from the Fermat ray. For a far-field
source or observer, |(Delta)(theta)[sub l]|(approximately equal to)[radical
2(pi)/(ka cos (theta)[inf l])[radical is a measure of the ray width. Fermat's
principle is also examined for a prompt backward wave mechanism [D. H. Hughes,
Ph.D. thesis, Washington State Univ. (1992)] for the high-frequency scattering
enhancement by shells. [Work supported by ONR.]