### ASA 127th Meeting M.I.T. 1994 June 6-10

## 1aSA5. Merging of launching or detachment points of weakly damped leaky
waves on S-shaped surfaces and complex launching or detachment points.

**Philip L. Marston
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*Dept. of Phys., Washington State Univ., Pullman, WA 99164-2814
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In previous work, Fermat's principle and properties of leaky waves on flat
surfaces were combined to obtain a high-frequency approximation to scattering
by cylinders of slowly varying curvature [P. L. Marston, J. Acoust. Soc. Am.
94, 1861 (A) (1993)]. The usual assumption was made that only the first
derivative of optical-path length (with respect to path variation) vanishes.
The present work considers situations where the second (or higher) derivatives
vanish at launching or detachment points. The simplest example is for coupling
to (or detachment from) a tilted S-shaped surface. Such surfaces may have pairs
of launching or detachment points; the pairs can merge at an appropriate
surface tilt that results in a k[sup 1/6] amplitude enhancement coefficient.
The launching or detachment factor becomes proportional to an Airy function of
complex argument and launching or detachment in a shadow region of the Airy
factor is described approximately by a complex ray. Higher-order launching or
detachment points may also result from a sufficiently rapid dependence of the
leaky-wave phase velocity on position. [Work supported by ONR.]