Non-Specular Reflection of Bounded Beams From Multilayer Fluid-Immersed Elastic Structures: Complex Ray Method Revisited

The excitation of various types of leaky waves in layered elastic media by beams incident from an exterior fluid at or near the leaky wave phase-matching angle is of interest for NDE applications. In particular, much attention has been given to the non-specular reflection of beams under such conditions of incidence. While various methods have been employed to study and clarify these phenomena for well collimated beams in plane layered environments [1–11], much less has been done on the corresponding effects when the incident beams are diverging and/or when the layers are curved. To extend the plane layer results to more general conditions, it is desirable to employ analytic modeling that adapts the wave phenomenology locally from planar to curved geometries. Because the phenomena occur in the range of high frequencies, ray field modeling affords an attractive option. By the complex-sourcepoint (CSP) technique, which places a radiating source at a complex coordinate location, a conventional line or point source excited field can be converted into a two-or three-dimensional quasi-Gaussian beam field that is an exact solution of the dynamical equations [12,13]. When the CSP field interacts with a plane or cylindrically layered elastic medium, the resulting internal and external fields can be expressed rigorously in terms of wavenumber spectral integrals [14]. Asymptotic reduction of these integrals, achieved by the method of saddle points applied to deformed contours in the complex spectral wavenumber plane, accounts for all relevant wave phenomena. For the reflected field, this yields explicit waveforms which are synthesized by interacting specularly reflected beam, leaky wave, and possible lateral wave contributions