Theory of the backward beam displacement on periodically corrugated surfaces and its relation to leaky Scholte-Stoneley waves

Abstract

A demonstration of the capability of the inhomogeneous wave theory to simulate backward displacement of ultrasonic-bounded beams [M. A. Breazeale and M. Torbett, Appl. Phys. Lett. 29, 456 (1976)] has been demonstrated recently [N. F. Declercq, J. Degrieck, R. Briers, and O. Leroy, Appl. Phys. Lett. 82, 2533 (2003)]. The current report applies the theory of the diffraction of inhomogeneous waves and shows how this theory is capable of simulating, explaining, and understanding the experiments mentioned above. The theory reveals the existence of leaky Scholte-Stoneley waves, a phenomenon suggested theoretically [N. F. Declercq, J. Degrieck, R. Briers, and O. Leroy, J. Acoust. Soc. Am. 112, 2414 (2002)] and observed experimentally [A. A. Teklu, M. A. Breazeale, J. Acoust. Soc. Am. 113, 2283 (2003)]. Moreover, the present paper shows that the classical Fourier decomposition of bounded beams is unable to simulate the backward beam displacement. This work also elucidates the nature of Wood anomalies in Diffraction spectra.

Acoustic diffraction effects at the Hellenistic amphitheater of Epidaurus: Seat rows responsible for the marvelous acoustics

“…[4][5][6][7][8][9] The theory of diffraction of sound is based on the concepts of the Rayleigh decomposition of the reflected and transmitted sound fields. [10][11][12] The theory, earlier applied to describe a number of diffraction effects for normal incident ultrasound on corrugated surfaces, 13 has been used successfully to understand the generation of ultrasonic surface waves in the framework of nondestructive testing.…”

The history and properties of ultrasonic inhomogeneous waves

“…An extension of the model from homogeneous solids to porous media also can be found in Briers and Leroy [77]. Recently the theory of the diffraction of inhomogeneous waves clarified the backward beam displacement phenomenon on periodically rough surfaces as experimentally found by Breazeale and Torbett [87], [103] and connected this phenomenon to a leaky Scholte-Stoneley wave [88], [94]. Some theoretical predictions, based on the diffraction of inhomogeneous waves, have recently been verified experimentally [104].…”

Observation of ultrasonic backward beam displacement in transmission through a solid having superimposed periodicity

“…Eventually, a theoretical technique consisting of the Rayleigh-Fourier method to simulate diffraction on periodic surfaces in combination with the decomposition of a bounded beam in terms of inhomogeneous waves emerged and this enabled further study of the phenomenon. 5,6 The use of this technique revealed that the ultrasonic phenomenon was most likely due to the generation of backward propagating leaky ScholteStoneley waves along the corrugated surface.…”

“…Expressions for the displacements 8 can be derived according to the methods outlined by Viktorov 9 and material parameters used in the calculation are identical to those in Ref. 6. Since the displacement amplitudes are dependent on an arbitrary constant, they have been normalized.…”