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This paper describes some achievements in the field of the diffraction of ultrasound on corrugated surfaces. Both single and double corrugated surfaces are considered. A demonstration of the capability of the inhomogeneous wave theory to simulate backward displacement of ultrasonic bounded beams (observed by Breazeale and Torbett, Appl. Phys. Let. 29(8), 456-458, 1976) has been demonstrated very recently [Nico F. Declercq, Joris Degrieck, Rudy Briers, Oswald Leroy, Appl. Phys. Let. 82(15), 2533-2534, 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, which is a novel phenomenon that was first reported from a theoretical point of view [Nico F. Declercq, Joris Degrieck, Rudy Briers, Oswald Leroy, J. Acoust. Soc. Am. 112(5), 2414, 2002] and was shortly after discovered experimentally [A.A. Teklu, M.A. Breazeale, J. Acoust. Soc. Am. 113(4), 2283-2284, 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. Furthermore, it is known that singly corrugated surfaces have the ability to stimulate surface acoustic waves by means of diffraction. However, this diffraction occurs in a single plane. Sound impinging a doubly corrugated surface is scattered in many directions. Therefore, such surfaces possess the ability to generate surface waves in many directions, depending on the corrugation and depending on the frequency. Numerical simulation is possible if continuity of stress and strain is considered. The present paper reports advanced numerical simulations based on all physical parameters of the system and shows what surface waves are generated, under what conditions and under what angle. Such a device may be used to send surfaces in directions that are determined by their frequency.
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