Inhomogeneous Waves Obliquely Incident on a Periodic Structure

With the growing interest in phononic crystals for al kinds of applications a deeper understanding of the interaction of sound with such structures is not only of interest while sound is passing through or is stopped by the crystal but also when externally applied sound fields strike a crystal and diffract upon it. To study a fundamental feature related to incident inhomogeneous waves, this report investigates a fundamental sign rule to describe reflected and transmitted sound at the boundary with a periodically corrugated surface. It hase been shown by Deschamps [J. Acoust. Soc. Am. 96(5), 2841-2848, 1994] that when inhomogeneous waves scatter from a plane interface, one should make an appropriate choice of the sign of the corresponding wave vectors. In an article of Briers et al. [J. Acoust. Soc. Am. 106(2), 682-687, 1999], an extension of that sign rule is incorporated apparently in order to meet the requirements of correspondence of the theory of diffraction on periodically corrugated surfaces, with experimentally obtained data. The current paper does not per se falisify the extention by Briers et al. but states that the theory of Deschamps is actually sufficiently correct and therefore needs no extension to meet agreement between theory and experiment. The conclusion is that Deschamps' result is correct on smooth surfaces as well as on periodic structures.