On the existence of a Brewster angle for solid side incidence on periodically rough surfaces Nico F. Declercq 1 , Joris Degrieck 1 , Rudy Briers 2 , Oswald Leroy 3 1 Soete Laboratory, Department of Mechanical Construction and Production Ghent University, St Pietersnieuwstr 41, B-9000 Ghent, Belgium. NicoF.Declercq@UGent.be 2 Katho-Reno dept, Torhout, Belgium 3 IRC – KULeuven Campus Kortrijk, Kortrijk, Belgium. Abstract Recently the authors have described the diffraction of horizontally polarized sound on periodically rough solid-liquid interfaces [Nico F. Declercq et al., IEEE- UFFC 49(11), 1516-1521]. This has lead to the simulation of generated Love waves. This in combination with the theory of the diffraction of vertically polarized sound, where the generation of Scholte-Stoneley waves can be simulated, has resulted in the possibility to simulate what happens to elliptically polarized incident sound. It is shown that the rough surface can act as a polarization filter for normal incident sound. The model also describes the existence of a Brewster angle, where reflected sound becomes pure shear polarized. Hence a device is possible that basically consists of an isotropic solid being periodically corrugated and being able to filter out longitudinal waves when pure shear waves are necessary for example for NDT. 1. Introduction The diffraction of sound by a periodically corrugated surface that is traction free, or is the interface between a solid and a liquid, has been a hot topic for many years [1-4] and many methods have been developed in order to tackle the diffraction problem. Claeys et al [8] and Mampaert et al [6] use one method, the mode conversion theory of diffraction. The method describes the diffracted field as a summation of plane waves, traveling in directions determined by the classical grating equation and having amplitudes and phases determined by continuity of normal stresses and normal displacements on the interface. They report calculations tackling diffraction of incident plane waves with polarization perpendicular to the corrugations, i.e. the grooves, on the surface. Their results correspond very well with experiments. The present work reports calculations, using the same mode conversion principle, for incidence from the solid side and for a polarization that is parallel to the grooves, i.e. horizontally polarized waves. Contrary to Claeys and Mampaert who solely consider normal incidence in their calculations, we also take a look at other angles of incidence, more specifically at an angle that we define as the Brewster angle, involving similar effects as in optical scattering at plane interfaces. The geometry of the solid-liquid corrugated interface is depicted in Fig 1. Figure 1: The geometry of the solid-liquid periodically corrugated interface 2. Horizontally Polarized incident plane waves In [11], it is shown that only shear horizontally polarized reflected waves are generated when horizontally polarized (shear) incident waves are considered. The velocity potential for the incoming plane wave is ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 i i x z i i x z i i xk zk i z x i i x z i i xk zk x z i i x z ik C e k k ik C e k k + + − = + + + ψ e e (1) while the velocity potential for the reflected sound is Fr3.C2.1 V - 3623