Behaviour of a shear-wave at a solid-smectic interface

Results of theoretical investigations into the behaviour of a shear wave at the boundary between an isotropic solid and a smectic A liquid crystal are presented. These results track the subsequent response of the smectic to the refracted wave. Using the techniques of Landau and Lifshitz for sound in isotropic fluids [1], we extend the results for smectic C by Gill and Leslie [2] and perform the analogous calculations for a sample of smectic A using the dynamic theory of Stewart [3]. These calculations enable a comparison between the results for smectic A and an extension, by the present authors, to the known results for smectic C. Motivated by the work of Auernhammer, Brand, and Pleiner [4, 5], mechanisms for determining the impact of perturbations upon the modes of response behaviour will be analysed, with plots demonstrating the amplitudes of these waves relative to that of the incident wave displayed for a range of typical physical parameters characteristic to smectic C and smectic A.