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Based on the formalism developed by Psarobas et al. [Phys. Rev. B 62, 278 (2000)], using the multiple-scattering theory to calculate properties of simple phononic crystals, we propose a very simple method to study NaCl-type phononic crystals. The NaCl-type phononic crystal consists of two kinds of nonoverlapping elastic spheres with different mass densities, L\'ame coefficients, and radius following the same periodicity of the ions in real NaCl crystals. We focus on the (001) surface and view the crystal as a sequence of planes of spheres, each plane of spheres having identical two-dimenssional periodicity. We obtained the complex band structure of the infinite crystal associated with this plane and also calculated the transmission, reflection, and absorption coefficients for an elastic wave (longitudinal or transverse) incident, at any angle, on a slab of the crystal of finite thickness.
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Chen et al. (2007) studied this question.
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