Numerical analysis of negative refraction of transverse waves in an elastic material

Abstract

A numerical analysis of negative refraction process is reported using a phononic crystal with an elastic solid matrix. The phononic crystal considered in this study is made of a periodic arrangement of holes in aluminum. Dispersion curves are discussed and conditions for which negative refraction can appear are identified. These conditions are obtained for the transverse waves, whereas the longitudinal waves are evanescent. A calculation is performed with a prism shaped phononic crystal, and it clearly exhibits a negative refraction angle. Several analyses are provided with a view to characterize the wave going out of the phononic crystal. Finally, improvements, with respect to the impedance matching and index tuning, are discussed.