Abstract

DEYMIER, P. A. et al. Focusing of acoustic waves by flat lenses made from negatively refracting two-dimensional phononic crystals. Rev. mex. fis. [online]. 2008, vol.54, suppl.2, pp.74-81. ISSN 0035-001X.

We investigate the phenomenon of imaging of elastic waves with flat lenses constituted of negatively refracting materials. We derive an analytical solution for the acoustic field produced by a point source near a flat lens composed of a homogeneous acoustic metamaterial (i.e. negative density and negative moduli) using the Green's function formalism of the Interface Response Theory. We then consider phononic crystals as a way of realizing negative refraction with materials possessing positive densities and moduli. The finite difference time domain (FDTD) simulation method is employed to investigate the properties of negative refraction and focusing of ultrasonic waves in a flat lens composed of a two-dimensional phononic crystal consisting of a triangular array of steel rods immersed in methanol. The flat lens is embedded in water. Focusing of the ultrasonic field emitted by a point source is analyzed with particular attention paid to the lateral resolution of the lens, i.e., the resolution along the direction parallel to the lens' surface. The FDTD image is compared to experimental measurements of the pressure amplitude field created by a similar source and lens. Agreements and differences between the calculated and measured images as well as resolutions are reported and discussed. The flow of energy in the phononic crystal lens is calculated and matched to a simple ray tracing analysis of negative refraction in a homogeneous negatively refracting medium.

Keywords : Ultrasonic waves; phononic crystals; negative refraction.

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