Funneled focusing of planar acoustic waves utilizing the metamaterial properties of an acoustic lens E. Walker a , D. Reyes b , M.M. Rojas b , A. Krokhin a , A. Neogi a a Dept. of Physics, University of North Texas, 210 Avenue A., Denton, TX USA 76201-1427 b Universidad Autónoma del Estado de México, Toluca, 50120 , Mexico ABSTRACT Metamaterial acoustic lenses are acoustic devices based on phononic crystal structures that take advantage of negative or near-zero indices of refraction. These unique properties arise due to either the antiparallel direction of the phase and group velocity or strongly anisotropic dispersion characteristics, usually above the first transmission band. In this study, we utilize an FDTD program to examine two phononic lenses that utilize anisotropic effects available in their second band to collimate and focus acoustic waves from a plane-wave source with a k 00 wavevector. The phononic crystals consist of stainless steel rods arranged in a square lattice with water as the ambient material. Results show collimation and focusing in the second band for select frequencies, f c ± 0.005  . Keywords: Metamaterial, phononic crystal, ultrasonic lens, references 1. INTRODUCTION The history of metamaterials can be traced back to the work of Veselago and the exploration of the feasibility of simultaneously negative permeability and permittivity in dielectrics [1]. Such materials exhibit left-handedness that is not observed in nature and results in peculiar effects such as negative index of refraction materials amongst other things [2, 3, 4, 5, 6]. However, there are no known materials that innately possess both negative permeability and permittivity, so the practical realization of such a material only occurred after the evolution of the effective medium theory for photonic crystals. Pendry et. al first demonstrated a metamaterial with a structure that possessed both negative permittivity and permeability through a periodic arrangement of metals [7]. Since that point, work pertaining to photonic metamaterials has grown exponentially with devices ranging from electromagnetic cloaks [8] to lenses that resolve beyond the diffraction limit [9, 10] realized both in theory and experiment. The underlying concepts of photonic crystals and the propagation of electronic or electromagnetic waves through an ordered lattice are readily applicable to the propagation of mechanical waves through a similarly ordered lattice [11, 12]. Permittivity and permeability become analogous to Lamé’s first parameter and inverse density leading to, roughly, the substitution of the physical material properties such as the density contrast, sound velocity, and attenuation, for the dielectric properties. For mechanical waves, however, the primary propagation mode being longitudinal, the ability of solids to support both longitudinal and transverse modes, and the lack of an innately negative density translates to some variation between the behavior of electromagnetic and mechanical waves in ordered structures. So, though the development of metamaterials was realized first using photonic crystals, the applications to phononic crystals were quickly realized and similar devices such as cloaks [13, 14] and negative index lenses [15, 16] have been demonstrated both theoretically and experimentally. Critical to the realization of a metamaterial for either type of wave is a dispersion relation that does not follow the usually linearly increasing type found in the long wavelength limit for periodic structures [17, 18, 19, 20, 21]. The peculiar effects of metamaterials arise from the application of a periodic structure in a frequency region where the dispersion relation is either non-linear, anisotropic, or anomalous [22]. In photonic and phononic crystals, negative effective indices of refraction are realized by utilizing the crystal at a frequency where the dispersion curve has a negative slope. These conditions occur near the band edge of the first Brillouin zone [19], or in the second transmission band where band folding can result in antiparallel direction between the wavevector and Poynting vector [12, 19]. Photonic and Phononic Properties of Engineered Nanostructures IV, edited by Ali Adibi, Shawn-Yu Lin, Axel Scherer, Proc. of SPIE Vol. 8994, 89940H · © 2014 SPIE · CCC code: 0277-786X/14/$18 · doi: 10.1117/12.2041051 Proc. of SPIE Vol. 8994 89940H-1 Downloaded From: http://spiedigitallibrary.org/ on 05/27/2014 Terms of Use: http://spiedl.org/terms