Negative refraction and backward waves in layered acoustic metamaterials

Abstract

We investigate layered acoustic metamaterials capable of exhibiting a wide variety of wave propagation phenomena, including backward and forward waves with and without negative refraction. The metamaterials are formed by periodically perforated hard plates, which we describe analytically in the limit of small holes compared to both the period and the separation between plates. In particular, we derive expressions for the index of refraction and the transmission and reflection coefficients of finite slabs. We provide illustrative examples of near fields for all four combinations of backward and forward waves with and without negative refraction, along with dispersion diagrams that explain the observed behavior. A comprehensive study of the range of geometrical parameters in which these distinct phenomena are observed is presented as well. These metamaterials hold great promise for achieving full control of sound using simple structures, with potential application to acoustic technologies relying on subwavelength control and imaging of sound.

Negative Refraction and Energy Funneling by Hyperbolic Materials: An Experimental Demonstration in Acoustics

“…The reader is referred to Ref. [6], where details of the expressions obtained using these simplifications are given.…”

“…1. Analytical expressions giving the acoustic band structure of the hyperbolic material are developed using a few simplifying assumptions [6]. First, the structure is perfectly rigid and, therefore, the sound waves only propagate in air and the normal derivative of acoustic pressure vanishes at the plate and hole-wall surfaces.…”

“…[5,6]. In brief, the model considers an infinite stack of rigid plates like the Plexiglas plates described in Fig.…”

“…A recent proposal [5,6] uses periodically perforated hard plates to obtain hyperbolic dispersion of sound waves. Negative refraction is theoretically obtained at certain incident angles tilted with respect to normal incidence.…”

Perfect absorption and no reflection in disordered photonic crystals

“…Finally, we note that our results may also be relevant to acoustic waves in layered media owing to the fact that acoustic and optical waves obey similar propagation equations [71][72][73][74]. To this extent, the realization of a coherently tunable and periodically modulated acoustic response may turn out to be an attractive prospect for acoustic metamaterials [75][76][77][78][79].…”