A technique for physical realization of anisotropic density matrices with application to acoustic beam shifters

Abstract

Physical realization of acoustic metamaterials is so far at its initial stages, with attempts to use periodic patterns of engineered material structures to achieve various material properties that would yield the required wave propagation patterns. Phononic crystals are by far the most advanced technique for such realization. In the current work, a new technique for developing a realizable engineered periodic material structure is developed, where the anisotropic material density matrix arising from the linear coordinate transformation of the acoustic domain is rotated to align with its principal axis, resulting in a decoupled diagonal density matrix with entries representing the eigenvalues of the original anisotropic matrix. This allows for selecting feasible material properties that would achieve the targeted wave propagation patterns. The proposed approach is then utilized in modeling an acoustic wave shifting device with controllable directivity and dispersion characteristics. The linear coordinate transformation of the proposed wave shifter is augmented with an additional degree of freedom to simultaneously control the directivity and dispersion characteristics. The resulting anisotropic density matrix is manipulated using the developed technique and corresponding isotropic phononic cell structure is developed. Implementing the new isotropic phononic cell structure resulted in achieving the targeted wave control patterns. The theory governing the design of this class of acoustic metamaterials is introduced, and the parameters that control the tuning of the directivity and dispersion characteristics are presented in detail. With such capabilities, the proposed feasibly realizable acoustic metamaterials will be capable of controlling the wave propagation both in the spatial and spectral domains.