Acoustic scattering from spatiotemporally modulated domains

Acoustic and elastic metamaterials with space- and time-dependent material properties have received significant attention recently as a means to realize systems that induce nonreciprocal wave propagation in the bulk or enable frequency and mode conversion of fields scattered from metasurfaces. A previous study derived a nonreciprocal Green’s function for flexural waves in a one- and two-dimensional finite plate with a spatiotemporal modulation of the Young’s modulus [Goldsberry et al., J. Acoust. Soc. Am. 150(4), 2021]. In this work, we generalize the nonreciprocal Green’s function approach to the acoustic case of scattering from an inhomogeneity whose properties are general functions of space and time. Canonical geometries where the analytical solution is known for the unmodulated case will be investigated. Computations of the scattered field directivity pattern will then be carried out as a function of the modulation parameters to determine cases that yield a large degree of control over the scattered field directivity pattern for each generated frequency harmonic. [Work supported by ONR.]