Acoustic Wave Scattering from Spatiotemporally Modulated Cylindrical Domains

Acoustic and elastic metamaterials with material properties that vary in time and space have received significant attention recently as a means to realize systems that induce non-reciprocal propagating waves in unbounded systems and coupling modes at different frequencies in bounded systems. These unique behaviors are the result of frequency- and wavenumber-conversion resulting from spatiotemporal modulation. In this work, we investigate the case of acoustic scattering from a fluid inhomogeneity in which the compressibility is a general function of space and time. A two-dimensional annular geometry is considered, which allows for unknown scattered field to be decomposed into simple mode shapes. Computations of the far field directivity pattern are then 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.