Standing waves in structures with spatiotemporally modulated material properties

Acoustic and elastic wave metamaterials with time- and space-dependent material properties have received great attention as a means to increase the degree of control over the propagation of linear waves through a medium. Previous works have shown that propagating waves in a modulated medium display non-reciprocity by means of asymmetric frequency and wavenumber conversion between two counter-propagating modes [K. Yi et al., Phys. Rev. B 96, 104110 (2017)]. In the present study, we investigate standing acoustic waves in a finite medium with time- and space-dependent material properties. A semi-analytical approach based on coupled mode theory is derived, as well as a finite element approach that can consider more complex geometries. The effects of space-only, time-only, and space-time modulations of the material properties on standing waves in a finite system are explored. The present analysis leads to potential applications in acoustic communications, vibration suppression, and energy harvesting. [Work supported by NSF EFRI.]