Coupled-mode theory for guided acoustic waves with spatiotemporally modulated boundaries

Recent research in optical, electromagnetic, and acoustical metamaterials has shown that spatiotemporal modulation (STM) of bulk material properties and interfaces between materials can increase the control of propagating waves and wave scattering at boundaries. Specifically, STM of bulk properties has been used to enable nonreciprocal wave propagation in unbounded systems and to couple modes at different frequencies in bounded systems through frequency and wavenumber conversion. This work considers the case of mode coupling in an acoustic waveguide using STM boundaries. As a first step in the design of STM boundaries, we investigate the effect of STM on one boundary of a two-dimensional acoustic waveguide that is coupled to a fluid half-space on its other boundary. The analysis first considers guided wave modes when the waveguide has spatially varying boundaries using coupled-mode theory. Temporal modulation is then introduced by expanding the solution for propagating and leaky modes using Fourier series expansion to consider scattering into harmonics of the modulation frequency and wavenumber. An analysis of mode conversion efficiency based on the modulation amplitude and frequency is presented and discussed.