How space-time modulations modify spoof surface plasmons and scattering properties in acoustic metagratings

We analyze the propagation of acoustic waves in a space-time (ST) modulated grating moving at constant velocity and surrounded by air. By means of asymptotic techniques, we derive in the subwavelength regime a homogenized nonreciprocal model in which the grating is replaced by an equivalent bianisotropic slab at the boundaries of which effective jump conditions apply, that encapsulate the effect of the evanescent fields. This effective framework allows to characterize analytically the properties of ST modulated metagratings in terms of scattering properties and guided wave dispersion. First we derive the closed-form dispersion relation of spoof surface plasmon polaritons (SPPs) and show the appearance of multiple redshifted or blueshifted branches due to the ST modulation. Next, we provide in the radiative region closed-form expressions for the Brewster angle and Fabry-Pérot resonances and show how the ST modulation heavily modifies the complex spectra. Finally, we illustrate the potential of such a system to achieve negative refraction or perfect transparency by playing on the modulation. Throughout the study, our analysis is validated by comparison with direct numerical simulations.