Acoustic wave scattering by spatio-temporal interfaces

Space-time materials are obtained by modulating a physical medium with a traveling-wave perturbation of one or several of its constitutive parameters, such as the density or the bulk modulus in the case of acoustic materials. When this modulation has the form of a moving and abrupt (subwavelength) transition between two parameter values, we refer to a spatio-temporal interface, which may be considered as a building block for more complex space-time materials. This work considers the problem interaction and scattering of acoustic waves with a single spatio-temporal interface, and a sequence of two interfaces forming a slab. Several regimes defined by the relation between the sound propagation velocities and the interface velocity (namely subsonic, intersonic, and supersonic regimes) are discussed. Analytical expressions for the frequency conversions and scattering coefficients are obtained, and compared with numerical simulations based on an equivalent FTFD squeme.