Acoustic wave scattering by spatio-temporal interfaces

TL;DR

The work analyzes acoustic wave scattering by moving spatio-temporal interfaces and slabs, deriving analytical expressions for frequency and wavelength conversions and scattering coefficients across subsonic, intersonic, and supersonic regimes. It introduces a reduced parameter framework with $oldsymbol{γ=c_2/c_1}$ and $oldsymbol{α=v/c_1}$, and develops closed-form results for single interfaces and two-interface slabs, including phase-accumulation effects. Numerical validation via a Centered-in-Time FDTD method with a uniform background flow confirms the analytical predictions, showing clear frequency shifts for reflected components and velocity-dependent effects in the intersonic regime, as well as robust slab interference behavior. The findings demonstrate precise spectral manipulation capabilities in acoustic space-time materials and establish a numerically stable approach for evaluating complex dynamic interfaces, with potential applications in spectral transformation without resonances in metamaterials.

Abstract

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.

Figures (11)

• Figure 1: Interaction in the subsonic case, with a co-propagating (left) and counter-propagating (right) interfaces.
• Figure 2: Interaction in the supersonic case, with a co-propagating (left) and a counter-propagating (right) interface.
• Figure 3: The four cases of intersonic interactions. Left colum shows the cases where $c_1>c_2$, in the co-propagating (top) and counter-propagating (bottom) cases. Right colum shows the case where $c_1<c_2$.
• Figure 4: Representation of the different regimes in the $\gamma-\alpha$ diagram.
• Figure 5: Wave interaction processes in a moving slab. Subsonic counter-propagating regime.