Abstract: The time reversal symmetry of the wave equation allows wave refocusing back at the source. However, this symmetry does not hold in lossy media. We present a new strategy to compensate wave amplitude losses due to attenuation. The strategy leverages the instantaneous time mirror (ITM) which generates reversed waves by a sudden disruption of the medium properties. We create a heterogeneous ITM whose disruption is unequal throughout the space to create waves of different amplitude. The time-reversed waves can then cope with different attenuation paths as typically seen in heterogeneous and lossy environments. We consider an environment with biological tissues and apply the strategy to a 2-D digital human phantom from the abdomen. A stronger disruption is introduced where the forward waves suffer a history of higher attenuation, with a weaker disruption elsewhere. Computer simulations show heterogeneous ITM is a promising technique to improve time reversal refocusing in heterogeneous, lossy, and dispersive spaces.

Abstract: We analyze the band structure of a single-phase metamaterial involving low-frequency flexural resonances by combining asymptotic homogenization and Bloch–Floquet analysis. We provide the closed-form expression of the dispersion relation in the whole Brillouin zone. The dispersion relation involves two effective, frequency-dependent, mass densities associated with symmetric and antisymmetric flexural resonances of the beams at the microscopic scale. We demonstrate that our simple locally-resonant structure produces at low-frequency band-gaps and, in the hyperbolic regions of the dispersion diagram, negative refraction. Our findings are validated by direct numerical calculations.