Tailoring Instantaneous Time Mirrors for Time Reversal Focusing in Absorbing Media

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 two-dimensional 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.