Numerical study of the time-reversal effects on super-resolution in random scattering media and comparison with an analytical model

Abstract

The time-reversal effects on super-resolution in random scattering media are analysed using numerical finite-difference time-domain (FDTD) simulations. The analytical solutions and results have been presented previously in the literature, which provide confirmation of spot-size reduction and also explanations of the shower curtain effects and backscattering enhancement. However, the analytical solutions are based on several approximations. Thus, validation of the analytical results against realistic scattering events is necessary. Two-dimensional FDTD Monte Carlo simulations have been employed for this investigation to simulate wave propagation and scattering in a random medium. The scattering environments are created by randomly locating cylindrical rods in the background medium. The simulation process involves a point source emitting a Gaussian pulse wave that propagates through the scattering medium, gets time-reversed, and then back-propagated into the same scattering medium. The focusing behaviours including the location of the focal point and its spot-size as a function of its transverse position are analysed. The shower curtain, particle size, and time domain effects are also investigated. In comparison, the behaviours of focusing derived by numerical results are consistent with those of previously reported analytical results. However, there are some differences, which we speculate to be mainly because of the different phase functions.