Direct numerical modeling of time-reversal acoustic subwavelength focusing

Focusing waves back to their original source position is possible both experimentally and numerically thanks to time reversal mirrors (TRM). For a TRM placed in the far field of the source, the focusing spot of the reversed wavefield is subject to the diffraction limit and cannot be smaller than half the minimum wavelength, even for a very small source. Yet, numerous time reversal experiments in resonating media have shown subwavelength focusing. In this work, we show that it is possible to model these subwavelength focusing observations with simple physics, only the 2-D standard acoustic wave equation, and with specific fine scale heterogeneity. Our work is based on the spectral element method to solve the wave equation and to model time reversal experiments. Such a method makes it possible to propagate very long time series in complex and strongly discontinuous media with high accuracy. The acoustic wave equations are solved at the fine scale in media with one or more split rings of size much smaller than the wavelength. Such split rings produce a Helmholtz resonance effect as well as propagation band-gaps. We show that, in such media, even with a single split ring resonator, subwavelength focusing down to 1/13th of the minimum wavelength can be observed.