Exploiting spatiotemporal degrees of freedom for far field subwavelength focusing using time reversal in fractals

TL;DR

This paper demonstrates a method to achieve deep subwavelength microwave focusing using fractal resonators and time reversal, overcoming bandwidth limitations of traditional metamaterials by coupling to complex media.

Contribution

It introduces a novel approach combining fractal resonators and time reversal to focus microwaves beyond the diffraction limit over wide bandwidths.

Findings

Subwavelength focusing of λ/15 achieved in experiments.

Wide bandwidth focusing enabled by fractal resonator and complex medium.

Single channel time reversal suffices with the coupled system.

Abstract

Materials which possess a high local density of states varying at a subwavelength scale theoretically permit to focus waves onto focal spots much smaller than the free space wavelength. To do so metamaterials -manmade composite media exhibiting properties not available in nature- are usually considered. However this approach is limited to narrow bandwidths due to their resonant nature. Here, we prove that it is possible to use a fractal resonator alongside time reversal to focus microwaves onto $\lambda/15$ subwavelength focal spots from the far field, on extremely wide bandwidths. We first numerically prove that this approach can be realized using a multiple channel time reversal mirror, that utilizes all the degrees of freedom offered by the fractal resonator. Then we experimentally demonstrate that this approach can be drastically simplified by coupling the fractal resonator to a complex medium, here a cavity, that efficiently converts its spatial degrees of freedom into temporal ones. This allows to achieve deep subwavelength focusing of microwaves using a single channel time reversal. Our method can be generalized to other systems coupling complex media and fractal resonators.