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Materials which possess a high local density of states varying at asubwavelength scale theoretically permit to focus waves onto focal spots muchsmaller than the free space wavelength. To do so metamaterials -manmadecomposite media exhibiting properties not available in nature- are usuallyconsidered. However this approach is limited to narrow bandwidths due to theirresonant nature. Here, we prove that it is possible to use a fractal resonatoralongside time reversal to focus microwaves onto $\lambda/15$ subwavelengthfocal spots from the far field, on extremely wide bandwidths. We firstnumerically prove that this approach can be realized using a multiple channeltime reversal mirror, that utilizes all the degrees of freedom offered by thefractal resonator. Then we experimentally demonstrate that this approach can bedrastically simplified by coupling the fractal resonator to a complex medium,here a cavity, that efficiently converts its spatial degrees of freedom intotemporal ones. This allows to achieve deep subwavelength focusing of microwavesusing a single channel time reversal. Our method can be generalized to othersystems coupling complex media and fractal resonators.

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