Focusing beyond the diffraction limit with far-field time reversal

We present an approach for subwavelength focusing of microwaves using both a time-reversal mirror placed in the far field and a random distribution of scatterers placed in the near field of the focusing point. The far-field time-reversal mirror is used to build the time-reversed wave field, which interacts with the random medium to regenerate not only the propagating waves but also the evanescent waves required to refocus below the diffraction limit. Focal spots as small as one-thirtieth of a wavelength are described. We present one example of an application to telecommunications, which shows enhancement of the information transmission rate by a factor of 3.