Time reversal and negative refraction

Time reversal and negative refraction have been shown to be intimately linked processes. We propose a scheme that exploits transitions between positive and negative frequencies to mimic negative refraction at an interface and hence to make a negatively refracting lens. The theory applies equally to electromagnetic and acoustic waves. We also propose an experimental realization, and under ideal circumstances this lens can exhibit subwavelength resolution, limited only by the strength of the time- reversed signal.