Time reversal is a physical concept that can focus waves both spatially and temporally regardless of the complexity of the propagation medium. Time reversal mirrors have been demonstrated first in acoustics, then with electromagnetic waves, and are being intensively studied in many fields ranging from underwater communications to sensing. In this paper, we will review the principles of time reversal and in particular its ability to focus waves in complex media. We will show that this focusing effect depends on the complexity of the propagation medium rather than on the time reversal mirror itself. A modal approach will be utilized to explain the physical mechanism underlying the concept. A particular focus will be given on the possibility to break the diffraction barrier from the far field using time reversal. We will show that finite size media made out of coupled subwavelength resonators support modes which can radiate efficiently in the far field spatial information of the near field of a source. We will show through various examples that such a process, due to reversibility, permits to beat the diffraction limit using far field time reversal, and especially that this result occurs owing to the broadband inherent nature of time reversal. 1. Introduction The reversibility of the equations governing the propagation of waves, whether acoustic or electromagnetic, is of major interest in many fields of wave physics. This property is quite intriguing on a fundamental point of view but has also led to many fascinating discoveries within the last years. Among them, time reversal (TR) has been a major subject of studies in various fields such as ultrasound acoustics, seismology, microwave, or more recently in the optical domain. In a typical TR experiment, a source emits a short pulse in a medium, which generates a wavefield that propagates away from it. Then this wavefield is measured onto a set of location on an array of sensors, the so-called time reversal mirror (TRM). The measured signals are digitized, memorized, and flipped in time. This first step, known as the “learning step”, results in the knowledge of a set of impulse responses between the source and the TRM, which are the broadband equivalents of the Green’s functions. In the second step, the time reversal one, these time reversed signals are sent back in the medium by the sensors, which results in a spatiotemporal focusing of the generated wavefield onto the initial source position, and at a specific time named the “collapse time” [1–3]. It has been shown that the temporal focusing of the wave
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