The Instantaneous Time Mirror for Electromagnetic Fields: A Simulation-Guided Study

Abstract

The time reversal symmetry of the wave equation allows wave refocusing back at the source, as if rewinding a video of ripples in a pond. For a forward propagating wave, a backward counterpart can be produced with a spatial disruption or a temporal disruption to the wave equation: a time reversal mirror (TRM) or an instantaneous time mirror (ITM), respectively. The two mirrors have been thoroughly theoretically examined in the past. Though TRM is a widespread solution due to its ease of practical implementation via the use of transducers, ITM has only recently been demonstrated experimentally in surface water waves via a sudden speed disruption to the entire space. We use computer simulations to analyze various properties of an ITM in 2D electromagnetic waves and investigate the qualities of the time-reversed foci generated. This work is intended as a stepping stone towards the ultimate, long-term aim which is to investigate the potential of ITMs in refocusing waves for medical applications, as a treatment or as an imaging technique. A comparative study between TRM and ITM is conducted, showing reversed waves generated by both mirrors are affected by attenuation in lossy media such as human tissues. This presents an opportunity to explore a novel technique to compensate attenuation that suits the instantaneous nature of ITMs, since existing methods for TRMs are incompatible as they rely on digital signal manipulation. After testing homogeneous disruptions using a uniform speed change over the entire medium, a new compensating strategy for ITM is introduced. The strategy leverages a heterogeneous disruption that is both unequal and localized in space, creating reversed waves of similar amplitude as they converge. The time-reversed waves can then cope with the different attenuation paths typical of heterogeneous environments, improving the focusing quality. The new technique is demonstrated in a digital human phantom with a complex arrangement of biological tissues and assessed on four metrics, two of which are novel, capturing the 2D resolution and time evolution of the reversed foci.

Date of Award	31 Dec 2022
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Graham Riley (Supervisor) & Fumie Costen (Supervisor)