Time Reversal in Electromagnetics

Abstract

This chapter addresses the reader who wishes to explore the theory and practice of time reversal, and to obtain an overview of the concepts, definitions, and applications of time reversal methods. Having no natural sense of negative time flow, we must resort to our imagination to describe what happens to physical phenomena, notably the behavior of waves in space and time, when time is reversed. The meaning of time reversal in mechanics and wave propagation is discussed in general terms, and the nature of one‐dimensional causal and acausal electromagnetic waves is explained by means of computer visualizations. The concept of the time reversal mirror as an active transmitter of time‐reversed incident fields is demonstrated and extended to two‐ and three‐dimensional scenarios. The principles of radiating and scattering source reconstruction in both open and closed ergodic structures are introduced and illustrated by means of typical modeling examples. Classical and algorithmic formulations of time reversal in terms of Green's functions lead to an interpretation of time reversal focusing in space and time as a correlation process. Superresolution as a consequence of multiple scattering or multipath propagation is demonstrated. A selected list of references containing seminal papers, books, reviews, and applications of time reversal in different areas of acoustics, electromagnetics, and optics concludes the chapter. The references provide in‐depth coverage of the fundamental concepts presented in this chapter and will guide the reader toward application‐specific extensions of the theory and numerical models for advanced researchers and practitioners of time reversal.

On the Theory and Experiments of Electromagnetic Time-Reversal Method

“…12. This means that the spatial resolution of the TR method is much improved with higher frequency and wider bandwidth as predicted [31]. The spatial radius of the red area in Fig.…”

“…They conducted experiments and showed the limited capabilities of electromagnetic TR. Hoefer published a book chapter on the fundamentals of TR in electromagnetics [31]. He presented theoretical and technical advances of TR and its possible future directions.…”

“…The reversal of time has stimulated our imagination throughout human history. Although the idea of TR is hard to imagine and realize, physicists and engineers keep studying related techniques; they utilize the time-symmetrical property of specific physical laws, such as the wave equation, to solve various inverse problems [31]. Take a look at a typical wave equation:…”

“…However, the negative time solution is a non-causal solution that is out of our physical reality and can only be mathematically or computationally realized. Thus, the idea of TR here often refers to computational TR or passive TR [31].…”

“…This leads to consideration of the use of an air-filled cavity bounded by perfect electric conducting (PEC) walls as the test fixture enclosing all the sources inside the cavity. Such a cavity confines the energy inside and generates many multipath field signals that many signal propagation inside the cavity almost ergodic [11], [31].…”