Time reversal of optical pulses

The idea of “reversing” waves has many potential applications, including for compensation of aberrations in optics and undoing the effects of scattering. The process of phase conjugation, which turns phase “leads” into phase “lags” and also reverses the direction of propagation of a wave, is well known to have many interesting and useful features, for example. However, there can be considerable confusion surrounding the question of whether such phase conjugation is really “time reversal”. Early literature refers to it that way, but in fact the issue is more subtle.

David Miller clarified these issues in a paper [1] that has been extensively cited in later literature on time reversal with waves generally. In this paper, which uses as an example the “four-wave mixing” approach often used in phase conjugation, he showed that phase conjugation may reverse the “phase envelope” of the wave, but it does not reverse the amplitude envelope. A complementary process, also based on four-wave mixing, that reverses the amplitude envelope but not the phase envelope, is quite possible; for definiteness and clarity, he described how to do that. Neither process is, however, a true time reversal of both amplitude and phase. Such “true” time reversal, especially in a process that would run in real time, is a much more complicated and challenging problem in optics.

[1] D. A. B. Miller, “Time Reversal of Optical Pulses by Four-Wave Mixing,” Optics Lett. 5, 300‑302 (1980)