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Phase conjugation is a physical transformation of a wave field where the resulting field has a reversed propagation direction but keeps is amplitudes and phases.
Description

It is distinguished from Time Reversal Signal Processing by the fact that phase conjugation uses an holographic or parametric pumping whereas time reversal records and re-emits the signal using transducers[1].

Holographic pumping makes the incident wave interact with a pump wave of the same frequency and records its amplitude-phase distribution. Then, a second pump wave reads the recorded signal and produces the conjugate wave. All those waves have the same frequency.
In parametric pumping, the parameters of the medium are modulated by the pump wave at double frequency. The interaction of this perturbation with the incident wave will produce the conjugate wave.

Both techniques allow an amplification of the conjugate wave compared to the incident wave[1].

As in time reversal, the wave re-emitted by a phase conjugation mirror will auto-compensate the phase distortion and auto-focus itself on its initial source, which can be a moving object[1].

Phase conjugation methods exist in two main domains:

Acoustic phase conjugation
Optical phase conjugation

References

^ a b c A. P. Brysev et al., Wave phase conjugation of ultrasonic beams, Physics-Uspekhi (1998)