Dynamic effect of phase conjugation on wave localization

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We investigate what would happen to the time dependence of a pulse reflected by a disordered single-mode waveguide, if it is closed at one end not by an ordinary mirror but by a phase-conjugating mirror. We find that the waveguide acts like a virtual cavity with resonance frequency equal to the working frequency omega₀ of the phase-conjugating mirror. The decay in time of the average power spectrum of the reflected pulse is delayed for frequencies near omega₀. In the presence of localization the resonance width is tauₛ⁻¹exp(-L/l), with L the length of the waveguide, l the mean free path, and tauₛ the scattering time. Inside this frequency range the decay of the average power spectrum is delayed up to times t simeq tauₛ exp(L/l).