Reflection of light from a disordered medium backed by a phase-conjugating mirror

This is a theoretical study of the interplay of optical phase conjugation and multiple scattering. We calculate the intensity of light reflected by a phase-conjugating mirror when it is placed behind a disordered medium. We compare the results of a fully phase-coherent theory with those from the theory of radiative transfer. Both methods are equivalent if the dwell time ${\tau }_{\mathrm{dwell}}$ of a photon in the disordered medium is much larger than the inverse of the frequency shift $2\Delta \omega$ acquired at the phase-conjugating mirror. When ${\tau }_{\mathrm{dwell}}\Delta \omega \lesssim 1$, in contrast, phase coherence drastically affects the reflected intensity. In particular, a minimum in the dependence of the reflectance on the disorder strength disappears when $\Delta \omega$ is reduced below $1/{\tau }_{\mathrm{dwell}}.$ The analogies and differences with Andreev reflection of electrons at the interface between a normal metal and a superconductor are discussed.