Optical Josephson effects using phase-conjugating mirrors: an analogy with superconductors

Motivated by the analogy between a phase-conjugating mirror (PCM) and a superconductor, we search for optical counterparts of the well-known DC and AC Josephson effects. We show that in a system consisting of two PCM's separated by vacuum an 'optical supercurrent' arises as a function of an applied phase difference between the PCM's, which is the optical analogue of the DC supercurrent flowing in a superconducting weak link. The corresponding AC effect occurs when the two PCM's are pumped by light of a different frequency, causing the phase difference to oscillate in time with the frequency difference.