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Optics Letters

Nondegenerate optical oscillation in a resonator formed by two phase-conjugate mirrors

Mark Cronin‐Golomb, Baruch Fischer, Sze-Keung Kwong, Jeffrey Owen White, Amnon Yariv

Published Jul 1, 1985• 18 citations
Publisher

Abstract

We find experimentally and explain theoretically that in a resonator bounded by two phase-conjugate mirrors (PCM's), unlike in resonators with one PCM and one conventional mirror, the oscillation frequency differs from that of the pumping beams. Using BaTiO(3) for the PCM, we find extremely small deltaomega/omega approximately 10(-15).

DOI
10.1364/ol.10.000353

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We find experimentally and explain theoretically that in a resonator bounded by two phase-conjugate mirrors (PCM's), unlike in resonators with one PCM and one conventional mirror, the oscillation frequency differs from that of the pumping beams. Using BaTiO(3) for the PCM, we find extremely small deltaomega/omega approximately 10(-15).
This paper is the second in a series describing propagation of electromagnetic radiation in phase-conjugate oscillators. We apply the formulation developed in the first paper to study the phase-conjugate resonator (PCR) and the Fabry–Perot cavity with an intracavity phase-conjugate mirror (PCM). Our results show that nondegenerate oscillation occurs in the PCR for large parametric gains and fixed separation between the conventional reflector and the PCM. The bandwidth is considerably reduced from that of a PCM alone. In the phase-conjugate oscillator, oscillation will occur at the pump frequency only if there is no separation between the conventional mirrors and the phase-conjugate element and if the nonlinear medium fills the entire Fabry–Perot cavity.
We have developed a theory for nondegenerate oscillations in optical resonators containing an intracavity phase-conjugate element. The phase-conjugate element consists of a nonlinear transparent medium that is pumped externally by a pair of counterpropagating laser beams of the same frequency and intensity. Phase conjugation of an input beam of slightly different frequency occurs because of nondegenerate four-wave mixing. The theory takes into account linear absorption (or gain) in the medium and is applied to study the threshold behavior of phase-conjugate oscillators. For the special case of no conventional mirrors, the phase-conjugate oscillator reduces to an ordinary phase-conjugate mirror, and our general formulation yields the results of previous studies. Our analysis shows that the parametric gain required for oscillation increases (or decreases) as a result of linear absorption (or gain) in the medium, and oscillation can occur at a frequency different from that of the pump beams in the presence of large linear gain (or loss). The effects of linear absorption (or gain) on the filter operation are also examined.
Photorefractive resonators exhibit an extremely small frequency difference (Deltaomega/omega~10(-15)) between the oscillating and pumping beams. The observed frequency difference is proportional to cavity-length detuning. This dependence is explained by a photorefractive phase shift that is due to slightly nondegenerate two-wave mixing that compensates for cavity detuning and satisfies the round-trip phase condition for steady-state oscillation. The measured onset or threshold of oscillation as a function of photorefractive gain and intensity agrees with theory.
Phase conjugate resonators (PCR) are optical resonators in which (at least) one of the mirrors is a phase-conjugate one (PCM), e.g. a four-wave mixing cell. These systems are of considerable experimental and theoretical interest, specially in view of their potential to eliminate phase distorsions within the resonator1. In recent work2, we discussed a PCR consisting of a Fabry-Perot resonator with one end mirror replaced by a lossless Kerr medium of infinitely fast response time pumped by two counterpropagating beams of same frequency. We described the PCM within the Raman-Nath approximation3, but including fully the effects of pump depletion. The normal mirror was positioned such as to couple the first order scattered field back into the PCM. We found that this system can break into self-oscillations corresponding to the half-axial modes predicted by linear theories1,4. For higher pump intensities, this is followed by a sequence of bifurcations to chaos, with in general the coexistence of several basins of attraction. We also showed5 that the first of this sequence of bifurcations is in general already sufficient to induce a quasi-periodic motion of the intracavity field phase, leading in practice to its complete indetermination.
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.