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Journal of the Optical Society of America B

Theory of phase-conjugate oscillators II

Wun-Shung Lee, Pochi Yeh, Ragini Saxena, Sien Chi

Published Jul 1, 1991• 2 citations
Publisher

Abstract

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.

DOI
10.1364/josab.8.001421

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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.
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.
We study the dynamics of a stable Fabry–Perot resonator in which one mirror is a phase-conjugate mirror (PCM) with instantaneous response. The temporal variations in the model are caused by round-trip effects. An exact solution is given in a form of an infinite series. The step-function response is summed exactly. Numerical studies with Gaussian input pulses and PCM reflectivity variations are presented, and their behavior is explained. Approximate formulas for responses to slowly varying pulses are derived. Noise effects are simulated with a model in which the phases of the probe and the amplitude reflection coefficient of the PCM make uncorrelated jumps with Poissonian statistics. The theoretical model is aimed for optimizing experiments on phase-conjugate resonators involving transients and fluctuating fields.
The interaction of a radiating dipole with a phase conjugate mirror (PCM) is enhanced due to wavefront reversal by the PCM as well as by possible gain. Moreover, decay at two frequencies is predicted when ω o = ω m and 4(α r + αnr) d/c ≪ 1, where ω o = free oscillation frequency of the dipole, ω m = pump frequency of PCM (four-wave mixing), α r , and α nr are the radiative and nonradiative decay rates, respectively, and d is the effective distance to the PCM. Decay at multiple frequencies is predicted when 4(α r + α nr ) d/c ≳ 1. Locking of decay frequencies to the pump frequency is predicted at a critical pump intensity and at a second critical point the dipole gains energy from the PCM.