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IEEE Journal of Quantum Electronics

Sensitivity of phase-conjugate resonators to intracavity phase perturbations

Amos A. Hardy

Published Aug 1, 1981• 17 citations
Publisher

Abstract

The sensitivity of phase-conjugate resonators to phase perturbations is analyzed numerically. It is shown that as long as the phase-conjugate mirror (PCM) intercepts most of the light traveling towards it, this type of resonator provides much improvement over conventional optical cavities.
DOI
10.1109/jqe.1981.1071279

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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.
The fidelity of the image beam produced by a phase conjugate mirror (PCM) is less when pump beams are not plane waves. On the other hand, high fidelity is a desirable property for most proposed applications, while energy or power should also be economized. We show that PCM fidelity may be characterized in terms of eigenfunctions—and values—of the reflection operator, and optimization may be achieved through use of an appropriate phase filter.1,2 In the present view, the filter has the role of transforming the incident object field into a (near) eigenfunction of the reflectivity operator. An equivalence theorem is presented which demonstrates parallels between the PCM and a certain kind of optical cavity. Perturbation theory applied in the small distortion case leads to an alternative approach to characterization and calculation technique.
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.