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Journal of the Optical Society of America B

Analytical description of noise in phase-conjugate resonators

Ari T. Friberg, Rainer Salomaa

Published Dec 1, 1988• 3 citations
Publisher

Abstract

An analytical method is derived for the evaluation of the average conjugate and specular reflections of a probe field from a phase-conjugate resonator. Statistical fluctuations described by Poissonian sudden jumps may simultaneously occur in the amplitude and phase of both the probe field and the complex reflectivity of the phase-conjugate mirror. In the possible noise scenarios any mixture of phase and amplitude jump probabilities can be included. The resonator is assumed to stay in the stable regime. It is shown that phase fluctuations have the strongest influence on the resonator performance. Amplitude noise is important only if jumps are infrequent and if the resonator operates close to the instability threshold or if the phase-conjugate-mirror reflectivity is approximately unity.

DOI
10.1364/josab.5.002502

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An analytical method is derived for the evaluation of the average conjugate and specular reflections of a probe field from a phase-conjugate resonator. Statistical fluctuations described by Poissonian sudden jumps may simultaneously occur in the amplitude and phase of both the probe field and the complex reflectivity of the phase-conjugate mirror. In the possible noise scenarios any mixture of phase and amplitude jump probabilities can be included. The resonator is assumed to stay in the stable regime. It is shown that phase fluctuations have the strongest influence on the resonator performance. Amplitude noise is important only if jumps are infrequent and if the resonator operates close to the instability threshold or if the phase-conjugate-mirror reflectivity is approximately unity.
An analytical method is derived for the evaluation of the average conjugate and specular reflections of a probe field from a phase-conjugate resonator. Statistical fluctuations described by Poissonian sudden jumps may simultaneously occur in the amplitude and phase of both the probe field and the complex reflectivity of the phase-conjugate mirror. In the possible noise scenarios any mixture of phase and amplitude jump probabilities can be included. The resonator is assumed to stay in the stable regime. It is shown that phase fluctuations have the strongest influence on the resonator performance. Amplitude noise is important only if jumps are infrequent and if the resonator operates close to the instability threshold or if the phase-conjugate-mirror reflectivity is approximately unity.
The spectra, coherence properties, and intensity fluctuations of waves generated by reflections of a noisy probe field from a phase-conjugate Fabry-Perot resonator are discussed. The emphasis of the analysis is on the spectral response of the resonator. The results obtained are in fill agreement with those derived using specific noise models in the time domain. Advantages of the frequency-domain analyses include full tractability of general probe-wave noise models and fast convergence of numerical computations. The reflected-wave coherence properties reveal an interesting periodic structure due to multiple intracavity reflections. The intensity fluctuation levels, which depend on the statistical models, are calculated explicitly for pure Markovian phase noise and Gaussian amplitude noise of the probe. Combinations of these two, yielding simple laser models, and other extensions of noise effects in phase-conjugate resonators are briefly discussed.>
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.