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IEEE Journal of Quantum Electronics

Coherence and intensity statistics in phase-conjugate resonators

Alexander M. Lazaruk, Ari T. Friberg, Rainer Salomaa

Published Jan 1, 1990• 2 citations
Publisher

Abstract

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.>

DOI
10.1109/3.44971

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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.
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.
Stochastic fluctuations of coherent and incoherent components of the resonance fluorescence intensity induced by Wiener-Levy laser phase noise are investigated. Statistical properties of the atomic dipole moment for different values of the laser linewidth and different strength of the driving field are calculated. The stochastic Mollow spectra of atomic dipole fluctuations are derived. It is shown that these spectra exhibit a triplet structure which is purely classical and entirely laser-noise dependent.
We report a rigorous derivation of the power spectral density (PSD) spectrum of the phase noise in the transmitted and reflected signals of a Fabry-P\'erot (FP) interferometer. In transmission off and on resonance, the PSD at low frequencies is found to be simply equal to the PSD of the single-pass phase noise (the phase noise acquired by a signal that has traveled once through the FP interferometer) times (ng/n)2{({n}_{g}/n)}^{2}(ng​/n)2, where ng{n}_{g}ng​ is the group index and nnn the phase index of the light inside the FP interferometer. Equivalently, the phase noise (in radians) is equal to the single-pass phase-noise times ng/n{n}_{g}/nng​/n. This result states that the phase noise is proportional to the number of passes light makes through the FP interferometer, as expected physically. This simple expression provides a quick means of calculating the phase noise in a linear Fabry-P\'erot interferometer of any length in the range of frequencies of interest to the most applications. At high frequencies, we show that the PSD spectrum can also be expressed in a simple closed-form expression on resonance, but that off resonance it must be calculated numerically. Numerical simulations show that the PSD oscillates between 3 dB below the low-frequency PSD and 3 dB below the single-pass PSD. Equivalent expressions are derived for the phase noise in the signal reflected by a Fabry-P\'erot interferometer, which is found to have the same magnitude at low frequencies, but to be typically significantly lower at high frequencies.