Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optics Letters

Reflectivity fluctuations in phase-conjugate resonators

Ari T. Friberg, Martti Olavi Kauranen, K. Nyholm, Rainer Salomaa

Published Mar 1, 1987• 5 citations
Publisher

Abstract

Behavior of the conjugate and specular reflections from a phase-conjugate resonator is studied in the presence of phase-conjugate mirror noise. Phase and amplitude fluctuations are described by a sudden-jump model. Analytical results show that the system is partially self-compensating for the phase noise. Numerical simulations of amplitude fluctuations reveal strong deviations from the coherent case when amplitude correlation time is long and the resonator is close to instability threshold.

DOI
10.1364/ol.12.000193

Related papers

Analytical description of noise in phase-conjugate resonators

Ari T. Friberg, Rainer Salomaa

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.

•Jan 1, 1987•0 citations

Analytical description of noise in phase-conjugate resonators

Ari T. Friberg, Rainer Salomaa

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.

Journal of the Optical Society of America B•Dec 1, 1988•3 citations

Dynamics of Fabry–Perot resonators with a phase-conjugate mirror

Ari T. Friberg, Martti Olavi Kauranen, Rainer Salomaa

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.

Journal of the Optical Society of America B•Dec 1, 1986•9 citations

Coherence and intensity statistics in phase-conjugate resonators

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

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.>

IEEE Journal of Quantum Electronics•Jan 1, 1990•2 citations

Stimulated Brillouin scattering phase-conjugation fidelity fluctuations

John J. Ottusch, David A. Rockwell

We observe shot-to-shot fluctuations in the far-field fidelity of stimulated Brillouin scattering phase-conjugate mirrors in the saturated reflectivity regime under various experimental conditions. The fluctuations, which are not seen in the reflectivity, reflect a partial breakdown in the discrimination mechanism that selectively amplifies the conjugate mode above the stimulated Brillouin scattering noise seed.

Optics Letters•Mar 15, 1991•50 citations

Self-oscillation in a cavity using a sodium vapor phase conjugate mirror

M. Pinard, E. Le Bihan, D. Grandclément +1 more

Self-oscillation of cavities closed by phase-conjugate mirrors has been observed with solids,1 liquids,2 and vapors.3 The case of vapors is particularly interesting because the nonlinearities are well known, and precise comparison between theory and experiments is possible. Furthermore, because of the huge nonlinearity close to a resonance transition, high reflectivities are obtained even with cw lasers.4 At last, the time response of the medium is expected to be of the order of the lifetime of the excited level.

Journal of the Optical Society of America B•Feb 1, 1986•0 citations
Behavior of the conjugate and specular reflections from a phase-conjugate resonator is studied in the presence of phase-conjugate mirror noise. Phase and amplitude fluctuations are described by a sudden-jump model. Analytical results show that the system is partially self-compensating for the phase noise. Numerical simulations of amplitude fluctuations reveal strong deviations from the coherent case when amplitude correlation time is long and the resonator is close to instability threshold.
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.
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 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.>
Self-oscillation of cavities closed by phase-conjugate mirrors has been observed with solids,1 liquids,2 and vapors.3 The case of vapors is particularly interesting because the nonlinearities are well known, and precise comparison between theory and experiments is possible. Furthermore, because of the huge nonlinearity close to a resonance transition, high reflectivities are obtained even with cw lasers.4 At last, the time response of the medium is expected to be of the order of the lifetime of the excited level.