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Journal of the Optical Society of America B

Two-level description of instabilities in nonlinear Fabry–Perot cavities

Robert Frey, Bruno J. Thedrez

Published May 1, 1988• 2 citations
Publisher

Abstract

The intracavity absorption (or gain) coefficient of two-level atoms embedded inside a Fabry–Perot cavity has been demonstrated to be well represented by an equivalent two-level system. The parameters of this new two-level system are simply related to that of the medium and to the cavity characteristics. When associated with well-known results of fluorescence spectra and nearly degenerate four-wave mixing in two-level media, this equivalence provides a universal description of intracavity resonance fluorescence and relaxation oscillations in any nonlinear absorptive, amplifying, or dispersive Fabry–Perot cavities.

DOI
10.1364/josab.5.001176

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The intracavity absorption (or gain) coefficient of two-level atoms embedded inside a Fabry–Perot cavity has been demonstrated to be well represented by an equivalent two-level system. The parameters of this new two-level system are simply related to that of the medium and to the cavity characteristics. When associated with well-known results of fluorescence spectra and nearly degenerate four-wave mixing in two-level media, this equivalence provides a universal description of intracavity resonance fluorescence and relaxation oscillations in any nonlinear absorptive, amplifying, or dispersive Fabry–Perot cavities.
A general formalism is developed to study intracavity phase conjugation through resonant degenerate four-wave mixing. The effects of spatial hole burning, arising from interference of the counterpropagating pump waves, are fully incorporated. The analysis is applied to discuss intracavity phase conjugation in nonlinear media that can be modeled using either a two-level system or a Λ-type three-level system. In both cases, the phase-conjugate reflectivity exhibits bistability for an appropriate choice of the input parameters. For a two-level system, the tuning characteristics of the Fabry–Perot cavity significantly affect the phase-conjugate spectrum that displays hysteresis when the cavity is detuned from the applied laser frequency.
Many important effects such as optical bistability or periodic and chaotic self-pulsations have their origin in the interaction of two counterpropagating optical beams of the same frequency in a nonlinear medium. The investigation of the actual behavior of the standing waves set up inside a nonlinear Fabry-Perot etalon by an external pump beam is generally performed by observation of the transmitted beam. As predicted theoritically(1), intracavity phase conjugation is another way to test this interaction between the two counterpropagating pump waves inside the nonlinear cavity.
In this work the different schemes of propagation and interaction of the light beams in nonlinear Fabry-Perot interferometer have been studied theoretically and experimentally. Degenerate and non-degenerate four-wave mixing have been realized in the cavity of Fabry-Perot type using Rhodamine-6G dye and polymethine dye 3274U solution as saturable absorber. The diffraction efficiency of intracavity dynamic grating has been studied in dependence on intensity of interacting beams and parameters of resonator. The theoretical model of the processes of intracavity degenerate and non-degenerate four-wave mixing has been developed and applied to the analysis of the efficiency of light beams conversion by mean of Bragg diffraction from intracavity dynamic gratings. For theoretical description of typical experimental situations we used the round-trip model of nonlinear interferometer adapted for the geometry of degenerate four-wave mixing, which can be realized in the scheme of symmetrical oblique incidence of pump, signal and probe beams to the front and back mirrors of cavity.