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Optics Letters

Quenching and enhancement of an optical nonlinearity by a phase-conjugate mirror

Erik J. Bochove

Published Jun 1, 1991• 0 citations
Publisher

Abstract

The nonlinear polarizabilities of a two-level atom and a nonlinear oscillator in front of a resonant phase-conjugate mirror are calculated as functions of the mirror reflectivity. The effect of the mirror is to quench the nonlinearity of the two-level system and most anharmonic oscillators. In the case of a weakly anharmonic oscillator the nonlinear polarizability can be extremely large.

DOI
10.1364/ol.16.000852

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The nonlinear polarizabilities of a two-level atom and a nonlinear oscillator in front of a resonant phase-conjugate mirror are calculated as functions of the mirror reflectivity. The effect of the mirror is to quench the nonlinearity of the two-level system and most anharmonic oscillators. In the case of a weakly anharmonic oscillator the nonlinear polarizability can be extremely large.
We present a brief review of optical phase conjugation by four-wave mixing in atomic vapors. We emphasize the particular properties of vapors for this process. We discuss the case of nearly resonant excitation for two-level atoms, the case of multilevel atoms where the nonlinearity arises from optical pumping and the nearly resonant two-photon excitation. We finally describe the modification of phase-conjugate signals when one goes from the Bragg regime to the Raman-Nath regime and we show how one can achieve a phase-contrast mirror rather than a phase-conjugate mirror in this last case.
We have developed a theory for nondegenerate oscillations in optical resonators containing an intracavity phase-conjugate element. The phase-conjugate element consists of a nonlinear transparent medium that is pumped externally by a pair of counterpropagating laser beams of the same frequency and intensity. Phase conjugation of an input beam of slightly different frequency occurs because of nondegenerate four-wave mixing. The theory takes into account linear absorption (or gain) in the medium and is applied to study the threshold behavior of phase-conjugate oscillators. For the special case of no conventional mirrors, the phase-conjugate oscillator reduces to an ordinary phase-conjugate mirror, and our general formulation yields the results of previous studies. Our analysis shows that the parametric gain required for oscillation increases (or decreases) as a result of linear absorption (or gain) in the medium, and oscillation can occur at a frequency different from that of the pump beams in the presence of large linear gain (or loss). The effects of linear absorption (or gain) on the filter operation are also examined.
The double phase-conjugate mirror is an oscillator in the framework of the one-dimensional theoretical model previously used for its description. Results of a more consistent two-dimensional approach qualitatively differ from those of a one-dimensional analysis, indicating that the double phase-conjugate mirror is a convective amplifier. The correct physical picture of the scattering development is revealed, and the transverse profiles of scattered beams and the dynamics of nonlinear reflectivity are calculated.
The spontaneous radiation of a classical oscillator and that of a two-level atom both in the vicinity of a phase-conjugate mirror are calculated and compared. In either case the phase-conjugate mirror may be replaced by a phase-conjugate "image" of the source. We study the dependence of the decay constants and the characteristic frequencies on the phase-conjugate reflectivity and the difference between the characteristic frequency of the radiator and the pump frequency of the phase-conjugate mirror.
It is often desirable that a phase conjugate mirror be able to correct for polarization distortions in addition to correcting for wavefront aberrations. Such a device is called a vector phase conjugate mirror. It has been predicted within the context of the third-order theory that vector phase conjugation can be achieved by degenerate four-wave mixing using atomic two-photon transitions between S-states.1 We recently developed a theory of the polarization properties of two-photon resonantly enhanced degenerate four-wave mixing which can treat saturation effects due to pump waves.2 Our results show that for the case of linear and parallel pump wave polarizations, vector phase conjugation occurs with high quality and high reflectivity for two-photon transitions for which the nonresonant Stark shift is very small. We have also found that for the case of circular and counterrotating pump wave polarizations, perfect vector phase conjugation occurs for equal pump wave intensities. We have studied experimentally the effects of saturation and Stark shifts for S → S two-photon transitions of atomic sodium. We have found that high fidelity vector phase conjugation can be obtained.