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Optics Letters

Vector phase conjugation by two-photon-resonant degenerate four-wave mixing

Michelle S. Malcuit, Daniel J. Gauthier, Robert W. Boyd

Published Aug 1, 1988• 23 citations
Publisher

Abstract

We have studied the polarization properties of phase conjugation by degenerate four-wave mixing resonantly enhanced by the sodium 3S1/2 → 6S1/2 two-photon-allowed transition. As predicted by third-order theories, this interaction leads to simultaneous conjugation of the optical wave front and state of polarization (vector phase conjugation) when the pump intensities are sufficiently weak. However, qualitatively different polarization behavior is observed for pump intensities near or above the two-photon saturation intensity.

DOI
10.1364/ol.13.000663

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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.

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Polarization properties of optical phase conjugation by two-photon resonant degenerate four-wave mixing

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We develop a semiclassical theory of the polarization properties of phase conjugation by two-photon resonant degenerate four-wave mixing. The theory includes the effects of saturation by the pump waves. We solve the density-matrix equations of motion in steady state for a nonlinear medium consisting of stationary atoms with a ground and excited state connected by two-photon transitions. As an illustration of the general results, we consider an ${S}_{0}$\ensuremath{\rightarrow}${S}_{0}$ two-photon transition, which is known to lead to perfect polarization conjugation in the limit of third-order theory. We show that the fidelity of the polarization-conjugation process is degraded for excessively large pump intensities. The degradation can occur both due to transfer of population to the excited state and due to nonresonant Stark shifts. Theoretical results are compared to those of a recent experiment [Malcuit, Gauthier, and Boyd, Opt. Lett. 13, 663 (1988)].

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Rigidly held molecules display nonlinear optical properties which differ substantially from the properties of isotropic absorbers.1 In particular, the absorption of a collection of randomly oriented, rigidly held molecules saturates differently for different polarization states. We show that the polarization properties of degenerate four-wave mixing in such a medium are dramatically modified by this polarization-dependent saturation. We predict theoretically that for linearly polarized pump waves and for an input intensity near the saturation intensity, degenerate four-wave mixing in this material system can lead directly to vector phase conjugation; that is, to the simultaneous reversal of the optical wavefront and conjugation of the polarization state of the incident optical field.2 We confirm these theoretical predictions through phase conjugation experiments using fluorescein doped boric acid glass as the material system, and we find that degenerate four-wave mixing leads to nearly perfect vector phase conjugation when pumped by linearly polarized pump waves for field strengths near the saturation intensity.

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Nonlinear optical interactions can depend in a complicated manner on the state of polarization of the incident optical waves. For the case of isotropic nonlinear optical materials, the third order nonlinear polarization is expressed in terms of two parameters A and B describing the material system and can be written as1,2 (1) where E → is the total field incident upon the medium. In this paper we present the results of investigations of the polarization properties of phase conjugation by degenerate four-wave mixing (DFWM) in fluorescein-doped boric acid glass and in sodium vapor utilizing the 3S1/2→6S1/2 two-photon allowed transition. We find that these two materials can be used for a vector phase conjugation. Vector phase conjugation (VPC) corrects for both wavefront and polarization distortions upon double pass through an aberrating medium.3

Nonlinear Optical Properties of Materials•Jan 1, 1988•0 citations
We have studied the polarization properties of phase conjugation by degenerate four-wave mixing resonantly enhanced by the sodium 3S1/2 → 6S1/2 two-photon-allowed transition. As predicted by third-order theories, this interaction leads to simultaneous conjugation of the optical wave front and state of polarization (vector phase conjugation) when the pump intensities are sufficiently weak. However, qualitatively different polarization behavior is observed for pump intensities near or above the two-photon saturation intensity.
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.
We have studied the polarization properties of phase conjugation by degenerate four-wave mixing utilizing the 3S\ensuremath{\rightarrow}4S two-photon-allowed transition of sodium. We have observed high-fidelity vector phase conjugation (simultaneous conjugation of the optical wave front and the state of polarization) at a reflectivity of \ensuremath{\sim}1% for the case where the states of polarization of the two counterpropagating pump waves were circular and counterrotating. High-fidelity polarization conjugation with high reflectivity was obtained only when the forward pump wave was much stronger than the backward pump wave. To explain these results, it is necessary to include the effects of grating washout due to atomic motion in the theoretical analysis.
We develop a semiclassical theory of phase conjugation by two-photon-resonant degenerate four-wave mixing. Our theory treats both the tensor nature of the interaction and the effects of saturation of the atomic system. Previous theories that include saturation effects have treated only the scalar case,1 while theories that include polarization properties have treated the problem only in lowest-order perturbation theory.2 We consider an S → S two-photon transition. This interaction is of Interest because it has been predicted theoretically2 and shown experimentally3 that in the limit of nonsaturating pump waves this interaction leads to the simultaneous conjugation of the wavefront and polarization of the incident probe wave (vector phase conjugation).
We develop a semiclassical theory of the polarization properties of phase conjugation by two-photon resonant degenerate four-wave mixing. The theory includes the effects of saturation by the pump waves. We solve the density-matrix equations of motion in steady state for a nonlinear medium consisting of stationary atoms with a ground and excited state connected by two-photon transitions. As an illustration of the general results, we consider an S0{S}_{0}S0​\ensuremath{\rightarrow}S0{S}_{0}S0​ two-photon transition, which is known to lead to perfect polarization conjugation in the limit of third-order theory. We show that the fidelity of the polarization-conjugation process is degraded for excessively large pump intensities. The degradation can occur both due to transfer of population to the excited state and due to nonresonant Stark shifts. Theoretical results are compared to those of a recent experiment [Malcuit, Gauthier, and Boyd, Opt. Lett. 13, 663 (1988)].
Rigidly held molecules display nonlinear optical properties which differ substantially from the properties of isotropic absorbers.1 In particular, the absorption of a collection of randomly oriented, rigidly held molecules saturates differently for different polarization states. We show that the polarization properties of degenerate four-wave mixing in such a medium are dramatically modified by this polarization-dependent saturation. We predict theoretically that for linearly polarized pump waves and for an input intensity near the saturation intensity, degenerate four-wave mixing in this material system can lead directly to vector phase conjugation; that is, to the simultaneous reversal of the optical wavefront and conjugation of the polarization state of the incident optical field.2 We confirm these theoretical predictions through phase conjugation experiments using fluorescein doped boric acid glass as the material system, and we find that degenerate four-wave mixing leads to nearly perfect vector phase conjugation when pumped by linearly polarized pump waves for field strengths near the saturation intensity.
Nonlinear optical interactions can depend in a complicated manner on the state of polarization of the incident optical waves. For the case of isotropic nonlinear optical materials, the third order nonlinear polarization is expressed in terms of two parameters A and B describing the material system and can be written as1,2 (1) where E → is the total field incident upon the medium. In this paper we present the results of investigations of the polarization properties of phase conjugation by degenerate four-wave mixing (DFWM) in fluorescein-doped boric acid glass and in sodium vapor utilizing the 3S1/2→6S1/2 two-photon allowed transition. We find that these two materials can be used for a vector phase conjugation. Vector phase conjugation (VPC) corrects for both wavefront and polarization distortions upon double pass through an aberrating medium.3