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Optics Letters

Phase conjugation of vector fields by degenerate four-wave mixing in a Fe-doped LiNbO_3

Sheng-Xia Qian, Yongnan Li, Ling‐Jun Kong, Chenghou Tu, Hui‐Tian Wang

Published Aug 12, 2014• 6 citations
Publisher

Abstract

We propose a method to generate the phase-conjugate wave of the vector field by degenerate four-wave mixing in a c-cut Fe-doped LiNbO3 crystal. We demonstrate experimentally that the phase-conjugate wave of the vector field can be generated. In particular, the phase-conjugate vector field has also the peculiar function of compensating the polarization distortion, as the traditional phase-conjugate scaler field can compensate the phase distortion.

DOI
10.1364/ol.39.004907

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Both backward and forward phase conjugate waves have been observed indegenerate four-wave mixing (DFWM) in a LiNbO 3 :Fe crystalline slab. Investigation shows that the observed forward phase conjugate wave consists of two main contributions. The dominant contribution is the phase conjugate wave of the reflected signal beam. The other contribution arises from the reflection of backward phase conjugate wave at the front surface of the crystal. The intensity of the forward phase conjugate wave is comparable with that of the backward phase conjugate wave.

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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 propose a method to generate the phase-conjugate wave of the vector field by degenerate four-wave mixing in a c-cut Fe-doped LiNbO3 crystal. We demonstrate experimentally that the phase-conjugate wave of the vector field can be generated. In particular, the phase-conjugate vector field has also the peculiar function of compensating the polarization distortion, as the traditional phase-conjugate scaler field can compensate the phase distortion.
Both backward and forward phase conjugate waves have been observed indegenerate four-wave mixing (DFWM) in a LiNbO 3 :Fe crystalline slab. Investigation shows that the observed forward phase conjugate wave consists of two main contributions. The dominant contribution is the phase conjugate wave of the reflected signal beam. The other contribution arises from the reflection of backward phase conjugate wave at the front surface of the crystal. The intensity of the forward phase conjugate wave is comparable with that of the backward phase conjugate wave.
This paper demonstrates dual-frequency phase conjugation waves via the high-order nonlinear effect by nondegenerate six-wave mixing in iron-doped lithium niobate. In the experiment, two conjugation waves of different frequency are generated. Conjugation wave 1 is similar to nondegenerate four-wave mixing; conjugation wave 2 is completely different. The experiments measure the relationships between two conjugation wave intensities and parameters, respectively, and compare the differences of the two conjugation waves. To explain the experimental results, we assume that there is a fifth-order nonlinear interaction in crystal, and we believe the two conjugation waves are generated via different level nonlinear interactions. The theory agrees with the experimental results.
DFWM as an useful tool to generate phase conjugate waves has recently been the subject of intensive study. In particular photorefractive crystals such as LiNbO3, KNbO3, BaTiO3 and SBN are widely used[1]. Among the published papers on DFWM most are concerned with backward phase conjugate waves and only a few with forward phase conjugate, waves.[2,3] In both of these papers the intensity of the forward phase conjugate wave has not been investigated. We report here a systematic study of the intensity of forward phase conjugate wave.
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.
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