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

Journal of the Optical Society of America B

Mulitigrating optical phase conjugation with considerations of phase effects

Ping Xie, Jian-Hua Dai, Zhang Hong-jun

Published Dec 1, 1992• 8 citations
Publisher

Abstract

We develop a numerical method to solve the coupled-wave equations for four-wave mixing phase conjugation in a photorefractive crystal with unequal complex coupling constants; by this method we can obtain both the intensities and the phases of various beams. We discuss the intensities and the phases of the interacting beams in a photorefractive crystal for the cases in which the phase shifts between the refractive-index gratings and the interference pattern are all π/2 and in which they are not all π/2.

DOI
10.1364/josab.9.002240

Related papers

Exact Solution to the Degenerate Four–Wave Mixing in Transmission Geometry in Photorefractive Media

Ying Wu, Guo-Qin Ge, Zhanping Xu

The exact solution of the degenerate four–wave mixing in transmission geometry in photore-fractive media for a zero phase shift between the refractive index grating and interference pattern of the optical beams is presented. Our solution gives both the intensities and the phases of various beams.

Communications in Theoretical Physics•Jul 1, 1991•3 citations

Phase shifts of photorefractive gratings and phase-conjugate waves

Ian C. McMichael, Pochi Yeh

We present measurements of the two-wave mixing gain as a function of frequency detuning in photorefractive crystals. In many cases, this function is asymmetric, indicating that the phase shift of the photorefractive inde grating with respect to the light interference pattern is not exactly 90 degrees , as is often assumed. In four-wave mixing, the phase of the phase-conjugate wave contains the phase of the pumping and probe waves and a phase shift determined by the interaction taking place in the nonlinear medium. This second term, the phase shift of the phase conjugator, is a function of the type of grating and the phase shift of this grating. The phase shift of the grating obtained from the two-wave mixing measurements compares well with that obtained from four-wave mixing measurements of the phase of the phase conjugator.

Optics Letters•Jan 1, 1987•34 citations

Photorefractive wave mixing with finite beams

Wieslaw Z. Krolikowski, Mark Cronin‐Golomb

While the interaction of optical beams in photorefractive crystals can often be accurately described in terms of 1-D plane-wave approximation, 2-D models are sometimes more suitable, as suggested by recent work.1 Here we discuss some aspects of photorefractive interaction of finite size optical beams. We have solved the system of partial differential equations governing two- and four-wave mixing numerically by using iterative procedures. Simulations of beam amplification in two-beam coupling show strong beam deformation even without any spatial information imposed on them. Spatially nonuniform energy transfer is responsible for this effect. The pump beam loses energy during propagation and at the end of its passage through the beam intersection region (which was completely inside the crystal) it is strongly depleted and cannot contribute significantly to beam amplification. As the pump beam crosses through the probe, it amplifies most strongly that side of the probe that it meets first. By the time the pump has reached the far side of the probe, it is strongly depleted and less effective at probe amplification. In the case of phase conjugation through four-wave mixing, we found that the conjugate beam is strongly deformed only when the coupling constant is negative (corresponding to deamplification of the probe input beam). For positive coupling constants the output conjugate beam is a good replica of the input probe beam.

Annual Meeting Optical Society of America•Jan 1, 1991•1 citation

Phase Conjugation by Diffraction Gratings in Photorefractive Crystals

M.H. Majles Ara, Mahdi Esmaeilzadeh

Here we present four wave mixing configuration as one of the most important methods of generation and explanation of process of generation phase conjugation light the coupled equation was solved by three methods: undepleted pump approximation exact solution and two wave mixing approximation. Although exact solutions can be derived for four-wave mixing, the results are difficult to use because of the complicated transcendental equation involved. Solved the coupled equations and introduce an approximation in which two-wave mixing is the dominant process.

Asia-Pacific Microwave Conference (APMC)•Mar 22, 2006•0 citations

Anisotropic four-wave mixing in cubic photorefractive crystals

Aleksander Błȩdowski, Wieslaw Z. Krolikowski

The anisotropic four-wave mixing in the scheme recently proposed by S.I. Stepanov and M.P. Petrov (Opt. Commun. vol.53, p.64-8, 1985) is studied. The main feature of this interaction arrangement is that the same phase hologram (index grating) has opposite contrasts for orthogonally polarized, counterpropagating waves. The coupled nonlinear equations, in the case of transmission and reflection gratings, for the pi /2 photorefractive phase shift are exactly solved, and their properties are discussed in detail. The numerical evidence of the effects of bistability and self-oscillation is included.>

IEEE Journal of Quantum Electronics•Apr 1, 1988•17 citations

Multigrating phase conjugation: exact results

Wieslaw Z. Krolikowski, Milivoj R. Belić

Multigrating operation of degenerate four-wave mixing in photorefractive media is considered in the strong pump regime. Closed-form expressions for the reflectivity are obtained for the cases of absorption and no absorption. An arbitrary phase mismatch between the intensity interference fringes and the refractive-index gratings is allowed.

Optics Letters•Feb 1, 1988•11 citations
We develop a numerical method to solve the coupled-wave equations for four-wave mixing phase conjugation in a photorefractive crystal with unequal complex coupling constants; by this method we can obtain both the intensities and the phases of various beams. We discuss the intensities and the phases of the interacting beams in a photorefractive crystal for the cases in which the phase shifts between the refractive-index gratings and the interference pattern are all π/2 and in which they are not all π/2.
We present measurements of the two-wave mixing gain as a function of frequency detuning in photorefractive crystals. In many cases, this function is asymmetric, indicating that the phase shift of the photorefractive inde grating with respect to the light interference pattern is not exactly 90 degrees , as is often assumed. In four-wave mixing, the phase of the phase-conjugate wave contains the phase of the pumping and probe waves and a phase shift determined by the interaction taking place in the nonlinear medium. This second term, the phase shift of the phase conjugator, is a function of the type of grating and the phase shift of this grating. The phase shift of the grating obtained from the two-wave mixing measurements compares well with that obtained from four-wave mixing measurements of the phase of the phase conjugator.
While the interaction of optical beams in photorefractive crystals can often be accurately described in terms of 1-D plane-wave approximation, 2-D models are sometimes more suitable, as suggested by recent work.1 Here we discuss some aspects of photorefractive interaction of finite size optical beams. We have solved the system of partial differential equations governing two- and four-wave mixing numerically by using iterative procedures. Simulations of beam amplification in two-beam coupling show strong beam deformation even without any spatial information imposed on them. Spatially nonuniform energy transfer is responsible for this effect. The pump beam loses energy during propagation and at the end of its passage through the beam intersection region (which was completely inside the crystal) it is strongly depleted and cannot contribute significantly to beam amplification. As the pump beam crosses through the probe, it amplifies most strongly that side of the probe that it meets first. By the time the pump has reached the far side of the probe, it is strongly depleted and less effective at probe amplification. In the case of phase conjugation through four-wave mixing, we found that the conjugate beam is strongly deformed only when the coupling constant is negative (corresponding to deamplification of the probe input beam). For positive coupling constants the output conjugate beam is a good replica of the input probe beam.
Here we present four wave mixing configuration as one of the most important methods of generation and explanation of process of generation phase conjugation light the coupled equation was solved by three methods: undepleted pump approximation exact solution and two wave mixing approximation. Although exact solutions can be derived for four-wave mixing, the results are difficult to use because of the complicated transcendental equation involved. Solved the coupled equations and introduce an approximation in which two-wave mixing is the dominant process.
The anisotropic four-wave mixing in the scheme recently proposed by S.I. Stepanov and M.P. Petrov (Opt. Commun. vol.53, p.64-8, 1985) is studied. The main feature of this interaction arrangement is that the same phase hologram (index grating) has opposite contrasts for orthogonally polarized, counterpropagating waves. The coupled nonlinear equations, in the case of transmission and reflection gratings, for the pi /2 photorefractive phase shift are exactly solved, and their properties are discussed in detail. The numerical evidence of the effects of bistability and self-oscillation is included.>