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

Optics Letters

Nonlinear vectorial two-beam coupling and forward four-wave mixing in photorefractive materials

Baruch Fischer, Jeffrey Owen White, Mark Cronin‐Golomb, Amnon Yariv

Published Apr 1, 1986• 25 citations
Publisher

Abstract

We present an exact solution of a nonlinear vector analysis of two-beam coupling and forward four-wave mixing in photorefractive media.In this Letter we present an exact solution with linear absorption for a system of nonlinear differential equations that model two separate photorefractive processes.The first is the coupling of two beams with general

DOI
10.1364/ol.11.000239

Related papers

Solutions to vector four-wave mixing in cubic photorefractive materials

David A. Fish, A. K. Powell

We present an eight-dimensional matrix formulation of vector four-wave mixing. We study the case of a nonoptically active photorefractive for the transmission grating. The coupled equations are represented in a group formalism and irreducible forms are found. We show that when cross-polarization coupling is neglected, the system of equations is governed by two coupled SU(2) groups. We develop a theory that allows for pump depletion and electric-field-induced bulk birefringence. Analytical solutions are found when cubic 4¯3m materials are considered in two standard experimental geometries, i.e., electric fields perpendicular to the (110) crystal faces and electric fields perpendicular to the (001) crystal faces. Results are presented that show the effects of linear and circular polarized beams, and the use of these materials for vector phase conjugation is discussed. Solution routes to other geometries and noncubic photorefractive materials are also presented.

Journal of the Optical Society of America B•Oct 1, 1997•3 citations

Approximate theory for degenerate four-wave mixing viareflection grating in photorefractive media

Hui‐Tian Wang, Shin Yoshikado, Tadashi Aruga +21 more

An approximate theory for degenerate four-wave mixing via reflection grating in photorefractive media is proposed.An analytic solution of the problem is derived.The theory is valid when the intensities of the two forward beams are much smaller than that of the backward beam.

The Review of Laser Engineering•Jan 1, 1997•0 citations

Simple theory for degenerate four-wave mixing in photorefractive media

Paul Michael Petersen, Per Michael Johansen

A simple analytic theory for degenerate four-wave mixing in photorefractive media is presented. The theory is valid when the backward pump-beam intensity is much smaller than the forward pump-beam and probe-beam intensities.

Optics Letters•Jan 1, 1988•4 citations

Exact solution to the degenerate four-wave mixing in reflection geometry in photorefractive media

Milivoj R. Belić

A method for exact solution of the stationary holographic degenerate four-wave mixing in reflection geometry in photorefractive media is presented. The effects of pump depletion and light absorption in the nonlinear dynamic medium are rigorously taken into account. Numerical steps in the procedure are reduced to the solution of one simple nonlinear first-order differential equation, or are absent altogether when the equation is linearized, or for the case of no absorption. The method of solution is applicable to other wave-mixing geometries as well.

Physical Review A•May 1, 1985•35 citations

A general theory of two-wave mixing in nonlinear media

Mingjun Chi, Jean‐Pierre Huignard, Paul Michael Petersen

A general theory of two-wave mixing (TWM) in nonlinear media is presented. Assuming a gain (or absorption) grating and a refractive index grating are generated because of the nonlinear process in a nonlinear medium, the coupled-wave equations of TWM are derived based on Maxwell's wave equation. The coupled-wave equations can be decoupled as coupled equations for the intensity and coupled equations for the phase of both beams, and these two sets of coupled equations can be solved analytically by using average total intensity in the medium instead of using the total intensity. Compared with the previous theory of TWM, the theory presented here is more general, and the applications of the theory to photorefractive materials, Kerr media, and semiconductor broad-area amplifiers are described.

Journal of the Optical Society of America B•Jul 14, 2009•29 citations

Exact solution of a nonlinear model of two-wave mixing in Kerr media

Pochi Yeh

The coupling of two electromagnetic waves in Kerr media is considered. An exact solution of the coupled-mode equations is derived in the most general case when both pump depletion and material absorption are considered.

Journal of the Optical Society of America B•May 1, 1986•63 citations
We present an exact solution of a nonlinear vector analysis of two-beam coupling and forward four-wave mixing in photorefractive media.In this Letter we present an exact solution with linear absorption for a system of nonlinear differential equations that model two separate photorefractive processes.The first is the coupling of two beams with general
We present an eight-dimensional matrix formulation of vector four-wave mixing. We study the case of a nonoptically active photorefractive for the transmission grating. The coupled equations are represented in a group formalism and irreducible forms are found. We show that when cross-polarization coupling is neglected, the system of equations is governed by two coupled SU(2) groups. We develop a theory that allows for pump depletion and electric-field-induced bulk birefringence. Analytical solutions are found when cubic 4¯3m materials are considered in two standard experimental geometries, i.e., electric fields perpendicular to the (110) crystal faces and electric fields perpendicular to the (001) crystal faces. Results are presented that show the effects of linear and circular polarized beams, and the use of these materials for vector phase conjugation is discussed. Solution routes to other geometries and noncubic photorefractive materials are also presented.
A method for exact solution of the stationary holographic degenerate four-wave mixing in reflection geometry in photorefractive media is presented. The effects of pump depletion and light absorption in the nonlinear dynamic medium are rigorously taken into account. Numerical steps in the procedure are reduced to the solution of one simple nonlinear first-order differential equation, or are absent altogether when the equation is linearized, or for the case of no absorption. The method of solution is applicable to other wave-mixing geometries as well.
A general theory of two-wave mixing (TWM) in nonlinear media is presented. Assuming a gain (or absorption) grating and a refractive index grating are generated because of the nonlinear process in a nonlinear medium, the coupled-wave equations of TWM are derived based on Maxwell's wave equation. The coupled-wave equations can be decoupled as coupled equations for the intensity and coupled equations for the phase of both beams, and these two sets of coupled equations can be solved analytically by using average total intensity in the medium instead of using the total intensity. Compared with the previous theory of TWM, the theory presented here is more general, and the applications of the theory to photorefractive materials, Kerr media, and semiconductor broad-area amplifiers are described.