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

Soviet Journal of Quantum Electronics

Solution of nonlinear equations for four-wave interactions in photorefractive media

A. A. Zozulya, Vladimir T Tikhonchuk

Published Aug 31, 1988• 17 citations
Publisher

Abstract

A system of nonlinear equations is solved to describe a four-wave interaction in photorefractive media generating transmission or reflection refractive index gratings in the case of a drift-diffusive nonlinearity mechanism with an arbitrary complex coupling constant. An analysis is made of the four-wave interaction in the geometry of a nonlinear ring resonator where a reflection grating is formed.

DOI
10.1070/qe1988v018n08abeh012389

Related papers

Theory of four-wave mixing in photorefractive media when the response of a medium is nonlinear in respect of the modulation parameter

A. A. Zozulya

A theoretical model is constructed for four-wave mixing in a photorefractive crystal where a transmission grating is formed by the drift–diffusion nonlinearity mechanism in the absence of an external electrostatic field and the response of the medium is nonlinear in respect of the modulation parameter. A comparison is made with a model in which the response of the medium is linear in respect of the modulation parameter. Theoretical models of four-wave and two-wave mixing are also compared with experiments.

Soviet Journal of Quantum Electronics•Dec 31, 1988•1 citation

Phase relationships in the case of a four-wave interaction in a photorefractive medium in which a reflection grating is recorded

O N Volkova, A. A. Zozulya

Derivation is given of relationships for determination of the complex amplitudes of waves interacting in a four-wave mixing process in a photorefractive crystal in which a reflection grating is recorded throughout the whole interaction zone. An analysis is made of the amplitude and phase of a nonlinear reflection coefficient. The role of the real and imaginary parts of the coupling constant in the appearance of multivalued solutions is identified.

Soviet Journal of Quantum Electronics•Jul 31, 1989•1 citation

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

Multistability in reflection grating real-time holography

Aleksander Błȩdowski, Wieslaw Z. Krolikowski, Adam Kujawski

In this paper, four-wave mixing in photorefractive media for the case of a reflection geometry is investigated. The exact solutions of appropriate nonlinear equations for a zero phase shift between the refractive index grating and interference pattern of the optical beams have been found. The existence of multistability in the process has been shown. In addition, numerical evidence of the effect is included.

IEEE Journal of Quantum Electronics•Sep 1, 1986•13 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

Exact solution of degenerate four-wave mixing in photorefractive media

Aleksander Błȩdowski, Wieslaw Z. Krolikowski

A novel method for the exact solution of four-wave mixing in photorefractive media is presented. This method allows us to treat exactly the effects of nonequal angles of incidence, different refractive-index modulation of interacting waves, and external incoherent illumination of the photorefractive crystal.

Optics Letters•Feb 1, 1988•17 citations
A system of nonlinear equations is solved to describe a four-wave interaction in photorefractive media generating transmission or reflection refractive index gratings in the case of a drift-diffusive nonlinearity mechanism with an arbitrary complex coupling constant. An analysis is made of the four-wave interaction in the geometry of a nonlinear ring resonator where a reflection grating is formed.
A theoretical model is constructed for four-wave mixing in a photorefractive crystal where a transmission grating is formed by the drift–diffusion nonlinearity mechanism in the absence of an external electrostatic field and the response of the medium is nonlinear in respect of the modulation parameter. A comparison is made with a model in which the response of the medium is linear in respect of the modulation parameter. Theoretical models of four-wave and two-wave mixing are also compared with experiments.
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.