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

Quantum Electronics

Spatial structure of holographic gratings in photorefractive crystals with a nonlocal response

S. A. Bugaichuk, A. G. Kutana, A I Khizhnyak

Published Aug 31, 1997• 4 citations
Publisher

Abstract

The structure and spatial positions of dynamic gratings responsible of steady-state four-wave mixing are determined for nonlinear media with a nonlocal response. It is shown that an analytic solution found for a double phase-conjugate mirror is fundamental and that it can be used to obtain solutions for such a mirror when two pump beams are present.

DOI
10.1070/qe1997v027n08abeh001024

Related papers

Steady state and dynamic gratings in photorefractive four-wave mixing

S. A. Bugaichuk, A I Khizhnyak

The structure and dynamics of the four-wave mixing transmission grating in a photorefractive crystal were investigated. The steady-state grating’s amplitude distribution looks like a motionless soliton. When the value of coupling strength is more than 2, there are three solutions for the steady-state grating: two stable and one unstable. The dynamics of all these gratings are described by the sine-Gordon equation. The four-wave mixing grating’s structure and location in space are determined by the input beams’ ratio, phase difference, or both.

Journal of the Optical Society of America B•Jul 1, 1998•11 citations

Dynamic grating structure investigation

S. Bugaychuk, Anatoliy I. Khizhnyak

The structure of the transmission dynamic grating, that is formed during four-wave mixing in photorefractive medium with non-local response, was theoretical investigated. It was obtained the steady state solution for the common case of four input waves with its arbitrary phases. It is shown, that the structure of the dynamic grating is differed by its grating amplitude distribution, which described by the `soliton'-like function. It was determined the manner, how the grating amplitude distribution is depending on parameters of input coupling beams: intensities ratio and phases of waves. Input variation of waves parameters brings two phenomena: (1) changing of the grating half-wide; (2) changing of the grating amplitude maximum position. It was shown what in case of four input wave it is possible to record any shape of the grating amplitude distribution by varying input waves intensities or phases.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Nov 18, 1999•2 citations

Recording of various grating amplitude shapes during four-wave mixing in strong-response PRC

S. Bugaychuk, A. I. Khyzniak, A. G. Kutana

The amplitude of the transmission dynamic grating recorded due to the backward four-wave mixing (BFWM) in the non-local response photorefractive crystal is investigated theoretical. The grating's amplitude distribution is described as a motionless soliton. Both the soliton localization degree and its location can be control by varying of input intensity's ratio or/and input waves' phase differences. When waves' phase differences equal to 0 of (pi) the steady stage double-phase-conjugation mirror is formed. The BFWM dynamic is described by sin-Gordan-like equation.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 23, 1998•0 citations

Phase conjugation via multiple gratings in photorefractive crystals

Milivoj R. Belić

We consider phase conjugation via degenerate four-wave mixing in photorefractive crystals when more than one grating mechanism is operative. A method for exact solution of the steady-state wave equations which include pump depletion is presented. It is discovered that equal-strength multigrating operation does not allow signal amplification.

Physical Review A•Mar 1, 1988•13 citations

Optical control of the four-wave mixing dynamic grating structure in photorefractive media

S. Bugaychuk, A I Khizhnyak

Recording of localized transmission gratings by four-wave mixing in non-local photorefractive media with strong response is considered. The input conditions to record dynamic gratings with a stable grating amplitude distribution as well as grating amplitude oscillations are defined. They are determined both by intensities and by a phase difference of input waves. The influence of fluctuations of wave phases on stability of the recorded gratings is considered. Methods of optical control of both the grating amplitude localization degree and the grating amplitude location are defined.

Journal of Optics B Quantum and Semiclassical Optics•Jun 1, 2000•3 citations

Parametric Oscillation in Photorefractive Crystals with Local Response in Unclosed Optical Cavities

Adam Mazur, A. D. Novikov, S. G. Odulov +1 more

Steady-state coherent oscillation in the ring-loop and double-side mirror geometries is first observed and studied in media with local nonlinear response. The results of calculation are presented stating that the oscillation becomes possible providing two necessary conditions are met: the oscillation waves appear 1) misaligned with respect to strictly backward to pumps directions to restore the phase matching, and 2) they are shifted in frequency with respect to the pump waves. By appropriate choice of frequencies of two incident waves in double-side mirror geometry one of oscillating waves may be done a perfect conjugate replica of an input wave with limited spatial spectrum.

Photorefractive Effects, Materials, and Devices•Jan 1, 1991•0 citations
The structure and spatial positions of dynamic gratings responsible of steady-state four-wave mixing are determined for nonlinear media with a nonlocal response. It is shown that an analytic solution found for a double phase-conjugate mirror is fundamental and that it can be used to obtain solutions for such a mirror when two pump beams are present.
The structure and dynamics of the four-wave mixing transmission grating in a photorefractive crystal were investigated. The steady-state grating’s amplitude distribution looks like a motionless soliton. When the value of coupling strength is more than 2, there are three solutions for the steady-state grating: two stable and one unstable. The dynamics of all these gratings are described by the sine-Gordon equation. The four-wave mixing grating’s structure and location in space are determined by the input beams’ ratio, phase difference, or both.
The structure of the transmission dynamic grating, that is formed during four-wave mixing in photorefractive medium with non-local response, was theoretical investigated. It was obtained the steady state solution for the common case of four input waves with its arbitrary phases. It is shown, that the structure of the dynamic grating is differed by its grating amplitude distribution, which described by the `soliton'-like function. It was determined the manner, how the grating amplitude distribution is depending on parameters of input coupling beams: intensities ratio and phases of waves. Input variation of waves parameters brings two phenomena: (1) changing of the grating half-wide; (2) changing of the grating amplitude maximum position. It was shown what in case of four input wave it is possible to record any shape of the grating amplitude distribution by varying input waves intensities or phases.
The amplitude of the transmission dynamic grating recorded due to the backward four-wave mixing (BFWM) in the non-local response photorefractive crystal is investigated theoretical. The grating's amplitude distribution is described as a motionless soliton. Both the soliton localization degree and its location can be control by varying of input intensity's ratio or/and input waves' phase differences. When waves' phase differences equal to 0 of (pi) the steady stage double-phase-conjugation mirror is formed. The BFWM dynamic is described by sin-Gordan-like equation.
Recording of localized transmission gratings by four-wave mixing in non-local photorefractive media with strong response is considered. The input conditions to record dynamic gratings with a stable grating amplitude distribution as well as grating amplitude oscillations are defined. They are determined both by intensities and by a phase difference of input waves. The influence of fluctuations of wave phases on stability of the recorded gratings is considered. Methods of optical control of both the grating amplitude localization degree and the grating amplitude location are defined.
Steady-state coherent oscillation in the ring-loop and double-side mirror geometries is first observed and studied in media with local nonlinear response. The results of calculation are presented stating that the oscillation becomes possible providing two necessary conditions are met: the oscillation waves appear 1) misaligned with respect to strictly backward to pumps directions to restore the phase matching, and 2) they are shifted in frequency with respect to the pump waves. By appropriate choice of frequencies of two incident waves in double-side mirror geometry one of oscillating waves may be done a perfect conjugate replica of an input wave with limited spatial spectrum.