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Journal of the Optical Society of America B

Steady state and dynamic gratings in photorefractive four-wave mixing

S. A. Bugaichuk, A I Khizhnyak

Published Jul 1, 1998• 11 citations
Publisher

Abstract

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.

DOI
10.1364/josab.15.002107

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Physical Review A•Mar 1, 1988•13 citations
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.
The stability of the steady-state solutions of four-wave mixing in photorefractive crystals has been studied. Two complementary methods have been used: linear stability analysis and time integration of the nonlinear equations. A critical dependence of the stability on the phase of the perturbation has been revealed. The existence of two stable solutions for certain values of some parameters has been found. Also, regimes of unstable behavior in cases with a unique steady-state solution for large values of the pump ratio have been found.