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Technical Physics

Generalized derivation of equations for four-wave interaction in photorefractive media

V. Yu. Petrun’kin, Ivan V. Murashko, Elena V. Mokrushina

Published Aug 1, 2006• 0 citations
Publisher

Abstract

The emergence of optical waves out of optical noise (fanning) in a photorefractive medium is considered in an unconventional manner, i.e., using the Lorentz lemma and ensemble averaging. The derivation of equations for four-wave interaction in the scheme of a double incoherent phase-conjugate mirror is described in detail. Numerical calculation based on the resulting system of equations provides insight into the effect of noise on the oscillation threshold and makes it possible to discover the “higher threshold” effect in saturation-free noisy materials.

DOI
10.1134/s1063784206080147

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The emergence of optical waves out of optical noise (fanning) in a photorefractive medium is considered in an unconventional manner, i.e., using the Lorentz lemma and ensemble averaging. The derivation of equations for four-wave interaction in the scheme of a double incoherent phase-conjugate mirror is described in detail. Numerical calculation based on the resulting system of equations provides insight into the effect of noise on the oscillation threshold and makes it possible to discover the “higher threshold” effect in saturation-free noisy materials.
We investigate the dynamics of multiple two-wave mixing in photorefractive materials. This is the first time to our knowledge that a study of the dynamics of many pairs of two-wave mixing interactions has taken place. A basic case with three waves undergoing multiple two-wave mixing is studied numerically. A numerical study is also performed in which many waves are used to model the time development of the fanning effect. Comparison of this numerical model with a basic experiment involving fanning in the presence of a two-wave mixing interaction is given. A qualitative agreement is exhibited. In addition, it is found that effectively reducing the coupling constant of a two-wave mixing interaction by the addition of an incoherent background beam can, under certain circumstances, significantly reduce the fanning without lowering the signal level.
The effect of biasing illumination on the degenerate four-wave mixing (DFWM) in absorbing photorefractive (PR) media has been investigated. The input beams are considered to be spatially uniform. The analysis has been made both for transmission and reflection geometry. Considering pump beam depletion and the slowly varying amplitude approximation, nonlinear coupled wave equations are obtained and have been solved numerically by a shooting method. The effect of different parameters such as input beam intensities ratio, thickness of the interacting medium on the phase conjugate reflectively (PCR) has been investigated. It has been observed that PCR can be controlled to a large extent by controlling the biasing intensity.
There is presently a growing interest in nearly degenerate four-wave mixing, both for application in optical phase conjugation and the generation of squeezed states. In particular, the self-oscillation of a system interacting with one or two pump beams has been investigated in great detail in the case of photorefractive materials, but very few experiments have been done in vapors in the cw regime. The results that we obtained using sodium are presented here. They are strikingly different from the results obtained with photorefractive materials. For example, the oscillating beam and pump beam frequencies coincide with a precision better than 10−2 Hz. Another interesting aspect of this oscillating beam is that it exhibits a phase sensitive noise: just above threshold, the noise on one quadrature of the field can be 10−2 times smaller than the noise on the other quadrature.