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Journal of Optics

Optical bistability in photorefractive nearly DFWM using orthogonally polarized pumps: transmission geometry

N Birla, Avinashi Kapoor

Published Sep 1, 1995• 0 citations
Publisher

Abstract

Optical bistability based on the theory of photorefractive nearly degenerate four-wave mixing (DFWM) is considered for the case of transmission geometry with orthogonally polarized pump beams. The coupled wave equations are solved to obtain a nonlinear algebraic equation. This equation is being solved iteratively using Muller's method. The effect of different parameters pump ratio (r), probe ratio (q), coupling strength ( Gamma ) and frequency shift ( Omega ) on the phase conjugate reflectivity (PCR) have been investigated and the results are reported.

DOI
10.1088/0150-536x/26/5/001

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Optical bistability based on the theory of photorefractive nearly degenerate four-wave mixing (DFWM) is considered for the case of transmission geometry with orthogonally polarized pump beams. The coupled wave equations are solved to obtain a nonlinear algebraic equation. This equation is being solved iteratively using Muller's method. The effect of different parameters pump ratio (r), probe ratio (q), coupling strength ( Gamma ) and frequency shift ( Omega ) on the phase conjugate reflectivity (PCR) have been investigated and the results are reported.
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.
Effects of cross-polarization coupling have been investigated in the case of degenerate four-wave mixing (DFWM) in absorbing semi-insulating compound semiconductor photorefractive (PR) crystals in transmission geometry. Considering pump beam depletion, and the slowly varying approximation, nonlinear coupled wave equations are obtained and have been solved numerically by a shooting method. Numerical results obtained from computer calculation are presented in graphical form. It is seen that if all the input beams are of the same polarization, cross-polarization coupling generates a phase-conjugate beam which is polarized in a plane orthogonal to that of the input beam.
Using perturbation theory, we examine the fidelity of the photorefractive degenerate four-wave mixing (DFWM) phase conju- gator when the probe wave is spatially and temporally varying. Previous theories are based on linearized undepleted pump approximation and Laplace transform technique. Fully nonlinear solutions assume a single monochromatic plane wave probe. We have considered instead the more general case in which the probe is spatially varying (a beam) and/or temporally varying (a pulse), and the pumps are allowed to deplete. The probe wave is expanded as a sum of monochromatic plane waves of frequencies ω j = ω p + Ω j , wavevectors k j , and complex amplitudes A j (Ω j , k j ), where ω p is the frequency of the pumps. Using a perturbation approach up to the third order, we found that the components of the probe interact in pairs, so that the component of the conjugate wave at −Ω l −k l is H(Ω l , k l ) is the linearized response, ρ(Ω l , k l ; Ω j , k j ) represents crosstalk when j ≠ l, and self-nonlinear effect otherwise. Both functions exhibit resonance behavior. We use Eq. (1) to determine the response of the conjugate to pulsed beams.
A mean field theory of nearly-degenerate four-wave mixing is developed for the optical bistability, which has recently been found in a phase-conjugate resonator consisting of a normal mirror and a phase-conjugate mirror under relatively strong pumping. The bistability in transmission of the probe beam occurs as the mirror separation or the probe offset frequency is changed, but for a limited range of probe beam intensity. This behavior is explained as occurring under injection-locked conditions because of combined effects of tilting and broadening, or narrowing of the resonance curves due to nonlinearities in the phase-conjugate reflectivity arising from pump depletion.