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Journal of Modern Optics

Phase modulated two-wave mixing in crystals with long photocarrier lifetimes

Shaoping Bian, Jaime Frejlich

Published Jan 1, 1996• 1 citation
Publisher

Abstract

The temporal frequency response is derived for phase modulation in two-wave mixing for photorefractive crystals with long charge photocarrier lifetimes. Theoretical analysis shows that when the photorefractive response time is comparable with the photocarrier lifetime, the effects of the latter on the frequency transfer function must be considered. The present analysis is applied for Bi12SiO20-type photoreafractive crystals.

DOI
10.1080/09500349608232796

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The temporal frequency response is derived for phase modulation in two-wave mixing for photorefractive crystals with long charge photocarrier lifetimes. Theoretical analysis shows that when the photorefractive response time is comparable with the photocarrier lifetime, the effects of the latter on the frequency transfer function must be considered. The present analysis is applied for Bi12SiO20-type photoreafractive crystals.
We show theoretically that the group velocity of light can be slowed down by means of phase coupling in the photorefractive two-wave mixing process. It is shown that the group velocity of light propagating in a photorefractive material could be significantly reduced because of a steep variation of the phase-coupling coefficient with respect to the angular frequency difference between two coupling beams in a two-wave mixing process. The results for the case of a photorefractive Bi12SiO20 crystal are presented and discussed in detail.
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.
Based on Kukhtarev's equations, we derive the formulae of intensity-coupling coefficient, the phase-coupling coefficient and the group velocity at large modulation depth. It is theoretically shown that the signal beam can be amplified after passing through the photorefractive crystal and the group velocity reduced to m/s, even cm/s. Meanwhile, we also analyse the influence of the thermal excitation rate and the large signal effects on optical amplification and reduction of light propagation in photorefractive two-wave mixing.
We present measurements of the two-wave mixing gain as a function of frequency detuning in photorefractive crystals. In many cases, this function is asymmetric, indicating that the phase shift of the photorefractive inde grating with respect to the light interference pattern is not exactly 90 degrees , as is often assumed. In four-wave mixing, the phase of the phase-conjugate wave contains the phase of the pumping and probe waves and a phase shift determined by the interaction taking place in the nonlinear medium. This second term, the phase shift of the phase conjugator, is a function of the type of grating and the phase shift of this grating. The phase shift of the grating obtained from the two-wave mixing measurements compares well with that obtained from four-wave mixing measurements of the phase of the phase conjugator.
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.