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Annual Meeting Optical Society of America

Subharmonics in photorefractive materials in the presence of an a.c. applied field

Chong Hoon Kwak, J. Takács, M. S. Shamonin, LASZLO SOLYMAR

Published Jan 1, 1992• 0 citations
Publisher

Abstract

It has been shown experimentally1 that a subharmonic beam may appear spontaneously between two pump beams without detuning either of the beams when a field varying sinusoidally or in the form of a square wave is applied across the crystal. That work has now been extended to cover the rise of the subharmonics as a function of time and their dependence under stationary conditions on the ratio between the pump intensities. The experiments were done on photorefractive bismuth silicate crystals. A simple theory is found to describe well the repetition frequency at which the subharmonics appear.

DOI
10.1364/oam.1992.mo2

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Annual Meeting Optical Society of America•Jan 1, 1988•0 citations
It has been shown experimentally1 that a subharmonic beam may appear spontaneously between two pump beams without detuning either of the beams when a field varying sinusoidally or in the form of a square wave is applied across the crystal. That work has now been extended to cover the rise of the subharmonics as a function of time and their dependence under stationary conditions on the ratio between the pump intensities. The experiments were done on photorefractive bismuth silicate crystals. A simple theory is found to describe well the repetition frequency at which the subharmonics appear.
We present an analysis of what is called parametric oscillation in photorefractive media. It is shown theoretically that when a running grating and a constant electric field are applied to a photorefractive medium it is possible for two secondary gratings to grow spontaneously. These theoretical predictions are subsequently verified experimentally in the crystal Bi12SiO20, and excellent qualitative agreement is obtained. In previous subharmonic experiments, only grating vectors K/2, K/3, and K /4 were observed. Now, however, a whole continuum of grating vectors has been observed. Thus subharmonic generation in photorefractive materials is simply a special case of parametric oscillation in which the two secondary gratings are identical.
A theoretical analysis is presented of two-wave mixing in photorefractive materials in which the complex amplitude of a weak signal beam has slowly varying but otherwise arbitrary spatial dependence and arbitrary time variation. The set of coupled partial differential equations that couple the dynamics of the optical fields to the photorefractive medium is solved analytically to give the complex amplitude of the transmitted signal in the undepleted pump regime. The results are compared with known results for the transient two-wave mixing of plane waves.
A self-consistent theory is used to derive the frequency shift presented by the oscillating mode in a cavity that contains a photorefractive crystal. A long-time-limit theory has been used to get the steady characteristics of the cavity field. The problem of the weak-field approximation is avoided. This approximation is useless in the case studied because the interaction along the crystal is so strong that one has to take in account the intensity exchange occurring inside the material between the pump and oscillating beams (two-wave mixing). We have fully analyzed the influence of the transverse nature of the beams on the intensity exchange in the two-wave mixing situation. In the photorefractive resonator case, the frequency shift of the oscillating beam is expressed in terms of a ratio that presents poles. The dependence on the problem parameters of these poles is studied and a perturbative method is developed; it is based on the smallness of the transverse overlap between the pump and cavity modes. An analytical expression for this frequency shift is obtained.
Two-wave mixing in photorefractive crystals has been shown to combine coherently a modulated optical signal beam with a strong pump optical field.’ For a phase-modulated signal beam, the induced index of refraction phase grating inside the crystal yields a coupling of the optical fields of the pump and signal so that subsequent intensity detection results in apparent intensity modulation of the transmitted signal or pump beams. This provides an easy way to detect phase differences between two optical beams. Some of the advantages the above scheme offers over commonly used coherent optical phase detection schemes are: no loss of 3 dB in the signal beam intensity at the 50/50 beam splitter (used to combine signal and local oscillator fields); automatic alignment of the index of refraction grating with the two incident optical wavefronts; insensitivity to slow random changes in the phases of both beams. Experimental results are given, and a new definition for the resulting mixing gain for the phase-modulated beam is introduced, through which optimal conditions for input beam intensity ratios can be found. Applications to coherent homodyne detection are discussed.