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Comparison of three wave mixing in photorefractive and nematic liquid crystals

David John Webb, LASZLO SOLYMAR

Published Sep 16, 1991• 0 citations
OpenAlex

Abstract

Consideration of the coupled wave equations governing three wave mixing in photorefractives and nematic liquid crystals, when both are exhibiting a local response, shows that the main difference between the two is the self phase modulation that occurs in the liquid crystals. It is this difference that explains the dissimilar variation of the exponential gain factor, as a function of inter-beam angle. The other difference between the two media is the dependence of gain on the total incident intensity for the case of nematic liquid crystals and on the detuning frequency for the case of photorefractive media. >

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Consideration of the coupled wave equations governing three wave mixing in photorefractives and nematic liquid crystals, when both are exhibiting a local response, shows that the main difference between the two is the self phase modulation that occurs in the liquid crystals. It is this difference that explains the dissimilar variation of the exponential gain factor, as a function of inter-beam angle. The other difference between the two media is the dependence of gain on the total incident intensity for the case of nematic liquid crystals and on the detuning frequency for the case of photorefractive media. >
Optical bistability has been observed in a new configuration consisting of a nematic liquid crystal (ROTN 403) and a photorefractive crystal (KNbO3). The nematic liquid crystal (NLC), placed between crossed polarizers, serves as an optically controlled gate. The transmitted signal beam is amplified by photorefractive two-wave mixing and sent back onto the NLC in such a way that it changes the transmission of the gate. Bistability of the optical signal in the feedback loop with a large hysteresis is found. The bistable hysteresis curve depends on the nonlinearities of the NLC and of the photorefractive crystal, on the intensity of the storage beam and on the losses in the feedback loop.
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.
We develop a numerical method to solve the coupled-wave equations for four-wave mixing phase conjugation in a photorefractive crystal with unequal complex coupling constants; by this method we can obtain both the intensities and the phases of various beams. We discuss the intensities and the phases of the interacting beams in a photorefractive crystal for the cases in which the phase shifts between the refractive-index gratings and the interference pattern are all π/2 and in which they are not all π/2.