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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Homodyne detection of phase-modulated optical signals through photorefractive crystals

Yan Li, Wanjun Sun, Zhongxiang Zhou, Yongyuan Jiang, Kebin Xu

Published Dec 31, 1996• 0 citations
Publisher

Abstract

Analytical solutions for the equations that describe the steady-state photorefractive two-wave mixing with rapidly phase-modulated beams are presented. The results show that the volume index of refraction grating automatically aligns so that it coherently couples the signal and local oscillator fields just like a fixed beamsplitter in a conventional homodyne receiver structure.

DOI
10.1117/12.263046

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Feb 1, 1991•0 citations
Analytical solutions for the equations that describe the steady-state photorefractive two-wave mixing with rapidly phase-modulated beams are presented. The results show that the volume index of refraction grating automatically aligns so that it coherently couples the signal and local oscillator fields just like a fixed beamsplitter in a conventional homodyne receiver structure.
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.
Photorefractively induced index-of-refraction phase gratings are shown to combine coherently the optical fields of a strong pump and a suitably amplitude- or phase-modulated signal beam in such a way that an apparent amplification of the modulating waveform appears as intensity modulation of the transmitted signal and pump beam intensities. The source of the signal gain is shown to be the square-law (intensity) detection of the coherently combined pump and modulated signal beams, just as in coherent optical communication systems in which a strong local-oscillator field is coherently added with a weak optical signal field by a beam splitter.
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.
The structure and dynamics of the four-wave mixing transmission grating in a photorefractive crystal were investigated. The steady-state grating’s amplitude distribution looks like a motionless soliton. When the value of coupling strength is more than 2, there are three solutions for the steady-state grating: two stable and one unstable. The dynamics of all these gratings are described by the sine-Gordon equation. The four-wave mixing grating’s structure and location in space are determined by the input beams’ ratio, phase difference, or both.
The properties of a self-pumped photorefractive phase conjugator as an amplifier of amplitude modulated signal beams are investigated. In principle the crystal acts as a self-adjusting beam combiner which allows homodyne detection of the weaksignalbeam superimposed on a stronger reference beam. In our experiments the mixing takes placevia a four wave interaction process in the crystal. In this paperwe investigate the salient characteristics ofthe self-pumped phase conjugate amplifier and explain details of the beam interaction inside the ciystal.