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Annual Meeting Optical Society of America

Photorefractive optical phase-sensitive detection

Charles L. Woods, J. Khoury, V. Ryan, Mark Cronin‐Golomb

Published Jan 1, 1990• 0 citations
Publisher

Abstract

Phase-sensitive detection can be realized optically by using degenerate four-wave mixing in photorefractive materials. Phase-sensitive detectors or lock-in amplifiers use a reference-triggered phase-sensitive mixer followed by a time-integrating low-pass filter. Mixing the two signals gives sum- and difference-frequency outputs, and a low-pass filter extracts the difference frequency. The phase encoded in the photorefractive hologram relative to the reference beam provides the mixing, and the response time of photorefractive material provides the time integration. Correctly modulating only the phase of the reference beam at a period much shorter than the photorefractive response time eliminates the phase-conjugate beam. Then modulating the phase of the signal input beam in the same waveform, but at a slightly different frequency from the reference, produces an oscillating phase-conjugate intensity. When the modulation frequencies of the two beams are phase-locked, a stable phase-conjugate signal is obtained with an intensity determined by the relative phase shift. These optical phase-sensitive detection experiments agree with calculations from dynamic photorefractive theory for the phase-conjugate intensity.

DOI
10.1364/oam.1990.fp4

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Physical Review A•Dec 1, 2011•11 citations
Phase-sensitive detection can be realized optically by using degenerate four-wave mixing in photorefractive materials. Phase-sensitive detectors or lock-in amplifiers use a reference-triggered phase-sensitive mixer followed by a time-integrating low-pass filter. Mixing the two signals gives sum- and difference-frequency outputs, and a low-pass filter extracts the difference frequency. The phase encoded in the photorefractive hologram relative to the reference beam provides the mixing, and the response time of photorefractive material provides the time integration. Correctly modulating only the phase of the reference beam at a period much shorter than the photorefractive response time eliminates the phase-conjugate beam. Then modulating the phase of the signal input beam in the same waveform, but at a slightly different frequency from the reference, produces an oscillating phase-conjugate intensity. When the modulation frequencies of the two beams are phase-locked, a stable phase-conjugate signal is obtained with an intensity determined by the relative phase shift. These optical phase-sensitive detection experiments agree with calculations from dynamic photorefractive theory for the phase-conjugate intensity.
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.
Phase conjugate reflectivity of the photorefractive four-wave mixing system is usually quite unstable and it is serious issue for practical use of these systems. The cause of this instability is mainly combination of the fluctuation of the phases of input signal and pump beams and the slow response time of the photorefractive crystal. When all input beams in the four-wave mixing system are mutually coherent and the phases of the input beams are not stable, four kinds of gratings are compete each other and the phase conjugate output becomes quite unstable. To avoid this problem, we can make one of the pump incoherent to the signal and another pump1. The phase conjugate output is, however, still unstable due to the rewriting of the grating caused by the fluctuation of the phase of the input beams. In this paper, we report our feedback system to stabilize the power of the phase conjugate output from the four-wave mixing system by controlling the phase of the signal beam. In this system, we detect the phase difference between signal and forward pump beam with lock-in amplifier and control the phase of the signal with a piezoelectric mirror to stabilize the phase difference.
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 present theory and experiments to show that the efficiency of four-wave mixing in photorefractive materials can be enhanced by use of optical waves of slightly different frequencies. The optimum frequency shift scales inversely with the response time of the material. We show that the \ensuremath{\sim}1-Hz frequency shift previously observed in the output of a self-pumped phase conjugator that used photorefractive BaTiO3{\mathrm{O}}_{3}O3​ is the result of this inherent property of four-wave mixing.
When the phase-conjugate replica of an optical beam is generated by traditional four-wave mixing with external pumping beams, the frequency of the phase-conjugate beam is fixed by the frequencies of the three input beams. In self-pumped phase conjugation, there is only one input beam, and the frequency of the output beam is free to roam. In photorefractive materials, this frequency difference between the incident and output beams is typically a few hertz. We present a method for controlling this frequency shift in the self-pumped phase-conjugate mirror that uses a ring configuration1 in photorefractive barium titanate. We show that two-beam coupling of an additional control beam with either of the optical beams already present in the ring cavity can alter the frequency of the phase-conjugate beam. We show that the control beam can alter the nonreciprocal phase shift2 of light propagating around the ring and thereby alter the frequency of the phase-conjugate beam. We also calculate the magnitude and the sign of the expected frequency shift as a function of the intensity, direction, and frequency of this control beam.
A slowing down of light pulses using backward-wave four-wave mixing is achieved in photorefractive crystals with different coupling strength. The delay and width of the output pulse are studied as a function of the input pulse width and pump intensity ratio for the amplified transmitted beam and for the phase-conjugated beam. The delay characteristics are compared with those of the two-beam coupling. It is demonstrated that the four-wave mixing process ensures a larger slowing down of short pulses (pulses with width shorter than the photorefractive response time) as compared to the photorefractive two-beam coupling scheme and guarantees the elimination of forerunners. The delay of long pulses in the four-wave mixing configuration is almost the same as the one that can be reached with two-beam coupling. The effect of absorption on the nonlinear shape transformation of the output pulses is discussed qualitatively.