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Applied Physics Letters

Adaptive interferometer based on wave mixing in a photorefractive crystal under alternating electric field

Alexei A. Kamshilin, Alexander I. Grachev

Published Oct 10, 2002• 43 citations
Publisher

Abstract

Coupling of two waves with different polarization states in a photorefractive crystal under an ac electric field allows us to achieve the linear transformation of a small transient phase shift into the intensity modulation without any output polarization filtering. This can lead to design of an adaptive interferometer with sensitivity that reaches the classical homodyne detection limit.

DOI
10.1063/1.1515131

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Coupling of two waves with different polarization states in a photorefractive crystal under an ac electric field allows us to achieve the linear transformation of a small transient phase shift into the intensity modulation without any output polarization filtering. This can lead to design of an adaptive interferometer with sensitivity that reaches the classical homodyne detection limit.
In a double two-wave mixing arrangement a signal wave couples with two different pump waves in a photorefractive Bi12TiO20 crystal with applied electric DC field. Both pump waves fall into the crystal at different locations (or at different times at the same location). A phase shift from steady state in the signal wave leads in both cases to different mixed signal intensities. Based on this, phase shifts of the incident signal wave can be measured with a resolution down to λ/50 (wavelength λ = 633 nm) and the sign of the phase shift can be determined.
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-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.
It is known that two-wave coupling in photorefractive crystal may result in an intensity-dependent phase shift as well as energy transfer between the two waves without phase crosstalk. In a sense, this kind of phase shift is similar to the intensity-dependent refractive-index effects in Kerr media. Consequently, optical bistability can be established in an optical cavity with a photorefractive crystal. We formulate the model and get the expected bistable transmission with numerical simulations. Several cases, including that of the codirectional coupling and the contradirectional coupling, are considered. The effects of the photorefractive crystal’s distribution absorption and the spatial phase shift between the index grating and the light interference pattern in the crystal on the nonlinear transmission characteristics have also been studied. It is interesting to note that the output of the pumping wave is dependent on the cavity intensity and thus shows bistable behavior with respect to the cavity input as well.