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Photorefractive Effects, Materials, and Devices

Double two-wave mixing with photorefractive crystals for measurement of sign and modulo of phase changes with high resolution

Gregor Cedilnik, Matthias Esselbach, Armin Kießling, Richard M. Kowarschik

Published Jan 1, 1999• 0 citations
Publisher

Abstract

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.

DOI
10.1364/apmed.1999.wmpc4

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When a weak optical signal is injected in a photorefractive crystal illuminated with a strong pump beam, it experiences gain via a two-wave mixing process.(1) A problem common to these amplifiers is the presence of noise sources that corrupt the quality of the emerging amplified optical signal. We propose and experimentally demonstrate the first technique, to our knowledge, capable of very significantly reducing the optical noise while maintaining high gain coefficients. Consider two-wave mixing in a slowly rotating crystal. First, we estimate the influence of a crystal rotation (angular velocity Ω around the point O) on the noise intensity in the output plane (Fig. 1a). A noise source located around point A radiates a complex wavefront whose component along the direction of the injected signal is represented by a plane wave of intensity IN (A is a crystal imperfection or interface). It is essential to note that the noise sources are bounded to the crystal and will consequently move with it. This is the basis for the process of discrimination between the noise gratings and the injected signal grating. In the Ox coordinate bounded to the rotating crystal, the interference pattern responsible for the formation of a noise grating around the point A is given by: IN(x,t) = I0 [1 + mN cos KN(t)x], where KN(t) ~ 2π(θ + Ωt)/λ is the time-dependent grating wave vector (we have assumed that the angles inside the crystal are small), I0 is the total incident intensity (I0 ~ IP0), θ is the angle between the beams inside the crystal, λ = λ0/n is the optical wavelength in the crystal with refractive index n, and mN is the fringe modulation.

Photorefractive Effects, Materials, and Devices•Jan 1, 1990•0 citations
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.
We present measurements of the two-wave mixing gain as a function of frequency detuning in photorefractive crystals. In many cases, this function is asymmetric, indicating that the phase shift of the photorefractive inde grating with respect to the light interference pattern is not exactly 90 degrees , as is often assumed. In four-wave mixing, the phase of the phase-conjugate wave contains the phase of the pumping and probe waves and a phase shift determined by the interaction taking place in the nonlinear medium. This second term, the phase shift of the phase conjugator, is a function of the type of grating and the phase shift of this grating. The phase shift of the grating obtained from the two-wave mixing measurements compares well with that obtained from four-wave mixing measurements of the phase of the phase conjugator.
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.
When a weak optical signal is injected in a photorefractive crystal illuminated with a strong pump beam, it experiences gain via a two-wave mixing process.(1) A problem common to these amplifiers is the presence of noise sources that corrupt the quality of the emerging amplified optical signal. We propose and experimentally demonstrate the first technique, to our knowledge, capable of very significantly reducing the optical noise while maintaining high gain coefficients. Consider two-wave mixing in a slowly rotating crystal. First, we estimate the influence of a crystal rotation (angular velocity Ω around the point O) on the noise intensity in the output plane (Fig. 1a). A noise source located around point A radiates a complex wavefront whose component along the direction of the injected signal is represented by a plane wave of intensity IN (A is a crystal imperfection or interface). It is essential to note that the noise sources are bounded to the crystal and will consequently move with it. This is the basis for the process of discrimination between the noise gratings and the injected signal grating. In the Ox coordinate bounded to the rotating crystal, the interference pattern responsible for the formation of a noise grating around the point A is given by: IN(x,t) = I0 [1 + mN cos KN(t)x], where KN(t) ~ 2π(θ + Ωt)/λ is the time-dependent grating wave vector (we have assumed that the angles inside the crystal are small), I0 is the total incident intensity (I0 ~ IP0), θ is the angle between the beams inside the crystal, λ = λ0/n is the optical wavelength in the crystal with refractive index n, and mN is the fringe modulation.