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Journal of the Optical Society of America B

Signal-to-pump ratio dependence of buildup and decay rates in photorefractive nonlinear two-beam coupling

Moshe Horowitz, Ron Daisy, Baruch Fischer

Published Sep 1, 1992• 18 citations
Publisher

Abstract

The buildup and the decay of photorefractive two-beam coupling are experimentally demonstrated to be strongly dependent on the intensity ratio of the two beams (signal-to-pump ratio). The experiment, done with a BaTiO3 crystal, shows good agreement with the theory of two-beam coupling in the depleted-pump regime. The deviation of the response behavior from the small-signal regime is seen for ratios as small as ∼10−5. These results are significant for applications of two-beam coupling as gain media, especially for the elimination of amplified noise (fanning).

DOI
10.1364/josab.9.001685

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Applied Physics Letters•Mar 30, 1992•2 citations
The buildup and the decay of photorefractive two-beam coupling are experimentally demonstrated to be strongly dependent on the intensity ratio of the two beams (signal-to-pump ratio). The experiment, done with a BaTiO3 crystal, shows good agreement with the theory of two-beam coupling in the depleted-pump regime. The deviation of the response behavior from the small-signal regime is seen for ratios as small as ∼10−5. These results are significant for applications of two-beam coupling as gain media, especially for the elimination of amplified noise (fanning).
Transfer of temporal fluctuations between the signal and pump beams in diffusion dominated photorefractive two-beam coupling is studied experimentally. The dependence on the gain, beam intensity ratio, and frequency of the fluctuations is found to agree well with a linearized analysis. The transfer of perturbations is frequency dependent at low frequencies, and becomes constant at frequencies large compared to the inverse material time constant. We discuss the possibility of pump noise suppression when amplifying weak signals.
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.
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.
While the interaction of optical beams in photorefractive crystals can often be accurately described in terms of 1-D plane-wave approximation, 2-D models are sometimes more suitable, as suggested by recent work.1 Here we discuss some aspects of photorefractive interaction of finite size optical beams. We have solved the system of partial differential equations governing two- and four-wave mixing numerically by using iterative procedures. Simulations of beam amplification in two-beam coupling show strong beam deformation even without any spatial information imposed on them. Spatially nonuniform energy transfer is responsible for this effect. The pump beam loses energy during propagation and at the end of its passage through the beam intersection region (which was completely inside the crystal) it is strongly depleted and cannot contribute significantly to beam amplification. As the pump beam crosses through the probe, it amplifies most strongly that side of the probe that it meets first. By the time the pump has reached the far side of the probe, it is strongly depleted and less effective at probe amplification. In the case of phase conjugation through four-wave mixing, we found that the conjugate beam is strongly deformed only when the coupling constant is negative (corresponding to deamplification of the probe input beam). For positive coupling constants the output conjugate beam is a good replica of the input probe beam.
It has been shown recently (see, e.g., Nature, 397, 594, 1999; 409, 490, 2001) that light pulses can be remarkably slowed down in resonant gases under very low temperatures. We show theoretically and experimentally that a similar in nature (and stronger in value) phenomenon occurs in photorefractive nonlinear media. The pulse-maximum velocity can be reduced here to the value of thickness/response time because of the two wave coupling effect. Specific properties of pulse propagation depend on the type of the photorefractive response and also duration and shape of the input pulse. Our theoretical results for the nonlocal nonlinear response are in a good agreement with experimental data obtained with BaTiO3 and Sn2P2S6 crystals.