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Applied Physics Letters

Transfer of temporal fluctuations in photorefractive two-beam coupling

Sussie Juul Jensen, Mark E. Saffman

Published Mar 24, 1997• 0 citations
Publisher

Abstract

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.

DOI
10.1063/1.118640

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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.
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).
A theoretical analysis is presented of two-wave mixing in photorefractive materials in which the complex amplitude of a weak signal beam has slowly varying but otherwise arbitrary spatial dependence and arbitrary time variation. The set of coupled partial differential equations that couple the dynamics of the optical fields to the photorefractive medium is solved analytically to give the complex amplitude of the transmitted signal in the undepleted pump regime. The results are compared with known results for the transient two-wave mixing of plane waves.
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.