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Photorefractive Effects, Materials, and Devices

Two-wave coupling under fast phase modulation

Klaus H. Ringhofer, Vladimir P. Kamenov, Boris I. Sturman, Alexander I. Chernykh, V. Ya. Gayvoronsky

Published Jan 1, 1999• 0 citations
Publisher

Abstract

Using the distinctive features of the photorefractive nonlinearity, we solve exactly the problem of the influence of an arbitrary (in strength and shape) fast phase modulation on 2W-coupling. We show that the fast modulation is a useful tool for shaping the characteristics of wave coupling, such as the value of the energy exchange and the diffraction efficiency of the recorded grating.

DOI
10.1364/apmed.1999.wmpc5

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Using the distinctive features of the photorefractive nonlinearity, we solve exactly the problem of the influence of an arbitrary (in strength and shape) fast phase modulation on 2W-coupling. We show that the fast modulation is a useful tool for shaping the characteristics of wave coupling, such as the value of the energy exchange and the diffraction efficiency of the recorded grating.
Using the distinctive features of the photorefractive nonlinearity, we derive a general self-consistent set of equations to describe two-wave coupling in the presence of fast and arbitrary strong-phase modulation. By considering a number of important particular cases, we show that phase modulation is a powerful and useful tool for shaping the characteristics of two-wave coupling such as the value of the energy exchange, the diffraction efficiency of the recorded grating, and the structure of the grating fringes. Finally, we analyze the role of the phase modulation in the active stabilization of wave coupling by means of an electronically introduced phase feedback.
We show that a certain phase feedback between output and input changes dramatically the characteristics of photorefractive two-beam coupling. The diffraction efficiency of the dynamic phase grating, $\ensuremath{\eta}$, reaches 1 or 0 (depending on the feedback sign) within a finite time for a wide range of experimental parameters. The spatial-temporal behavior of the wave amplitudes is strongly nonlinear and the grating fringes for $\ensuremath{\eta}=1$ or 000 are bended but not tilted. The theory elucidates a number of empirical observations and reveals the great potential of active stabilization for applications.
We present a closed-form solution for the two-wave coupling process, resulting in a solution with an interesting part, the arbitrary function Lambda(t), not being considered in the previous works. In the photorefractive medium, it has been shown that a moving grating will produce a phase shift in the coupling constant. To our knowledge, this has not been derived directly from the grating dynamic equations. We will also show that the temporal dynamics does not have any asymptotically stable equilibrium points of an exponential form. As an example, we have developed resonance conditions resulting in a new expression for the frequency detuning of a resonator with a photorefractive gain medium.
Here we present four wave mixing configuration as one of the most important methods of generation and explanation of process of generation phase conjugation light the coupled equation was solved by three methods: undepleted pump approximation exact solution and two wave mixing approximation. Although exact solutions can be derived for four-wave mixing, the results are difficult to use because of the complicated transcendental equation involved. Solved the coupled equations and introduce an approximation in which two-wave mixing is the dominant process.
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.