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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Shaping of photorefractive two-wave coupling by fast phase modulation

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

Published Feb 1, 2000• 17 citations
Publisher

Abstract

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.

DOI
10.1103/physreve.61.2029

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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.
Recording of localized transmission gratings by four-wave mixing in non-local photorefractive media with strong response is considered. The input conditions to record dynamic gratings with a stable grating amplitude distribution as well as grating amplitude oscillations are defined. They are determined both by intensities and by a phase difference of input waves. The influence of fluctuations of wave phases on stability of the recorded gratings is considered. Methods of optical control of both the grating amplitude localization degree and the grating amplitude location are defined.