Weakly multimode dynamics of a photorefractive oscillator

Abstract

The dynamics of a photorefractive oscillator has been studied in the weakly multimode case. It is shown that the eigenmodes of the empty cavity provide the bases in which the transverse patterns of this oscillator should be analysed. The concept of mode families I.e. sets of frequency degenerate modes, is very efficient to classify the different ranges of operation of the oscillator with Fresnel number up to 5-7. As the complexity of the pattems increases, the interpretation in terms of optical defects or phase singularities greatly simplifies the analysis. Photorefractive materials have been shown to be efficient in many applications, such as pattern recognition, volume hologriphic storage, phase conjugated lasers, II. The knowledge and the understanding of the dynamics that they could develop when they are placed inside a cavity is important from two points of view (I) they can help in building devices whose stable pattems are used as a basis for the manipulation of complex images, for example by reducing images to the components of their projection on a limited number of « eigen-patterns » (2) (it) more fundamentally, photorefractive oscillators (PRO) have analogies with lasers (3), and thus could contribute to understand the spatio-temporal dynamics of nonlinear optical systems. Indeed, some properties of PROS, and in particular their relatively long response time, allow us to access more easily to the inforrnation needed to analyse the spatio-temporal behavior of nonlinear optical systems. In fact, as the analogy with lasers has been demonstrated through the Ginzburg-Landau equation, dynamics of photorefractive oscillators should show analogies with a much larger class of physical systems, namely those in which complex spatio-temporal behaviors lead to turbulence. In order to determine the basic mechanisms of transverse dynamics in nonlinear optical systems, we have chosen to study first the behavior of a simple system with few spatio- temporal degrees of freedom. Here we have used an optical cavity whose gain is provided by two-wave mixing (2 WM) in a photorefractive crystal, and with small transverse dimensions such that only few modes are able to oscillate in the empty cavity. By varying the diameter of an intracavity aperture, we change the number of degrees of freedom of the transverse variables and study the evolution of transverse patterns in situations of different complexity. The dynamics is interpreted in terms of the empty-cavity modes (ec modes) and of their