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Europhysics Letters (EPL)

On the speckle correlation in nonlinear random media

R. Bressoux, R. Maynard

Published May 15, 2000• 8 citations
Publisher

Abstract

We calculate the intensity-intensity correlation functions for the light transmitted through a slab made of a nonlinear and random medium at the lowest order of the nonlinear interaction. We obtain the short-range correlation function as a function of the intensity and angles: it depends on a characteristic length of the nonlinear system. This characteristic length decribes the loss of correlation due to the phase shift through the change of the refractive index inside the nonlinear random medium.

DOI
10.1209/epl/i2000-00286-8

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We calculate the intensity-intensity correlation functions for the light transmitted through a slab made of a nonlinear and random medium at the lowest order of the nonlinear interaction. We obtain the short-range correlation function as a function of the intensity and angles: it depends on a characteristic length of the nonlinear system. This characteristic length decribes the loss of correlation due to the phase shift through the change of the refractive index inside the nonlinear random medium.
Measurements of the microwave field transmitted through a random medium allows direct access to the field correlation function, whose complex square is the short range or C1 contribution to the intensity correlation function C. The frequency and spatial correlation function are compared to their Fourier pairs, the time of flight distribution and the specific intensity, respectively. The longer range contribution to intensity correlation is obtained directly by subtracting C1 from C and is in good agreement with theory.
In this complement we discuss several examples of optical phenomena in media where the refractive index depends nonlinearly on the intensity , known as optical Kerr media. This nonlinear effect exists in all materials, even isotropic ones, like glass or fused silica, but it is particularly marked in certain physical systems to be exemplified in Section 7B.1. After investigating the propagation of light through such media in Section 7B.2, we shall discuss three applications of the optical Kerr effect (which can be studied in any order). We begin by describing a bistable optical system , when this nonlinear medium is inserted in a Fabry–Perot cavity (Section 7B.3). We then study phase conjugate mirrors and examine their potential applications in adaptive optics (Section 7B.4). Finally, we discuss certain effects occurring during the propagation of an isolated wave, bounded either transversely or temporally, in a Kerr medium, and describe self-focusing effects (Section 7B.5) and self-phase-modulation effects (Section 7B.6). In particular, we shall show that nonlinear effects and dispersion effects can compensate to produce stable structures known as solitons , which maintain their shape during propagation. Examples of third-order nonlinearities Nonlinear response of two-level atoms We begin by studying a simple case of a nonlinear interaction, namely a two-level quantum system under the effects of a plane wave.