Temporal fluctuations of waves in weakly nonlinear disordered media

Abstract

We consider the multiple scattering of a scalar wave in a disordered medium with a weak nonlinearity of Kerr type. The perturbation theory, developed to calculate the temporal autocorrelation function of scattered wave, fails at short correlation times. A self-consistent calculation shows that for nonlinearities exceeding a certain threshold value, the multiple-scattering speckle pattern becomes unstable and exhibits spontaneous fluctuations even in the absence of scatterer motion. The instability is due to a distributed feedback in the system "coherent wave + nonlinear disordered medium". The feedback is provided by the multiple scattering. The development of instability is independent of the sign of nonlinearity.

Dynamic instability of speckle patterns in nonlinear random media

“…where ∆I(r) denotes the change of intensity during the time ∆t, we take into account the fact that the nonlinear part of the refractive index is simply n 2 I(r) in the considered case of instantaneous nonlinearity, and the integral is along the wave path. In the limit of weak nonlinearity, it can be shown 40,49 that the mean values of both ∆φ L and ∆φ NL are zeroes, while their variances are related by ∆φ 2 NL = ∆φ 2 L k 2 n 2 2 × s 0 ds 1 s 0 ds 2 δI(r 1 )δI(r 2 ) , (16) where both integrals are along the same diffusion path. Because we have assumed nonlinearity to be weak, we can proceed by perturbation and replace the correlation function of intensity fluctuations δI(r 1 )δI(r 2 ) in Eq.…”

Diffusing-wave spectroscopy of nonergodic media

“…can be taken into account within the framework of the diffusion model. Recently, the theory of DWS has been extended to nonlinear random media [45,46].…”

Propagation of nonlinear waves in disordered media

“…To estimate the instability threshold it is sufficient to expand the nonlinear Langevin equations in powers of β (see diagrams shown in Fig.2 in [7], or in Fig.4 in [14]). This is why the authors of [13][14][15] were able to reproduce the instability criterion γ > 1 obtained in [7].…”