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Frontiers in Optics

Dynamic correlation in wave propagation in random media

Azriel Z. Genack, A. A. Chabanov, Ben Yu-Kuang Hu

Published Jan 1, 2004• 0 citations
Publisher

Abstract

The time-resolved intensity correlation function for an incident pulse of linewidth σ has a universal form in terms of the square of the time-independent field correlation function and the time-varying degree of intensity correlation, κσ(t). The probability distribution of intensity is determined exclusively by κσ(t).
DOI
10.1364/fio.2004.ftum6

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Transfer-matrix methods are used to study the probability distributions of spin-spin correlation functions G in the two-dimensional random-field Ising model, on long strips of width L=3-15 sites, for binary field distributions at generic distance R, temperature T, and field intensity h(0). For moderately high T, and h(0) of the order of magnitude used in most experiments, the distributions are singly peaked, though rather asymmetric. For low temperatures the single-peaked shape deteriorates, crossing over towards a double-delta ground-state structure. A connection is obtained between the probability distribution for correlation functions and the underlying distribution of accumulated field fluctuations. Analytical expressions are in good agreement with numerical results for R/L > or approximately 1, low T, h(0) not too small, and near G=1. From a finite-size ansatz at T=T(c)(h(0)=0), h(0)-->0, averaged correlation functions are predicted to scale with L(y)h(0), y=7/8. From numerical data we estimate y=0.875+/-0.025, in excellent agreement with theory. In the same region, the rms relative width W of the probability distributions varies for fixed R/L=1 as W approximately h(kappa)(0) f(L h(u)(0)) with kappa approximately 0.45, u approximately 0.8; f(x) appears to saturate when x-->infinity, thus implying W approximately h(kappa)(0) in d=2.