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Field and intensity correlations in random media

Patrick Sebbah, Pnini, R., Genack, A. Z.

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

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.

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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.
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.
We have measured the correlation in frequency-dependent intensity fluctuations in the total transmission through random dielectric samples, using visible light in a (essentially) plane-wave geometry. The correlation function, of which the width at half maximum is proportional to ${\mathit{L}}^{\mathrm{\ensuremath{-}}2}$ (L is the thickness of the sample), decays as (\ensuremath{\Delta}\ensuremath{\omega}${)}^{\mathrm{\ensuremath{-}}1/2}$. This constitutes the experimental proof for the buildup of long-range intensity correlations in the propagation of classical waves by multiple scattering.
We investigate the fluctuations of light transmitted through static disordered media in time and frequency domains. When the pulse duration of the incident light is much shorter than the typical time of flight through the medium, fluctuations appear both in time and frequency domains and the uncertainty relation, δτδω∼1 or δτδE∼ℏ\delta \tau \delta E \sim \hbarδτδE∼ℏ, holds good in these fluctuations. We discuss the necessary condition to observe this relation. Precise calculations of the correlation functions also reveal that the exact shape and width of the correlation functions depend on the pulse duration and the observation time. Experimental results with picosecond pulses through thick and thin samples show good agreement with the theoretical calculations.
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