Short-range interference effect in the diffusion of light in random media

We study the interference effect of multiply scattered waves in the diffusive light propagation in random media. We take porous glass samples of various pore radii $a$ as an example of random media, and measure the transport mean free path $l^{*}$ and the diffusion constant $D$ for various light wavelengths $\lambda$ over a wide range of the size parameter $a/\lambda =0.05\mathrm{}$–0.85. A crossover is observed from the Rayleigh scattering region to the geometrical optics region. The transport velocity $v_{\mathrm{E}}{=3D/l}^{*}$ determined from the data is found to decrease monotonically with $a/\lambda ,$ falling well below the light velocity in glass. We also present a framework of theoretical analysis of wave energy diffusion in a most general setting, taking explicit account of the broadening of light dispersion and paying attention to the requirement of Ward-Takahashi identity. We calculate diffusion parameters as functions of $a/\lambda$ for a model of spatially fluctuating dielectric constant, using two types of self-consistent scattering approximation to the self-energy and the scattering kernel. Comparison of the experiment against the calculation with and without interference terms of multiple scattering reveals the importance of short-range interference effects in the diffusive propagation of light.