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.

• Received 23 January 1998

DOI:https://doi.org/10.1103/PhysRevB.58.6180