Static and dynamic transport of light close to the Anderson localization transition

Abstract

Anderson localization of light refers to an inhibition of wave transport in scattering media due to the interference of multiple scattered waves. We present wavelength dependent midinfrared optical transport measurements in slabs of randomly packed germanium (Ge) micron-sized particles, using a free electron laser as a tunable source of pulsed radiation. Because of their high refractive index and low absorption, Ge and similar semiconductors are excellent systems to study Anderson localization of light. To characterize the samples fully, we have employed several complementary optical techniques: total diffuse transmission, total diffuse reflection, coherent transmission, and time-resolved speckle interferometry. In this way we obtained the scattering ${(l}_s)$ and transport (l) mean free paths, the absorption coefficient $\left(\alpha \right),$ the diffusion constant $\mathrm{}\left(D\right),$ and the energy transport velocity ${(v}_e).\mathrm{}$ These measurements have been made as a function of midinfrared wavelength, so that the scattering cross section and absorption coefficients can be varied in the same samples. We found that the Ge samples are close ${(kl}_s\approx 3)$ to the localization transition, but still above it. Our measurements of $l_s$ and l suggest that l is renormalized due to interference at the proximity of the localization transition. We also found that the diffusion constant is significantly reduced in samples thinner than $\approx 7l.$