Statistical signatures of photon localization

The realization that electron localization in disordered systems (Anderson localization) is ultimately a wave phenomenon has led to the suggestion that photons could be similarly localized by disorder. This conjecture attracted wide interest because the differences between photons and electrons--in their interactions, spin statistics, and methods of injection and detection--may open a new realm of optical and microwave phenomena, and allow a detailed study of the Anderson localization transition undisturbed by the Coulomb interaction. To date, claims of three-dimensional photon localization have been based on observations of the exponential decay of the electromagnetic wave as it propagates through the disordered medium. But these reports have come under close scrutiny because of the possibility that the decay observed may be due to residual absorption, and because absorption itself may suppress localization. Here we show that the extent of photon localization can be determined by a different approach--measurement of the relative size of fluctuations of certain transmission quantities. The variance of relative fluctuations accurately reflects the extent of localization, even in the presence of absorption. Using this approach, we demonstrate photon localization in both weakly and strongly scattering quasi-one-dimensional dielectric samples and in periodic metallic wire meshes containing metallic scatterers, while ruling it out in three-dimensional mixtures of aluminium spheres.

Delay-time statistics for diffuse waves.

We formulate a theory for the statistics of the dynamics of a classical wave propagating in random media by analyzing the frequency derivative of the phase under the assumption of a Gaussian process. We calculate frequency correlations and probability distribution functions of dynamical quantities, as well the first non-Gaussian C2 correction. In A. Z. Genack, P. Sebbah, M. Stoytchev, and B. A. van Tiggelen, Phys. Rev. Lett. 82, 715 (1999), microwave measurements have been performed to which this theory applies.

Observations of non-Rayleigh statistics in the approach to photon localization.

We measure the distribution of intensity of microwave radiation transmitted through absorbing random waveguides of lengths L up to localization length xi . For large intensity values the distribution is given by a negative stretched exponential to the 1/2 power, in agreement with predictions by Nieuwenhuizen and van Rossum [Phys. Rev. Lett. 74, 2674 (1995)] for diffusing waves in nonabsorbing samples, as opposed to a negative exponential given by Rayleigh statistics. The intensity distribution is well described by a transform derived by Kogan and Kaveh [Phys. Rev. B 52, R3813 (1995)] of the measured distribution of total transmission.