Signatures of photon localization

Signatures of photon localization are observed in a constellation of transport phenomena which reflect the transition from diffusive to localized waves. The dimensionless conductance, g, and the ratio of the typical spectral width and spacing of quasimodes, \delta, are key indicators of electronic and classical wave localization when inelastic processes are absent. However, these can no longer serve as localization parameters in absorbing samples since the affect of absorption depends upon the length of the trajectories of partial waves traversing the sample, which are superposed to create the scattered field. A robust determination of localization in the presence of absorption is found, however, in steady-state measurements of the statistics of radiation transmitted through random samples. This is captured in a single parameter, the variance of the total transmission normalized to its ensemble average value, which is equal to the degree of intensity correlation of the transmitted wave, \kappa. The intertwined effects of localization and absorption can also be disentangled in the time domain since all waves emerging from the sample at a fixed time delay from an exciting pulse, t, are suppressed equally by absorption. As a result, the relative weights of partial waves emerging from the sample, and hence the statistics of intensity fluctuations and correlation, and the suppression of propagation by weak localization are not changed by absorption, and manifest the growing impact of weak localization with t.Comment: RevTex 16 pages, 12 figures; to appear in special issue of J. Phys. A on quantum chaotic scatterin

Extended quasimodes within nominally localized random waveguides

We have measured the spatial and spectral dependence of the microwave field inside an open absorbing waveguide filled with randomly juxtaposed dielectric slabs in the spectral region in which the average level spacing exceeds the typical level width. Whenever lines overlap in the spectrum, the field exhibits multiple peaks within the sample. Only then is substantial energy found beyond the first half of the sample. When the spectrum throughout the sample is decomposed into a sum of Lorentzian lines plus a broad background, their central frequencies and widths are found to be essentially independent of position. Thus, this decomposition provides the electromagnetic quasimodes underlying the extended field in nominally localized samples. When the quasimodes overlap spectrally, they exhibit multiple peaks in space.Comment: 4 pages, submitted to PRL (23 December 2005

Measurement of the Probability Distribution of Total Transmission in Random Waveguides

Measurements have been made of the probability distribution of total transmission of microwave radiation in waveguides filled with randomly positioned scatterers which would have values of the dimensionless conductance g near unity. The distributions are markedly non-Gaussian and have exponential tails. The measured distributions are accurately described by diagrammatic and random matrix calculations carried out for nonabsorbing samples in the limit g >> 1 when g is expressed in terms of the variance of the distribution, which equals the degree of long-range intensity correlation across the output face of the sample.Comment: 5 pages, 5 post script figures, RevTe

Field and intensity correlations in random media

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.Comment: 9 pages, 5 figures, submitted to Phys.Rev.

Crossover from Conserving to Lossy Transport in Circular Random Matrix Ensembles

In a quantum dot with three leads the transmission matrix t_{12} between two of these leads is a truncation of a unitary scattering matrix S, which we treat as random. As the number of channels in the third lead is increased, the constraints from the symmetry of S become less stringent and t_{12} becomes closer to a matrix of complex Gaussian random numbers with no constraints. We consider the distribution of the singular values of t_{12}, which is related to a number of physical quantities. Changing the number of channels in the third lead corresponds to increasing the amount of loss in the system (and is distinct from prior uses of a third lead to model dephasing)

Universal and nonuniversal scaling of transmission in thin random layered media

The statistics of transmission through random 1D media are generally presumed to be universal and to depend only upon a single dimensionless parameter, the ratio of the sample length and the mean free path, s=L/l. For s much larger than unity, the probability distribution function of the logarithm of transmission, P(ln T) is Gaussian with average value -s and variance 2s. Here we show in numerical simulations and optical measurements that in random binary systems, and most prominently in systems for which s less than unity, the statistics of transmission are universal for transmission near an upper cutoff of unity and depend upon the character of the discrete disorder near a lower cutoff. The universal behavior of P(ln T) closely resembles a segment of a Gaussian and arises in random binary media with as few as three binary layers. Above the lower cutoff, but below the crossover to a universal expression, the shape of P(ln T) also depends upon the reflectivity of the interface between the layers. For a given value of s, P(ln T) evolves towards a universal distribution given by random matrix theory in the dense weak scattering limit as the numbers of layers increases. P(ln T) found in simulations is compared to results of random matrix calculations in the dense weak scattering limit but with an imposed minimum in transmission. Optical measurements in stacks of glass coverslips are compared to random matrix theory, and differences are ascribed to transverse disorder in the layers.Comment: 7 pages, 7 figure