N. Garcia

Electromagnetic localization and photonics

We show that characteristics of localized waves in nonabsorbing media, such as narrow resonances, giant transmission fluctuations, strong spatial correlation, and extreme sensitivity to variations in the dielectric function of the medium, may make possible a new class of compact filters, transducers, and switches. Precursors of these effects are observed in microwave propagation through random mixtures of metallic and dielectric spheres.

Intensity Statistics and Correlation in Absorbing Random Media

Measurements of the distribution of normalized intensity of a single polarization component of microwave radiation transmitted through absorbing random dielectric samples contained in a copper tube are fit by an expression derived by Shnerb and Kaveh in the weak-correlation limit for non-dissipative systems. We show that the single parameter in the theory is one-half the degree of long-range correlation which is the inverse of the dimensionless conductance. The equivalence of these parameters and their weak dependence upon absorption suggests that the proximity to the localization threshold is nearly independent of absorption for extended waves. Systematic departures of calculated moments from the measured values indicate the contribution of higher-order corrections to the intensity distribution.

Influencing the approach to the localization threshold

Abstract We argue that the Thouless criterion for localization is universal. Because the Thouless number δ is the ratio of the width and spacing of the modes of the sample, it can be adjusted by changing the macroscopic characteristics of the sample, such as the transverse dimensions, the reflectivity at the boundaries and the character of internal microstructure resonances. We find the dependence of the correlation parameter δ-1 and hence of the proximity to the localization threshold upon these characteristics. These results are illustrated by microwave and optical experiments.

Intensity statistics and the finesse of electromagnetic radiation in random structures

The correlation function of microwave intensity with frequency shift is measured in random mixtures of Teflon and aluminum spheres at a metallic filling fraction of 0.20. We observe the first three terms in an expansion of the correlation function in a parameter that is the ratio of the spacing to the width of modes of the random medium. The expansion also applies to optical and electron waves. The expansion parameter is equivalent to the finesse of optical resonators. The intensity distribution at all sample thicknesses is found to be a stretched exponential.

Photon propagation and the statistics of electromagnetic modes in random media

We argue that the statistical character of wave propagation in random media can be described in terms of two universal parameters which are average properties of eigenmodes of the field. We show that the width and spacing of electromagnetic modes can be determined from the measurement of the intensity correlation function with frequency shift. The ratio δ of the typical level width to the spacing of modes, which is essentially the Thouless number, gives the proximity to the localization threshold. Its inverse δ-1 gives the degree of long range intensity correlation in the sample.

Long-range intensity correlation and the approach to localization

Abstract The influence of internal surface reflectivity is incorporated into a heuristic model of long-range intensity correlation. This allows us to identify the spatial intensity correlation function in a sample of randomly positioned polystyrene spheres as the sum of a first-order term in the correlation parameter κ, which falls linearly with detector separation, and a constant term, which is of order κ2. κ is a measure of the proximity to the localization threshold. In a sample which is a mixture of metallic and dielectric spheres and in which κ becomes large, the probability of large intensity fluctuations increases. The distribution of intensities is then found to be stretched exponential even for sample lengths which are comparable to the wavelength of the radiation.