Andrey A. Chabanov

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.

Avoiding cracks in self-assembled photonic band-gap crystals

Thin colloidal crystals (or synthetic opals) composed of Stober silica spheres typically develop cracks when they are utilized to obtain photonic band-gap crystals (or inverted opals). We find that, by sintering the silica spheres prior to assembly of the opal, these cracks can be avoided. We report the effects of temperature and duration of the heat treatment on 850 nm silica spheres using electron microscopy, thermogravimetry, and light scattering. We also find a large dependence of the refractive index of the silica on the temperature of the heat treatment. This may allow tuning of the refractive index of silica spheres.

Random Lasing in Weakly Scattering Systems

We present detailed experimental and numerical studies of random lasing in weakly scattering systems. The interference of scattered light, which is weak in the passive systems, is greatly enhanced in the presence of high gain, providing coherent and resonant feedback for lasing. The lasing modes are confined in the vicinity of the pumped volume due to absorption of emitted light outside it. In the ballistic regime where the size of the gain volume is less than the scattering mean free path, lasing oscillation occurs along the direction in which the gain volume is most extended, producing directional laser output. The feedback for lasing originates mainly from backscattering of particles near the boundaries of the pumped region. It results in nearly constant frequency spacing of lasing modes, which scales inversely with the maximum dimension of the gain volume.

Breakdown of diffusion in dynamics of extended waves in mesoscopic media.

We report the observation of nonexponential decay of pulsed microwave transmission through quasi-one-dimensional random dielectric media signaling the breakdown of the diffusion model. The decay rate of transmission falls nearly linearly in time corresponding to a nearly Gaussian distribution of the coupling strengths of quasinormal electromagnetic modes to free space at the sample surfaces. The peak and width of this distribution scale as L(-2.05) and L(-1.81), respectively.

Photon Localization in Resonant Media

We report measurements of microwave transmission over the first five Mie resonances of alumina spheres randomly positioned in a waveguide. Though precipitous drops in transmission and sharp peaks in the photon transit time are found near all resonances, measurements of transmission fluctuations show that localization occurs only in a narrow frequency window above the first resonance. There the drop in the photon density of states is found to be more pronounced than the fall in the photon transit time above the resonance, leading to a minimum in the Thouless number.

Statistics of Dynamics of Localized Waves

The measured distribution of the single-channel delay time of localized microwave radiation and its correlation with intensity differ sharply from the behavior of diffusive waves. The delay time is found to increase with intensity, while its variance is inversely proportional to the fourth root of the intensity. The distribution of the delay time weighted by the intensity is found to be a double-sided stretched exponential to the 1/3 power centered at zero. The correlation between dwell time and intensity provides a dynamical test of photon localization.

Dynamic correlation in wave propagation in random media.

Field spectra are analyzed to yield the time-resolved statistics of pulsed transmission through quasi-one-dimensional dielectric media with static disorder. The normalized intensity correlation function with displacement and polarization rotation for an incident pulse of linewidth sigma at delay time t is a function only of the field correlation function, which is identical to that found for steady-state excitation, and of kappa(sigma)(t), the residual degree of intensity correlation at points at which the field correlation function vanishes. The dynamic probability distribution of normalized intensity depends only upon kappa(sigma)(t). Steady-state statistics are recovered in the limit sigma-->0, in which kappa(sigma=0) is the steady-state degree of correlation.

Strongly Resonant Transmission of Electromagnetic Radiation in Periodic Anisotropic Layered Media

Department of Physics and Astronomy, University of Texas, San Antonio, TX 78249(Dated: September 9, 2007)The electromagnetic dispersion in periodic layered media can be tailored and their resonant prop-erties can be considerably improved by utilizing anisotropic materials. Periodic structures with aphotonic band edge split into two parts, or so-called split band edge, exhibit superior resonant prop-ertiesincludingexceptionally high Q-valuesof transmission resonances andnearly perfectimpedancematching at the boundaries, even when the number of unit cells N is not large. A microwave trans-mission resonance with Q∼220 is demonstrated in a periodic stack of form-birefringent layers withN=12 realized in a waveguide geometry.

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, δ, 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 effect 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, κ. 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.

Mesoscopic correlation with polarization rotation of electromagnetic waves

Mesoscopic correlations are observed in the polarization of microwave radiation transmitted through a random waveguide. These measurements, supported by diagrammatic theory, permit an unambiguous decomposition of the intensity correlation function of a vector wave into short, long, and infinite range components. Infinite range correlation that leads to universal conductance fluctuations is measured and found to be in agreement with calculations. The long and infinite range components include nonuniversal frequency-independent terms associated with coupling into and out of the sample.