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Light transport in a dilute photonic crystal is considered. The analytical expression for the transmission coefficient is derived.Straightening of light under certain conditions in a one-dimensional photonic crystal is predicted. Such behavior is caused by the formation of a localized state in transversal motion. The main contribution to the central diffracted wave transmission coefficient is due to states, that either close to the conductance bands bottom or deeply localized in the forbidden gap. Both these states suppress mobility in the transverse direction and force light to be straightened. Straightening of light in the optical region along with small reflection make these systems very promising for use in solar cells., Comment: 8pages, 2figures

We investigate, experimentally and theoretically, polarization rotation effects in dilute photonic crystals with transverse permittivity inhomogeneity perpendicular to the traveling direction of waves. A capsize, namely a drastic change of polarization to the perpendicular direction is observed in a one-dimensional photonic crystal in the frequency range $10\div 140$ GHz. To gain more insights into the rotational mechanism, we have developed a theoretical model of dilute photonic crystal, based on Maxwell's equations with a spatially dependent two dimensional inhomogeneous dielectric permittivity. We show that the polarization's rotation can be explained by an optical splitting parameter appearing naturally in Maxwell's equations for magnetic or electric fields components. This parameter is an optical analogous of Rashba like spin-orbit interaction parameter present in quantum waves, introduces a correction to the band structure of the two-dimensional Bloch states, creates the dynamical phase shift between the waves propagating in the orthogonal directions and finally leads to capsizing of the initial polarization. Excellent agreement between theory and experiment is found., Comment: 11pages,6figures

Light transport in a metal with two-dimensional hole arrays is considered. Analytical expression for a transmission coefficient in periodic, isolated and disordered cases are derived, assuming the existence of waveguide modes transverse tunneling in two-dimensional plane perpendicular to traveling direction of light. The one dimensional case of periodic holes, due to its simplicity, is investigated in detail. In the dilute metal regime, when metal fraction is small, our numerical study of the transmission coefficient of central diffracted wave indicates the existence of a minimum which is completely independent of an incident wavelength. Further increasing of metal fraction leads to the unusual monotonic increasing of central diffracted wave transmission. The role of the surface plasmons is discussed., Comment: 14pages, 2figures

The origin of continuous energy spectra in large disordered interacting quantum systems is one of the key unsolved problems in quantum physics. While small quantum systems with discrete energy levels are noiseless and stay coherent forever in the absence of any coupling to external world, most large-scale quantum systems are able to produce thermal bath and excitation decay. This intrinsic decoherence is manifested by a broadening of energy levels which aquire a finite width. The important question is what is the driving force and the mechanism of transition(s) between two different types of many-body systems - with and without intrinsic decoherence? Here we address this question via the numerical study of energy level statistics of a system of spins-1/2 with anisotropic exchange interactions and random transverse fields. Our results present the first evidence for a well-defined quantum phase transition between domains of discrete and continous many-body spectra in a class of random spin models. Because this model also describes the physics of the superconductor-insulator transition in disordered superconductors like InO and similar materials, our results imply the appearance of novel insulating phases in the vicinity of this transition., Comment: 18 pages, 7 figures, original version of the paper accepted for publication (in slightly revised form) in Nature Communications

In the weak disordered regime we provide analytical expressions for the electron localization lengths in quasi-one dimensional (Q1D) disordered quantum wire with hard wall and periodic boundary conditions. They are exact up to order $W^2$ ($W$ being the disorder strength) for an arbitrary number of channels. Detailed numerical analysis of the Anderson localization, based on Kubo's formula for conductivity, show excellent agreement with analytical calculations. We establish relationship between various lengths in Q1D systems., Comment: RevTex4, 4 two-column pages, 3 .eps figures

The propagation of waves in highly inhomogeneous media is a problem of interest in multiple fields including seismology, acoustics and electromagnetism. It is also relevant for technological applications such as the design of sound absorbing materials or the fabrication of optically devices for multi-wavelength operation. A paradigmatic example of a highly inhomogeneous media is one in which the density or stiffness has fractal or multifractal properties. We investigate wave propagation in one dimensional media with these features. We have found that, for weak disorder, localization effects do not arrest wave propagation provided that the box fractal dimension D of the density profile is D < 3/2. This result holds for both fractal and multifractal media providing thus a simple universal characterization for the existence of localization in these systems. Moreover we show that our model verifies the scaling theory of localization and discuss practical applications of our results., Comment: 4 pages, 5 figures

We provide evidence that as a general rule Anderson localization effects become weaker as the degree of differentiability of the disordered potential increases. In one dimension a band of metallic states exists provided that the disordered potential is sufficiently correlated and has some minimum degree of differentiability. Several examples are studied in detail. In agreement with the one parameter scaling theory the motion in the metallic region is ballistic if the spectral density is smooth. Finally, we study the most promising settings to observe these results in the context of cold atoms., Comment: 5 pages, 3 figures, journal version

We study the dependence on the spatial dimensionality of different quantities relevant in the description of the Anderson transition by combining numerical calculations in a $3 \leq d \leq 6$ disordered tight binding model with theoretical arguments. Our results indicate that, in agreement with the one parameter scaling theory, the upper critical dimension for localization is infinity. Typical properties of the spectral correlations at the Anderson transition such as level repulsion or a linear number variance are still present in higher dimensions though eigenvalues correlations get weaker as the dimensionality of the space increases. It is argued that such a critical behavior can be traced back to the exponential decay of the two-level correlation function in a certain range of eigenvalue separations. We also discuss to what extent different effective random matrix models proposed in the literature to describe the Anderson transition provide an accurate picture of this phenomenon. Finally, we study the effect of a random flux in our results., Comment: RevTex4, 8 two-column pages, 5 .eps figures

Anderson localization is a universal quantum feature caused by destructive interference. On the other hand chiral symmetry is a key ingredient in different problems of theoretical physics: from nonperturbative QCD to highly doped semiconductors. We investigate the interplay of these two phenomena in the context of a three-dimensional disordered system. We show that chiral symmetry induces an Anderson transition (AT) in the region close to the band center. Typical properties at the AT such as multifractality and critical statistics are quantitatively affected by this additional symmetry. The origin of the AT has been traced back to the power-law decay of the eigenstates; this feature may also be relevant in systems without chiral symmetry., Comment: RevTex4, 4 two-column pages, 3 .eps figures, updated references, final version as published in Phys. Rev. B

We study spectral statistics of a Gaussian unitary critical ensemble of almost diagonal Hermitian random matrices with off-diagonal entries $<|H_{ij}|^{2} > \sim b^{2} |i-j|^{-2}$ small compared to diagonal ones $<|H_{ii}|^{2} > \sim 1$. Using the recently suggested method of {\it virial expansion} in the number of interacting energy levels (J.Phys.A {\bf 36},8265 (2003)), we calculate a coefficient $\propto b^{2}\ll 1$ in the level compressibility $\chi(b)$. We demonstrate that only the leading terms in $\chi(b)$ coincide for this model and for an exactly solvable model suggested by Moshe, Neuberger and Shapiro (Phys.Rev.Lett. {\bf 73}, 1497 (1994)), the sub-leading terms $\sim b^{2}$ being different. Numerical data confirms our analytical calculation., Comment: several typos and the unfolding factor are corrected, Erratum has been added

This paper presents the new photometer CE318-T, able to perform daytime and night-time photometric measurements using the sun and the moon as light source. Therefore,this new device permits a complete cycle of diurnal aerosol and water vapour measurements valuable to enhance atmospheric monitoring to be extracted. In this study wehave found significantly higher precision of triplets when comparing the CE318-T master instrument and the Cimel AErosol RObotic NET work (AERONET) master (CE318-AERONET) triplets as a result of the new CE318-T tracking system. Regarding the instrument calibration, two new methodologies to transfer the calibration from a reference instrument using only daytime measurements (Sun Ratio and Sun-Moon gain factor techniques) are presented and discussed. These methods allow the reduction of the previous complexities inherent to nocturnal calibration. A quantitative estimation of CE318-T AOD uncertainty by means of error propagation theory during daytime revealed AOD uncertainties (u(sup D)(sub AOD)) for Langley-calibrated instruments similar to the expected values for other reference instruments (0.002-0.009). We have also found u(sup D)(sub AOD) values similar to the values reported in sun photometry for field instruments (approximately 0.015). In the case of the night-time period, the CE318-T-estimated standard combined uncertainty (u(sup N)(sub AOD)) is dependent not only on the calibration technique but also on illumination conditions and the instrumental noise. These values range from 0.011-0.018 for Lunar Langley-calibrated instruments to 0.012-0.021 for instruments calibrated using the Sun Ratio technique. In the case of moon-calibrated instruments using the Sun-Moon gain factor method and sun calibrated using the Langley technique, we found u(sup N)(sub AOD) ranging from 0.016 to 0.017 (up to 0.019 in 440 nm channel), not dependent on any lunar irradiance model. A subsequent performance evaluation including CE318-T and collocated measurements from independent reference instruments has served to assess the CE318-T performance as well as to confirm its estimated uncertainty. Daytime AOD evaluation, performed at Izana station from March to June 2014, encompassed measurements from a reference CE318-T, a CE318-AERONET master instrument, a Precision Filter Radiometer (PFR) and a Precision Spectroradiometer (PSR) prototype, reporting low AOD discrepancies between the four instruments (up to 0.006). The nocturnal AOD evaluation was performed using CE318-T- and starphotometer-collocated measurements and also by means of a day/night coherence transition test using the CE318-T master instrument and the CE318 daytime data from the CE318-AERONET master instrument. Results showed low discrepancies with the star photometer at 870 and 500 nm channels(less tna or equal to 0.013) and differences with AERONET daytime data (1 h after and before sunset and sunrise) in agreement with the estimated u(sup N)(sub AOD) values at all illumination conditions in the case of channels within the visible spectral range, and only for high moon's illumination conditions in the case of near infrared channels. Perceptible water vapour (PWV) validation showed a good agreement between CE318-T and Global Navigation Satellite System (GNSS) PWV values for all illumination conditions, within the expected precision for sun photometry. Finally, two case studies have been included to highlight the ability of the new CE318-T to capture the diurnal cycle of aerosols and water vapour as well as short-term atmospheric variations, critical for climate studies.