Degree of polarization of light scattered from correlated surface and bulk disorders.

Using a single scattering theory, we derive the expression of the degree of polarization of the light scattered from a layer exhibiting both surface and volume scattering. The expression puts forward the intimate connection between the degree of polarization and the statistical correlation between surface and volume disorders. It also permits a quantitative analysis of depolarization for uncorrelated, partially correlated and perfectly correlated disorders. We show that measuring the degree of polarization could allow one to assess the surface-volume correlation function, and that, reciprocally, the degree of polarization could be engineered by an appropriate design of the correlation function.

Switchable Ultra-Wideband All-Optical Quantum Dot Reflective Semiconductor Optical Amplifier.

A comprehensive study has been conducted on ultra-broadband optically pumped quantum dot (QD) reflective semiconductor optical amplifiers (QD-RSOAs). Furthermore, little work has been done on broadband QD-RSOAs with an optical pump. About 1 µm optical bandwidth, spanning 800 nm up to 1800 nm, is supported for the suggested device by superimposing nine groups of QDs. It has been shown that the device can be engineered to amplify a selected window or a group of desired windows. Moreover, the operation of the device has been thoroughly investigated by solving the coupled differential rate and signal propagation equations. A numerical algorithm has been suggested to solve these equations. As far as we are concerned, a broadband optically pumped QD-RSOA that can operate as a filter has been introduced.

An Optical Modeling Framework for Coronavirus Detection Using Graphene-Based Nanosensor.

The outbreak of the COVID-19 virus has faced the world with a new and dangerous challenge due to its contagious nature. Hence, developing sensory technologies to detect the coronavirus rapidly can provide a favorable condition for pandemic control of dangerous diseases. In between, because of the nanoscale size of this virus, there is a need for a good understanding of its optical behavior, which can give an extraordinary insight into the more efficient design of sensory devices. For the first time, this paper presents an optical modeling framework for a COVID-19 particle in the blood and extracts its optical characteristics based on numerical computations. To this end, a theoretical foundation of a COVID-19 particle is proposed based on the most recent experimental results available in the literature to simulate the optical behavior of the coronavirus under varying physical conditions. In order to obtain the optical properties of the COVID-19 model, the light reflectance by the structure is then simulated for different geometrical sizes, including the diameter of the COVID-19 particle and the size of the spikes surrounding it. It is found that the reflectance spectra are very sensitive to geometric changes of the coronavirus. Furthermore, the density of COVID-19 particles is investigated when the light is incident on different sides of the sample. Following this, we propose a nanosensor based on graphene, silicon, and gold nanodisks and demonstrate the functionality of the designed devices for detecting COVID-19 particles inside the blood samples. Indeed, the presented nanosensor design can be promoted as a practical procedure for creating nanoelectronic kits and wearable devices with considerable potential for fast virus detection.

Perfect depolarization in single scattering of light from uncorrelated surface and volume disorder.

We demonstrate that single scattering of p-polarized waves from uncorrelated surface and volume disorder can lead to perfect depolarization. The degree of polarization vanishes in specific scattering directions that can be characterized based on simple geometric arguments. Depolarization results from a different polarization response of each source of disorder, which provides a clear physical interpretation of the depolarization mechanism.

Experimental studies of the transmission of light through low-coverage regular or random arrays of silica micropillars supported by a glass substrate.

The transmission of light through low-coverage regular and random arrays of glass-supported silica micropillars of diameters 10-40 µm and height 10 µm is studied experimentally. Angle-resolved measurements of the transmitted intensity are performed at visible wavelengths by either a goniospectrophotometer or a multimodal imaging (Mueller) polarimetric microscope. It is demonstrated that for the regular arrays, the angle-resolved measurements are capable of resolving many of the densely packed diffraction orders that are expected for periodic structures of lattice constants 20-80 µm, but they also display features ("halos" and fringes) that are due to the scattering and guiding of light in individual micropillars or in the supporting glass slides. These latter features are also found in angle-resolved measurements on random arrays of micropillars of the same surface coverage. Finally, we perform a comparison of direct measurements of haze in transmission for our patterned glass samples with what can be calculated from the angle-resolved transmitted intensity measurements. Good agreement between the two types of results is found, which testifies to the accuracy of the angle-resolved measurements that we report.

Experimental and numerical studies of the scattering of light from a two-dimensional randomly rough interface in the presence of total internal reflection: optical Yoneda peaks.

The scattering of polarized light from a dielectric film sandwiched between two different semi-infinite dielectric media is studied experimentally and theoretically. The illuminated interface is planar, while the back interface is a two-dimensional randomly rough interface. We consider here only the case in which the medium of incidence is optically more dense than the substrate, in which case effects due to the presence of a critical angle for total internal reflection occur. A reduced Rayleigh equation for the scattering amplitudes is solved by a rigorous, purely numerical, nonperturbative approach. The solutions are used to calculate the reflectivity of the structure and the mean differential reflection coefficient. Optical analogues of Yoneda peaks are present in the results obtained. The computational results are compared with experimental data for the in-plane mean differential reflection coefficient, and good agreement between theory and experiment is found.

Time-scale effects on the gain-loss asymmetry in stock indices.

The gain-loss asymmetry, observed in the inverse statistics of stock indices is present for logarithmic return levels that are over 2%, and it is the result of the non-Pearson-type autocorrelations in the index. These non-Pearson-type correlations can be viewed also as functionally dependent daily volatilities, extending for a finite time interval. A generalized time-window shuffling method is used to show the existence of such autocorrelations. Their characteristic time scale proves to be smaller (less than 25 trading days) than what was previously believed. It is also found that this characteristic time scale has decreased with the appearance of program trading in the stock market transactions. Connections with the leverage effect are also established.

Dispersion of polarization coupling, localized and collective plasmon modes in a metallic photonic crystal mapped by Mueller Matrix Ellipsometry.

We report a spectroscopic Mueller matrix experimental study of a plasmonic photonic crystal consisting of gold hemispheroidal particles (lateral radius 54 nm, height 25 nm) arranged on a square lattice (lattice constant 210 nm) and supported by a glass substrate. Strong polarization coupling is observed for ultraviolet wavelengths and around the surface plasmon resonance for which the off-block-diagonal Mueller matrix elements show pronounced anisotropies. Due to the Rayleigh anomalies, the block-diagonal Mueller matrix elements produce a direct image of the Brillouin Zone (BZ) boundaries of the lattice and resonances are observed at the M-point in the first and at the X-point in the second BZ. These elements show also the dispersion of the localized surface plasmon resonance.

Coherent effects in the scattering of light from two-dimensional rough metal surfaces.

We investigate numerically multiple light-scattering phenomena for two-dimensional randomly rough metallic surfaces, where surface plasmon polaritons (SPPs) mediate several surface scattering effects. The scattering problem is solved by numerical solution of the reduced Rayleigh equation for reflection. The multiple scattering phenomena of enhanced backscattering and enhanced forward scattering are observed in the same system, and their presence is due to the excitation of SPPs. The numerical results discussed are qualitatively different from previous results for one-dimensionally rough surfaces, as one-dimensional surfaces have a limited influence on the polarization of light.

Scattering of electromagnetic waves from two-dimensional randomly rough penetrable surfaces.

An accurate and efficient numerical simulation approach to electromagnetic wave scattering from two-dimensional, randomly rough, penetrable surfaces is presented. The use of the Müller equations and an impedance boundary condition for a two-dimensional rough surface yields a pair of coupled two-dimensional integral equations for the sources on the surface in terms of which the scattered field is expressed through the Franz formulas. By this approach, we calculate the full angular intensity distribution of the scattered field that is due to a finite incident beam of p-polarized light. We specifically check the energy conservation (unitarity) of our simulations. Only after a detailed numerical treatment of both diagonal and close-to-diagonal matrix elements is the unitarity condition found to be well satisfied for the nonabsorbing case (U>0.995), a result that testifies to the accuracy of our approach.

Persistent collective trend in stock markets.

Empirical evidence is given for a significant difference in the collective trend of the share prices during the stock index rising and falling periods. Data on the Dow Jones Industrial Average and its stock components are studied between 1991 and 2008. Pearson-type correlations are computed between the stocks and averaged over stock pairs and time. The results indicate a general trend: whenever the stock index is falling the stock prices are changing in a more correlated manner than in case the stock index is ascending. A thorough statistical analysis of the data shows that the observed difference is significant, suggesting a constant fear factor among stockholders.

Transient dynamics increasing network vulnerability to cascading failures.

We study cascading failures in networks using a dynamical flow model based on simple conservation and distribution laws. It is found that considering the flow dynamics may imply reduced network robustness compared to previous static overload failure models. This is due to the transient oscillations or overshooting in the loads, when the flow dynamics adjusts to the new (remaining) network structure. The robustness of networks showing cascading failures is generally given by a complex interplay between the network topology and flow dynamics.

Modularity and extreme edges of the internet.

We study the spectral properties of a diffusion process taking place on the Internet network focusing on the slowest decaying modes. These modes identify an underlying modular structure roughly corresponding to individual countries. For instance, in the slowest decaying mode the diffusion current flows from Russia to U.S. military sites. Quantitatively the modular structure manifests itself in a 10 times larger participation ratio of its slow decaying modes compared to a random scale-free network. We propose to use the fraction of nodes participating in slow decaying modes as a general measure of the modularity of a network. For the 100 slowest decaying modes of the Internet this fraction is approximately 30%. Finally, we suggest that the degree of isolation of an individual module can be assessed by comparing its participation in different diffusion modes.

Fast algorithm for generating long self-affine profiles.

We introduce a fast algorithm for generating long self-affine profiles. The algorithm, which is based on the fast wavelet transform, is faster than the conventional Fourier filtering algorithm. In addition to increased performance for large systems, the algorithm, named the wavelet filtering algorithm, a priori gives rise to profiles for which the long-range correlation extends throughout the entire system independently of the length scale.