Concave and Convex photonic Barriers in Gradient Optics

Propagation and tunneling of light through photonic barriers formed by thin dielectric films with continuous curvilinear distributions of dielectric susceptibility across the film, are considered. Giant heterogeneity-induced dispersion of these films, both convex and concave, and its influence on their reflectivity and transmittivity are visualized by means of exact analytical solutions of Maxwell equations. Depending on the cut-off frequency of the film, governed by the spatial profile of its refractive index, propagation or tunneling of light through such barriers are examined. Subject to the shape of refractive index profile the group velocities of EM waves in these films are shown to be either increased or deccreased as compared with the homogeneous layers; however, these velocities for both propagation and tunneling regimes remain subluminal. The decisive influence of gradient and curvature of photonic barriers on the efficiency of tunneling is examined by means of generalized Fresnel formulae. Saturation of the phase of the wave tunneling through a stack of such films (Hartman effect), is demonstrated. The evanescent modes in lossy barriers and violation of Hartman effect in this case is discussed

Thermodynamics of tin clusters

We report the results of detailed thermodynamic investigations of the Sn$_{20}$ cluster using density-functional molecular dynamics. These simulations have been performed over a temperature range of 150 to 3000 K, with a total simulation time of order 1 ns. The prolate ground state and low-lying isomers consist of two tricapped trigonal prism (TTP) units stacked end to end. The ionic specific heat, calculated via a multihistogram fit, shows a small peak around 500 K and a shoulder around 850 K. The main peak occurs around 1200 K, about 700 K higher than the bulk melting temperature, but significantly lower than that for Sn$_{10}$. The main peak is accompanied by a sharp change in the prolate shape of the cluster due to the fusion of the two TTP units to form a compact, near spherical structure with a diffusive liquidlike ionic motion. The small peak at 500 K is associated with rearrangement processes within the TTP units, while the shoulder at 850 K corresponds to distortion of at least one TTP unit, preserving the overall prolate shape of the cluster. At all temperatures observed, the bonding remains covalent.Comment: Latex File and EPS Figures. 18 pages,11 Figures. Submitted to Phys. Rev.

Волновое уравнение: от эйконального к неэйкональному приближению

When the refractive index changes very slowly compared to the wave-length we may use the eikonal approximation to the wave equation. In the opposite case, when the refractive index highly variates over the distance of one wave-length, we have what can be termed as the anti-eikonal limit. This situation is addressed in this work. The anti- eikonal limit seems to be a relevant tool in the modelling and design of new optical media. Besides, it describes a basic universal behaviour, independent of the actual values of the refractive index and, thus, of the media, for the components of a wave with wave-length much greater than the characteristic scale of the refractive index.В случае медленного изменения коэффициента преломления на расстояниях порядка длины волны для решения волнового уравнения можно использовать известное эйкональное приближение. Рассмотрена противоположная ситуация, когда коэффициент преломления резко меняется на протяжении одной длины волны, и имеет место так называемый антиэйкональный предел. Антиэйкональный предел оказывается удобным инструментом для моделирования и проектирования новых оптических сред. Кроме того, он позволяет описывать базовое универсальное поведение независимо от реальных значений коэффициента преломления и, следовательно, от параметров самой среды, в случае волновых компонентов с длиной волны, значительно превышающей характерную длину изменения коэффициента преломления

Нелокальная дисперсия и ультразвуковое туннелирование в материалах с градиентной структурой

The non-local dispersion of longitudinal ultrasonic waves is shown to appear in the heterogeneous solids due to continuous spatial distributions of their density and/or elasticity (gradient solids). This dispersion gives rise to the diversity of ultrasonic transmittance spectra, including the broadband total reflectance plateau, total transmission and tunneling spectral ranges. The ultrasonic wave fields in gradient solids, formed by interference of forward and backward travelling waves as well as by evanescent and antievanescent modes are examined in the framework of exactly solvable models of media with continuously distributed density and elasticity. Examples of transmittance spectra for both metal and semiconductor gradient structures are presented, and the generality of concept of artificial non-local dispersion for gradient composite materials is considered. It should also be noted that the wave equation for acoustic waves in gradient media with a constant elasticity modulus and a certain predetermined density distribution reduces to an equation describing the electromagnetic wave propagation in transparent dielectric media. This formal similarity shows that the concept of nonlocal dispersion is common for both optical and acoustic phenomena, which opens the way to the direct use of physical concepts and exact mathematical solutions, developed for gradient optics, to solve the corresponding acoustic problems.Показано, что в материалах с пространственным распределением (градиентом) плотности и/или упругости имеет место нелокальная дисперсия продольных ультразвуковых волн. Эта дисперсия приводит к возникновению ультразвуковых спектров, таких как широкодиапазонное плато полного отражения, туннельные спектральные области и области полного пропускания. В рамках точно решаемых моделей сред с непрерывно распределенными плотностью и упругостью исследованы ультразвуковые волны в градиентных материалах, сформированные интерференцией прямых и обратных волн, а также затухающими и незатухающими модами. Приведены примеры спектров пропускания как для металлических, так и для полупроводниковых градиентных структур, а также рассмотрена общая концепция искусственной нелокальной дисперсии для градиентных композитных материалов. Необходимо заметить, что волновое уравнение для акустических волн в градиентных средах с постоянным модулем упругости и определенным заданным распределением плотности сводится к уравнению, описывающему распространение электромагнитных волн в прозрачных диэлектрических средах. Это формальное сходство свидетельствует о том, что концепция нелокальной дисперсии является общей как для оптических, так и для акустических явлений, что позволяет напрямую использовать разработанные для градиентной оптики физические принципы и точные математические решения при реализации соответствующих акустических задач

Effect of hydrogen on ground state structures of small silicon clusters

We present results for ground state structures of small Si$_{n}$H (2 \leq \emph{n} \leq 10) clusters using the Car-Parrinello molecular dynamics. In particular, we focus on how the addition of a hydrogen atom affects the ground state geometry, total energy and the first excited electronic level gap of an Si$_{n}$ cluster. We discuss the nature of bonding of hydrogen in these clusters. We find that hydrogen bonds with two silicon atoms only in Si$_{2}$H, Si$_{3}$H and Si$_{5}$H clusters, while in other clusters (i.e. Si$_{4}$H, Si$_{6}$H, Si$_{7}$H, Si$_{8}$H, Si$_{9}$H and Si$_{10}$H) hydrogen is bonded to only one silicon atom. Also in the case of a compact and closed silicon cluster hydrogen bonds to the cluster from outside. We find that the first excited electronic level gap of Si$_{n}$ and Si$_{n}$H fluctuates as a function of size and this may provide a first principles basis for the short-range potential fluctuations in hydrogenated amorphous silicon. Our results show that the addition of a single hydrogen can cause large changes in the electronic structure of a silicon cluster, though the geometry is not much affected. Our calculation of the lowest energy fragmentation products of Si$_{n}$H clusters shows that hydrogen is easily removed from Si$_{n}$H clusters.Comment: one latex file named script.tex including table and figure caption. Six postscript figure files. figure_1a.ps and figure_1b.ps are files representing Fig. 1 in the main tex