Photonic crystals--a step towards integrated circuits for photonics.

The field of photonic crystals has, over the past few years, received dramatically increased attention. Photonic crystals are artificially engineered structures that exhibit a periodic variation in one, two, or three dimensions of the dielectric constant, with a period of the order of the pertinent light wavelength. Such structures in three dimensions should exhibit properties similar to solid-state electronic crystals, such as bandgaps, in other words wavelength regions where light cannot propagate in any direction. By introducing defects into the periodic arrangement, the photonic crystals exhibit properties analogous to those of solid-state crystals. The basic feature of a photonic bandgap was indeed experimentally demonstrated in the beginning of the 1990s, and sparked a large interest in, and in many ways revitalized, photonics research. There are several reasons for this attention. One is that photonic crystals, in their own right, offer a proliferation of challenging research tasks, involving a multitude of disciplines, such as electromagnetic theory, nanofabrication, semi-conductor technology, materials science, biotechnology, to name a few. Another reason is given by the somewhat more down-to-earth expectations that photonics crystals will create unique opportunities for novel devices and applications, and contribute to solving some of the issues that have plagued photonics such as large physical sizes, comparatively low functionality, and high costs. Herein, we will treat some basics of photonic crystal structures and discuss the state-of-the-art in fabrication as well give some examples of devices with unique properties, due to the use of photonic crystals. We will also point out some of the problems that still remain to be solved, and give a view on where photonic crystals currently stand.     

Lattice path combinatorics and asymptotics of multiplicities of weights in tensor powers

We give asymptotic formulas for the multiplicities of weights and irreducible summands in high-tensor powers V_λ^⊗N of an irreducible representation V_λ of a compact connected Lie group G. The weights are allowed to depend on N, and we obtain several regimes of pointwise asymptotics, ranging from a central limit region to a large deviations region. We use a complex steepest descent method that applies to general asymptotic counting problems for lattice paths with steps in a convex polytope.     

用于高数值孔径物镜的可调光瞳滤波器

根据矢量衍射理论，提出了一种用于提高高数值孔径显微物镜纵向分辨率的可调二元环形光瞳滤波器，通过改变滤波器的环半径获得不同的纵向分辨率，并利用共焦显微术点扩散函数的乘积性大大地降低了旁瓣相对主瓣的比值。模拟结果表明，这种新型滤波器不仅可以提高高数值孔径物镜的纵向分辨率，同时基本上不影响横向分辨率。     

The K–nucleus cross sections in relativistic non-linear models

The K⁺−nucleus cross sections have been calculated in relativistic non-linear models taking into account the in-medium modifications of nucleons and mesons properties. More precisely, we have taken into account both the dressing of the nucleon effective mass by the scalar nuclear field in the target and the coupling of the mesons exchanged between the K⁺ and the nucleons to the polarization of the medium. First, using the most recent relativistic non-linear models, the in-medium σ, ω and ρ meson masses have been obtained in the nuclear matter rest frame. The influence of the non-linear contributions on the K⁺−nucleus cross sections has then been studied. Finally, we have compared our results with the experimental data.     

A comparative study of the propagation of vectorial nonparaxial beams in the use of different approaches

Starting from the vectorial Rayleigh diffraction integral formula and using a simple expansion of the nucleus in the Rayleigh formula, an analytical propagation equation of vectorial nonparaxial Gaussian beams in free space is derived, which permits us to perform numerical calculations in comparison with the expression derived by Ciattoni et al. and with the direct numerical integration of the Rayleigh formula. It is found that as usual the use of expansion of vectorial Rayleigh diffraction integral is sufficient to provide satisfactory numerical results as compared with the direct integration of the Rayleigh formula. The above two analytical expressions are valid under certain conditions, however both are applicable in the far field.     

α-Fe2O3-In2O3 mixed oxide nanoparticles synthesized under hydrothermal supercritical conditions

α-Fe₂O₃-In₂O₃ mixed oxide nanoparticles system has been synthesized by hydrothermal supercritical and postannealing route, starting with (1−x)Fe(NO₃)₃·9H₂O·xIn(NO₃)₃·5H₂O aqueous solution (x=0-1). X-ray diffraction and Mössbauer spectroscopy have been used to study the phase structure and substitutions in the nanosized samples. The concentration regions for the existence of the solid solutions in the α-Fe₂O₃-In₂O₃ nanoparticle system together with the solubility limits of In³⁺ ions in the hematite lattice and of Fe³⁺ ions in the cubic In₂O₃ structure have been evidenced. In general, the substitution level is considerably lower than the nominal concentration x. A justification of the processes leading to the formation of iron and indium phases in the investigated supercritical hydrothermal system has been given.     

Application of the Volterra filter in experimental diffraction data processing

The effective signal in x-ray diffraction analysis of material properties often contains high frequency (noise) and low frequency (trend) components as additive parts. It is necessary to extract the effective signal from the noise to ensure high quality of signal processing. Digital filters of Volterra type are proposed for filtering purposes and a comparison of Volterra filtration implemented on x-ray diffraction data versus results from a set of other digital filters is given.     

Measurement of wire diameter by optical diffraction

A combined interference and diffraction pattern, in the form of equidistant interference fringes, resulting from illuminating a vertical metallic wire by a laser beam is analyzed to measure the diameter of four standard wires. The diameters range from 170 to 450 μm. It is found that the error in the diameter measurements increases for small metallic wires and for small distances between the wire and the screen due to scattering effects. The intensity of the incident laser beam was controlled by a pair of sheet polaroids to minimize the scattered radiation. The used technique is highly sensitive, but requires controlled environmental conditions and absence of vibration effects. The expanded uncertainty for k=2 is calculated and found to decrease from U(D)=±1.45 μm for the wire of nominal diameter 170 μm to ±0.57 μm for the diameter 450 μm.     

Solid state phase equilibria in the Gd-Si-B system at 1270 K

Solid state phase equilibria in the ternary Gd-Si-B phase diagram have been proposed at 1270 K using X-ray diffraction, scanning electron microscopy and electron probe microanalysis. Prior to this work, the binary systems Gd-B, Gd-Si and Si-B have also been reinvestigated. The main characteristic of the ternary diagram is the occurrence of two new ternary compounds Gd₅Si₂B₈ and Gd₅Si₃B_0.64. The former crystallizes in tetragonal symmetry, space group P4/mbm with unit cell parameters a=7.2665(3), c=8.2229(7) Å, the second one presents hexagonal symmetry, space group P6₃/mcm with unit cell parameters a=8.5080(4),c=6.4141(2) Å. The X-ray structures of the two structurally related phases Gd₅Si₃B_0.64 and host binary Gd₅Si₃ have been refined from three-dimensional single-crystal intensity data to the final R values of 0.036 (R_w=0.046) and 0.046 (R_w=0.055) for 457 and 401 reflections, respectively with [F>4σ(F)]. Both structures exhibit the Mn₅Si₃-type structure, with in addition for Gd₅Si₃B_0.64 a partial occupancy by boron of the normally vacant interstitial site at the center of the Gd₆ octahedron, which corresponds to the origin of the unit cell. Bonding between the interstitial boron atoms and the gadolinium ones forming the Gd₆B polyhedra is indicated by the decrease in the corresponding Gd-Gd distances and consequently in the unit cell volume. Finally, the Gd-Si-B phase diagram is compared with the previously reported Er-Si-B, at 1070 K.