Light beams with helical phasefronts are characterized by an azimuthal phase. The centre of these beams is often termed an optical vortex and the surrounding annulus of high intensity carries an orbital angular momentum with a ratio between angular momentum and energy corresponding to per photon. Such beams can induce rotation in microscopic objects and, when they are rotated, undergo a frequency shift. The light’s orbital angular momentum is a valid description and measurement on both a macroscopic scale and at the level of single photons. Most recently, orbital angular momentum has been shown to be subject to an uncertainty relationship between angular momentum and angular position.

In recent years, twisted laser beams and optical vortices have attracted considerable interest, in terms of both their fundamental quantum properties and also their potential technical applications. Here we examine what novel features might emerge from the interaction of such beams with chiral matter. In this connection we assess the possible scope for exploiting similarities between the angular momentum properties of circularly polarised light and optical vortices - both with regard to their mechanical torque and also the associated spectroscopic selection rules. Twisted beams have generally been studied only in their interactions with achiral matter, with the theory largely developed for electric dipole coupling. In chiral systems, the low symmetry enables many optical transitions to be allowed under the selection rules for both electric and magnetic multipoles, and the entanglement of spin and orbital photon angular momentum requires careful extrication. Specific issues to be addressed are: what new features, if any, can be anticipated when such beams are used to interrogate a chiral system, and whether in such cases enantiomeric specificity can be expected. To this end we develop theory that goes to a higher order of multipole expansion, also engaging magnetic dipole and electric quadrupole transitions. Finally, we study the response of nematic liquid crystal media to the throughput of twisted laser light. Specific attention is focused on the spatial evolution of the director orientation angle.

Optical vortices are phase singularities in electromagnetic waves that constitute a unique and fascinating class of phenomena within the context of the physics of light. We present a brief overview of the recent advances in the study of optical vortices propagating in nonlinear media. We demonstrate that self-focusing nonlinearity leads, in general, to the azimuthal instability of a vortex-carrying beam, but it can support novel types of stable (or quasi-stable) self-trapped beams carrying nonzero angular momentum, such as vortex solitons, necklace beams, and soliton clusters. We also describe the properties of the discrete vortex solitons in periodic photonic lattices.

We present a method for manipulating individual sites in an optical lattice which enables the creation of defects within otherwise periodic light patterns. The modified optical lattice is created by interference of plane waves and spiral phase waves. Spiral phase modulation and the optical vortices that result are well suited for addressing single rows of fringes in the lattice owing to the localized wrap of the phase front. The size and shape of local fringes can be tuned or dynamically split and recombined by controlling the relative phase of the incident waves.

A design paradigm for Bragg multilayers made of columnar thin films (CTFs) is provided approximating both the ordinary and extraordinary refractive indexes of CTFs as Gaussian functions of the vapor incidence angle. Furthermore, we use a quadratic approximation of the same two quantities to design a cascade of chiral sculptured thin films (STFs) with successive pitches forming a geometric series to function as a wideband circular polarization filter.

Effective medium theory is applied to nanoengineered inorganic coatings in which a primary chiral medium (A) threads through a second medium (B) that may be isotropic, birefringent or chiral. In general A and B are represented by thin locally-birefringent layers with axes that rotate through the thickness of the coating. Local properties of the complex medium are represented by a Herpin birefringent period (A/2)B(A/2), with effective principal refractive indices and with thickness much less than the chiral period. The effect of changing the fraction fB of material B is considered. With simplicity of fabrication in mind, the special case in which A and B are identical apart from thickness and azimuthal orientation is developed. Then, by maintaining a constant optical thickness for the Herpin period, the circular Bragg resonant wavelength of the primary medium can be retained. As an example of the potential use of threaded-chiral materials, handed resonant reflectors for elliptically-polarized light are considered.

We have produced chiral fiber Bragg gratings with double-helix symmetry and measured the polarization and wavelength selective transmission properties of these structures. These gratings interact only with circularly polarized light with the same handedness as the grating twist and freely transmit light of the orthogonal polarization. The optical characteristics of chiral fibers are compared to those of planar cholesteric structures. The resonant standing wave at the band edge or at a defect state within the band gap, as well as the evanescent wave within the band gap is comprised of two counterpropagating components of equal amplitude. The electric field vector of such a circularly polarized standing wave does not rotate in time; rather it is linearly polarized in any given plane. The standing wave may be described in terms of the sense of circular polarization of the two counterpropagating components. The wavelength dependence of the angle q between the linearly polarized electromagnetic field and the extraordinary axis, which is constant throughout a long structure, is obtained in a simple calculation. The results are in good agreement with scattering matrix calculations. Resonant chiral gratings are demonstrated for microwave radiation whereas chiral gratings with pitch exceeding the wavelength are demonstrated at optical wavelengths in single-mode glass fibers. The different functionalities of these fibers are discussed.

The problem of coupling a surface dielectric grating consisting of a sinusoidal corrugation to a structurally chiral volume grating has been formulated and solved with results showing the robust co-existence of phenomena characteristic of both types of grating: namely Rayleigh-Wood anomalies and Bragg zones. A mechanism to strengthen the coupling between both grating types has now been included in the model, namely a quarter wave plate whose birefringence converts normally incident linearly polarised light of the chiral Bragg wavelength into transmitted circularly polarised light. It is possible to tailor the period of the sinusoidal surface grating such that the scattering of obliquely incident light from above, by the surface grating, will lead to a specific non-zero order being scattered onto a path which is normally incident on the rest of the structure. Significantly, such orders exhibit the circular Bragg phenomenon in reflection and transmission only if both grating types are present, making this a truly coupled grating effect.

We derive the equations describing a sculptured dielectric film with simultaneous chiral and nematic features, and solve analytically a special case where these features are present symmetrically and with equal periods. A number of interesting and novel features emerge, including a handedness reversal of circularly polarized light outside the Bragg regime.

The Post constraint for linear electromagnetic materials arises from two basic tenets of modern electromagnetism. The first is the microscopic basis of all electromagnetic phenomenons. The second is that E(x,t) and B(x,t) are the fundamental fields, whereas D(x,t) and H(x,t) are merely secondary constructs. The latter is in contrast to the older version of electromagnetism, wherein the roles of B(x,t) and H(x,t) are the opposite, and which does not admit the Post constraint. A comprehensive view of the Post constraint is presented.

The depolarization dyadic provides the scattering response of a single inclusion particle embedded within a homogenous background medium. These dyadics play a central role in formalisms used to estimate the effective constitutive parameters of homogenized composite mediums (HCMs). Conventionally, the inclusion particle is taken to be vanishingly small; this allows the pointwise singularity of the dyadic Green function associated with the background medium to be employed as the depolarization dyadic. A more accurate approach is pursued in this communication by taking into account the nonzero spatial extent of inclusion particles. Depolarization dyadics corresponding to inclusion particles of nonzero volume are incorporated within the strong-permittivity-fluctuation theory (SPFT). The linear dimensions of inclusion particles are assumed to be small relative to the electromagnetic wavelength(s) and the SPFT correlation length. The influence of the size of inclusion particles upon SPFT estimates of the HCM constitutive parameters is investigated for anisotropic dielectric HCMs.In particular, the interplay between correlation length and inclusion size is explored.

We simulated the negative capacitance-frequency curves for the organic semiconductor Alq3 using the Drude model equation to assess the applicability of the "universality of photocurrent transients". Using the data reported by Berleb et al, shape invariance was observed in these curves after normalization with respect to frequency and taking into account the bias dependence. Our results suggested that the reported frequency shifts in Berleb's measurements were primarily related to changes in the complex carrier mobility at the different biases. Normalization of the capacitance-frequency curves at different temperatures also showed shape invariance when normalized. The observed changes in the carrier mobility as a function of temperature were essentially the same as what one would expect from a disordered solid with Gaussian density of states. Our model therefore provided an alternative venue to determine the "universality of photocurrent transients" with focus on the complex carrier mobility.

The evidence that double negative media, with an effective negative permittivity, and an effective negative permeability, can be manufactured to operate at frequencies ranging from microwave to optical is ushering in a new era of metamaterials. They are referred to here as 'left-handed', even though a variety of names is evident from the literature. In anticipation of a demand for highly structured integrated practical waveguides, this paper addresses the impact of this type of medium upon waveguides that can be also nonlinear. A planar guide is investigated first, in which the waveguide is a slab consisting of a double negative medium, sandwiched between a substrate and cladding that are simple dielectrics. The TE modes are addressed because they lend themselves to accurate analysis when the substrate and cladding display a Kerr-type nonlinear response. Because of the nonlinear properties of the Kerr media, the power flow direction can be controlled by the intensity of the electric field. The rest of the paper addresses a comprehensive finite difference- time-domain analysis. It uses spatial soliton behaviour in the advanced example section. An interesting soliton-lens arrangement is presented that deploys positive and negative slabs to create a novel cancellation effect.

It is predicted that metal nanostructures can have a magnetic plasmon resonance (MPR) in the optical spectral range. Similarly to the known electrical surface plasmon resonance (SPR), the MPR depends only on metal properties and geometry of the system, rather than on the wavelength, and it can occur in structures much smaller in size than the optical wavelength. The MPR can have as large optical cross-section as the SPR so that nanostructures supporting the two resonances can provide a strong coupling to both field components of light, electrical and magnetic. Above the resonance, the magnetic plasmon polarizability may acquire negative values making possible to use this phenomena for developing left-handed materials in the optic range.

We analyze nonlinear properties of microstructured materials with negative refraction, the so-called left-handed metamaterials. We demonstrate that the hysteresis-type dependence of the magnetic permeability on the field intensity allows changing the material properties from left- to right-handed and back. We predict also that nonlinear left-handed metamaterials can support both TE- and TM-polarized self-trapped localized beams, spatial electromagnetic solitons. Such solitons appear as single- and multi-hump beams, being either symmetric or antisymmetric, and they can exist due to the hysteresis-type magnetic nonlinearity and the effective domains of negative magnetic permeability.

Today's progress in the materials sciences and nano-structure technologies open up a conception of novel photonic materials and devices with designed characteristics and functionalities: Photonic crystals and synthetic opals guide and control light, semiconductor quantum dots become customized coherent photon sources and base material for new lasers. The paper gives an overview of the (super-) computer simulation of these novel complex photonic materials and devices. It reports on advances in three-dimensional Finite-Difference Time-Domain (FDTD) simulations of the materials properties and the design the functionality of complex layered planar photonic crystals and inverse opals. Multi-scale non-linear partial differential Maxwell-Bloch equations form a basis for the simulation of three-dimensional inhomogeneous quantum dot ensembles that give an insight into the complex dynamics of quantum dot lasers.

Periodic two-dimensional arrays of straight, conducting wires have been used to create structures with negative permittivity and have been incorporated into structures exhibiting a negative index of refraction or phase velocity. In these cases the electromagnetic wave propagating through the structure has its electric field parallel to the wires. Solutions to Maxwell's equations for transverse electromagnetic waves in these structures have been found previously using either an approximate permittivity appropriate to the long wavelength limit or been determined numerically using a finite element analysis. The calculation presented here is an exact solution of Maxwell's equations for a square wire array valid for wavelengths larger that the wire diameter. The permittivity calculated in the long wavelength limit predicts propagation constants which agree remarkably well with the exact solution down to wavelengths comparable to the lattice constant of the wire array, with the first serious discrepancy occurring at the first Bragg reflection. The exact solution shows that the gaps in the frequency versus propagation constant relation in the [10] direction decrease in size as the order of the Bragg reflection increases. Also the second, fourth, sixth, etc., Bragg reflections are complicated by the emergence of higher order grating modes which result in dispersion relation crossings near the Bragg reflection.

It is now well established that, in azo-dye polymers repeated trans-cis-trans isomerization cycles induces molecular reorientation leading to quasi-permanent birefringence and dichroism. More recently, it has been shown that irradiation of an azo-polymer thin film with an interference pattern between polarized laser beams can lead to a direct and reversible topographic modification of the polymer film surface resulting in the induction of surface relief gratings in conjunction with the light interference pattern. Here, we provide experimental evidence of an original spontaneous light-assisted submicrometer patterning process. We show that uniform irradiation of an azo-dye polymer using a single collimated laser beam with normal incidence leads to the formation of organized hexagonal patterns. These structures geometry depends on the laser beam polarization : their period is about the irradiation wavelength and their modulation amplitude can reach one hundred nanometers. Possible origin of such process is discussed. Although showing similar features with models or experiments already described in the literature, the origin of light-assisted spontaneous patterning in azo-polymers is still unclear and further complementary investigations are needed. Indeed, accurate determination of the relevant parameters at the origin of such process should enable a full control of the process together with further possible generation of more complex structures.

Electromagnetic wave propagation in a one-dimensional magnetic photonic crystal made of bigyrotropic magnetic yttrium-iron garnet and nonmagnetic gadolinium-gallium garnet is theoretically investigated using the 4×4 transfer matrix method for longitudinal magneto-optical configuration. Band gaps in the electromagnetic spectrum are numerically obtained and appear to depend on the helicity and direction of light propagation through the magnetic photonic crystal.

This paper presents an analytical theory describing excitation of a semi-infinite electromagnetic crystal by plane electromagnetic wave. A three-dimensional crystal with orthorhombic elementary cell, formed by scatterers which can be substituted by point dipoles with known polarizability and fixed orientation is considered. The closed-form analytical formulae for the amplitudes of excited modes and Floquet harmonics of scattered field for the semi-infinite electromagnetic crystal are derived in terms of the infinite crystal eigenmodes wavevectors. Generalized Ewald-Oseen extinction principle for electromagnetic crystals under consideration has been formulated. It is extended for electromagnetic crystals of general kind characterized by three-periodical dielectric permittivity distribution.

The homogeneous optical response in conducting nanostructured layers, and in insulating layers containing dense arrays of self assembled conducting nanoparticles separated by organic linkers, is examined experimentally through their effective complex indices (n*, k*). Classical effective medium models, modified to account for the 3-phase nanostructure, are shown to explain (n*, k*) in dense particulate systems but not inhomogeneous layers with macroscopic conductance for which a different approach to homogenisation is discussed. (n*, k*) data on thin granular metal films, thin mesoporous gold, and on thin metal layers containing ordered arrays of voids, is linked to properties of the surface plasmon states which span the nanostructured film. Coupling between evanescent waves at either surface counterbalanced by electron scattering losses must be considered. Virtual bound states for resonant photons result, with the associated transit delay leading to a large rise in n* in many nanostructures. Overcoating n-Ag with alumina is shown to alter (n*, k*) through its impact on the SP coupling. In contrast to classical optical homogenisation, effective indices depend on film thickness. Supporting high resolution SEM images are presented.

On the basis of spectral-expansion Green’s function theory, we theoretically describe the topography, polarization, and spatial-coherence properties of the second-harmonic (SH) local fields at rough metal surfaces. The spatial distributions of the fundamental-frequency and SH local fields are very different, with highly-enhanced hot spots of the SH. The spatial correlation functions of the amplitude, phase, and direction of the SH polarization all show spatial decay on the nanoscale in the wide range of the metal fill factors. This implies that SH radiation collected from even nanometer-scale areas is strongly depolarized and dephased, i.e., has the nature of hyper- Rayleigh scattering, in agreement with recent experiments. The present theory is applicable to nanometer-scale nonlinear-optical illumination, probing, and modification.

We review our recent work on lasing in active random media. Light scattering, which had been regarded detrimental to lasing action for a long time, actually provided coherent feedback for lasing. We also trapped laser light in micrometer-sized random media. The trapping was caused by disorder-induced scattering and inference. This nontraditional way of light confinement has important application to microlasers. The threshold of random laser can be reduced by incorporating some degree of order into an active random medium. Our calculation result shows that by optimizing the degree of order one can dramatically reduce the threshold of random laser to the values comparable to those of photonic bandgap defect lasers.

We report numerical and experimental studies on multiple scattering media with gain. We describe Monte Carlo simulations that model the behavior of such a system through a three dimensional random walk of photons in a disordered medium with amplification. Two experimentally observed phenomena, viz. temperature tunable random lasing and ultra-narrow lasing modes, are analyzed using the model. We compare the results of our model with previous experimental results on a disordered dielectric of which the scattering strength could be tuned by changing the external temperature. The agreement between the numerical and experimental results enables us to predict the spectral features of the emission from the tunable random laser under various conditions. Results obtained from new experimental data are consistent with the predictions of the simulations. The model also explains the observation of ultra-narrow emission modes in random lasers without requiring optical cavities. The introduction of exponential gain in a multiple light scattering process strongly increases the importance of very long light paths. Such long paths are often neglected in passive disordered materials but we show that they can dominate the emission spectrum from an amplifying disordered system.

The luminescence properties of the Nd3+:LaAlO3 nanocrystalline powders characterized by different sizes of grains in the range of 25-50 nm were investigated. The effect of the nanocrystallites sizes on the luminescence behavior of Nd3+ was observed. In particular decreasing the grain sizes was found to increase emission from the thermally populated 4F5/2 state. It's intensity increased with the increase of excitation power density. The spectroscopic parameters of Nd3+ doped LaAlO3 nanocrystallites were determined from luminescence spectra by using the Judd-Ofelt method and compared to those obtained for a single crystal of Nd3+:LaAlO3.

Copper based catalysts are of great importance as catalysts for NO removal from exhaust industrial gases. Earlier authors have shown that NO reaction with acetone oxime (AO) is the rate determining step of NO catalytic reduction by propane over Cu-ZSM-5 catalyst at temperatures below 300oC. Aim of the present work is to clarify the peculiarities of acetone oxime coordination over surface of H-ZSM-5 zeolite and that doped with Cu(II) and Cu(I)-cations. We studied AO coordination in CCl4 solutions and then data obtained were used for analysis of spectra of AO adsorbed on pure zeolite and that dopped with Cu (I) and Cu (II) cations. It was shown that there are monomers and several associates of AO in CCl4 solution differing in size and type of bonding with their own characteristic bands in IR spectra. The spectrum of acetone oxime adsorbed on pure zeolite includes non symmetrical band at 1710 cm-1 due to AO strongly bonded with zeolite surface through H-bond. There are four AO adspecies on zeolite dopped with copper with two different types of AO coordination to Cu(I) or to Cu(II) cations: one with participation of O atom and another one with N atom. Complexes of AO with Cu(I) ions are much more stable then those with Cu(II) ions.

Copper incorporation into zeolites by the ion-exchange from Cu(II) solutions followed by different heat treatments results in a production of a number of species. Redistribution among different sites after dehydration, spontaneous and forced reduction, cluster and particle aggregation, etc. can occur, and a final copper state depends on type of zeolite, SiO2/Al2O3 molar ratio and processing conditions. Various species where observed: copper ions Cu2+ and Cu+, small particles and clusters Cun. We concentrate on the appearance of small copper clusters feasible in zeolites with size of cavities those match the cluster size. The clusters were simulated with ab initio quantum chemical calculations in the range of sizes 5 < n < 10 those are probable within zeolites cavities. Experimental data available on optical absorption of the reduced copper in the three types of zeolites can argue on the occurrence of the clusters stabilized within channels under mild reduction conditions while the larger copper nanoparticles appear under the harder reduction. The model calculation proposes some few-atomic copper clusters (Cun) as the candidates to fit the zeolite cavities with correspondence of the calculated absorption bands with the experimental spectra.

Cu-mordenites catalysts are among the most active available for de-NOx at moderate temperatures. Silica-alumina molar ratio of mordenite supports strongly affects conversion efficiency for NOx. Copper mordenites' rapid deactivation by water has led us to investigate the effects of adsorbed water on framework and extra-framework ions, mainly using NMR of 27Al and 1H. Adsorbed water content has been monitored and controlled in mordenite samples via TGA, as well as by vacuum calcination. Several NMR measurements have been performed to aid in the interpretation of spectra, including variable pulse-delay spin echo and 1H-27Al TRAPDOR. A number of surface characterization techniques have been applied to both H- and Cu-mordenites. Catalytic experiments showed that the reduction of NOx to N2 and O2 by hydrocarbons reach 95-98 % depending on the catalyst composition.

We analyze the diffraction of a plane wave by a diffraction (surface-relief) grating made of an isotropic negative phase-velocity material. Three different approaches are employed, and the results are compared with those for conventional (i.e., positive phase-velocity) materials. Resonant excitation of surface waves on the new types of gratings is examined.

According to HAUP measurements, two ferroelectric boracites, Fe3B7O13I and Cu3B7O13Cl, manifest peaks of a gyration component g11 at each Curie point. These phenomena are entirely unintelligible from the usual concepts of the origin of ferroelectricity. Besides, the electrogyration effects of both crystals and also quite different. As has already been determined boracite crystals exhibit characteristic features of being improper ferroelectric. A phenomenological theory of improper ferroelectricity developed by Kobayashi is applied to these anomalous phenomena, and qualitative interpretations are successfully obtained.

By expanding the spatial distribution of a dielectric constant in random media into Fourier series, we analyze the assumption that the resonant feedback is provided by the presence of components with spatial periods satisfying the condition of the Braff diffraction. Numerical simulations of random media allow us to predict specific features of eigenfrequencies of lasing modes, which are similar to those obtained in the literature from the numerical solution of the Maxwell equations. Thus, a plausible explanation of the physical nature of frequency selection in random lasers is revealed. Furthermore, using a simplified description of the Bragg feedback, we show why the threshold gain decreases with the increase in the sizes of the active region.