Scalar Approximation Research Articles

Phase delay and group velocity determination at a planar defect state in three dimensional photonic crystals

Phase sensitive optical transmission measurements have been performed on three dimensional opal-based photonic crystals containing a planar defect. From numerical derivation of the measured phase, the group velocity has been retrieved. Strong modulations in the group velocity are seen to correlate with a recovery in the transmission inside the forbidden spectral interval, demonstrating the presence of a localized defect state. Accordingly, the phase change measured across the forbidden interval doubles in the lattice containing a planar defect with respect to the defect-free crystal, as expected when introducing a localized state inside the pseudogap. All results have been modeled with a scalar wave approximation in a two band model including extinction.

A Density Functional Study of the Electronic Structure and Spin Hamiltonian Parameters of Mononuclear Thiomolybdenyl Complexes

The electron paramagnetic resonance spin Hamiltonian parameters of mononuclear thiomolybdenyl complexes based upon the tris(pyrazolyl)borate ligand, together with their molybdenyl analogues, are calculated using density functional theory. The electronic g matrix and 95Mo hyperfine matrix are calculated as second-order response properties from the coupled-perturbed Kohn-Sham equations. The scalar relativistic zero-order regular approximation (ZORA) is used with an all-electron basis and an accurate mean-field spin-orbit operator which includes all one- and two-electron terms. The principal values and relative orientations of the g and A interaction matrices obtained from the experimental spectra in a previous EPR study are compared with those obtained from unrestricted Kohn-Sham calculations at the BP86 and B3LYP level, and the latter are found to be in good quantitative agreement. A quasi-restricted approach is used to analyze the influence of the various molecular orbitals on g and A. In all complexes the ground state magnetic orbital is dX2-Y2-based and the orientation of the A matrix is directly related to the orientation of this orbital. The largest single contribution to the orientation of the g matrix arises from the spin-orbit coupling of the dYZ-based lowest-unoccupied molecular orbital into the ground state. A number of smaller, cumulative charge-transfer contributions augment the d-d contributions. A comparison of the theoretical EPR parameters obtained using both crystallographic and gas-phase geometry-optimized structures of Tp*MoO(bdt) (Tp* = hydrotris(3,5-dimethylpyrazol-1-yl)borate, bdt = 1,2-benzenedithiolate) suggests a correspondence between the metal-dithiolate fold angle and the angle of noncoincidence between g and A.

A 2-D/3-D cartesian geometry non-conforming spherical harmonic neutron transport solver

A new 2-D/3-D transport core solver for the time-independent Boltzmann transport equation is presented. This solver, named Fiesta, is based on the second-order even-parity form of the transport equation. The angular discretization is performed through the expansion of the angular neutron flux into spherical harmonics ( P N method). The novelty of this solver is the use of non-conforming finite elements for the spatial discretization. Such elements lead to a discontinuous scalar flux approximation. This interface continuity requirement relaxation property is shared with mixed-dual formulations discretized using Raviart–Thomas finite elements. Encouraging numerical results are presented.

The creation–annihilation process of phase singularities of flat-topped beams in the focal plane

The creation–annihilation process of phase singularities of flat-topped beams in the focal plane is studied within the framework of the scalar paraxial approximation, where the new expression for flat-topped beams introduced by Li is taken as the beam model. It is shown that by suitably varying the truncation parameter, the phase singularities reorganize themselves, which leads to the annihilation of singularities in the focal plane, the creation of singularities outside the focal plane and subwavelength structures. Apart from the truncation parameter, the beam order of flat-topped beams additionally affects the spatial distribution of phase singularities.

Calculations of a fibre amplifier with the hexagonal waveguide structure

An ytterbium-doped fibre amplifier with the hexagonal structure containing seven waveguides is simulated by using a numerical program based on the scalar paraxial optics approximation. The influence of the scatter in parameters of active fibre cores on spontaneous phasing discovered earlier is studied numerically for the first time. The critical scatter in the core parameters at which the phase locking of radiation is preserved is found. It is shown that a decrease in the numerical aperture of fibre cores facilitates the stabilisation of phase locking.

Analysis of multifrequency interferometry in a cylindrical plasma

A microwave interferometer operating simultaneously at 70, 90, and 110GHz is used to measure line integrated electron density in a plasma column in the VX-20 experiment. Interferometer beam sizes are a significant part of the plasma radius at some locations. We model the wave propagation through the plasma using a scalar wave approximation with assumptions of a Gaussian beam profile and plasma spatial profile. The phase shifts obtained from this model are compared with standard thin beam calculations and experimental data.

Electronic Structures and Absorption Spectra of Linkage Isomers of Trithiocyanato (4,4‘,4‘ ‘-Tricarboxy-2,2‘:6,2‘ ‘-terpyridine) Ruthenium(II) Complexes: A DFT Study

Black dye (BD), isomer 1 ([Ru(II)(H3-tctpy)(NCS)3](-1), where H3-tctpy = 4,4',4' '-tricarboxy-2,2':6,2' '-terpyridine) is known to be an excellent sensitizer for dye-sensitized solar cells and exhibits a very good near-IR photo response, compared to other ruthenium dyes. Because isothiocyanate is a linear ambidentate ligand, BD has three other linkage isomers, [Ru(H3-tctpy)(NCS)2(SCN)](-1), isomer 2 and 2', and [Ru(H3-tctpy))(SCN)3](-1), isomer 3. In this study, we have calculated the geometry of BD and its isomers by DFT. Further, we have analyzed the bonding in these isomers using NBO methods. TDDFT calculations combined with scalar relativistic zero-order regular approximations (SR-ZORA) have been carried out to simulate the absorption spectra. Calculations have been performed for the isomers both in vacuo and in solvent (ethanol). The inclusion of the solvent is found to be important to obtain spectra in good agreement with the experiment. The first absorption bands are dominated by the metal-to-ligand charge transfer (MLCT) and ligand-to-ligand charge transfer (LLCT).

Iterative demodulation/decoding methods based on Gaussian approximations for lattice based space-time coded systems

In this letter, we study iterative demodulation and decoding methods for lattice based space-time coded systems concatenated with convolutional codes. We first apply the optimal MAP demodulation and the suboptimal linear MMSE methods to lattice based space-time demodulation and decoding. We then propose two other methods based on the idea of soft interference cancellation and in one method vector Gaussian approximation is used and in the other method scalar Gaussian approximation is used. We also present the EXIT chart analyses for the performance analyses for these iterative methods. Both theoretical and simulation results show that the performance of the vector Gaussian approximation method is the same as that of the linear MMSE method but in some cases the vector Gaussian approximation method has lower complexity. The complexity of the scalar Gaussian approximation method is the lowest among these different methods and grows linearly with the transmission rate while it still has an acceptable performance. Full diversity and full rate lattice based space-time coding is compared with the BLAST scheme and simulations show that the former has a better performance than the later even with the proposed suboptimal iterative demodulation and decoding methods.

Analysis of error yielded by scalar approximation to the properties of laser diode beams

Based on the vector Rayleigh-Sommerfeld far-field diffraction integral formula, a vector model for describing the far field of a laser diode is proposed beyond the paraxial approximation. Through the analysis of the error yielded by the scalar approximation to the properties of laser diode beams, it is found that the error is only correlative with propagation distance and the coordinate perpendicular to the junction plane, and there is a certain relationship between the error and a space angle.

Influence of lateral dimensions of the irregularities on the optical quantities of rough surfaces

In this paper the influence of lateral dimensions of the irregularities on the optical quantities, i.e. on reflectance, transmittance, scattering losses and ellipsometric ratio of randomly rough surfaces, is discussed in detail. This discussion is based on theoretical (simulated) data calculated using the Rayleigh–Rice theory (RRT). It is shown that the optical quantities mentioned are strongly dependent on the quantities characterizing the lateral dimensions of the irregularities, e.g. on the autocorrelation length. The simulated data are also used to investigate the possibilities and limitations of the scalar diffraction theory (SDT) and effective medium approximation (EMA) in treating the experimental data in practice. On the basis of these theoretical studies it is, moreover, shown that a combination of the SDT and EMA can be employed as a reasonable approximation for describing the interaction of light with randomly rough surfaces. Thus, from the results presented in this paper, it is evident that this combination could be a promising treatment for experimental data corresponding to the optical quantities of randomly rough surfaces.

Relativistic Density Functional Theory Study of Dioxoactinide(VI) and -(V) Complexation with Alaskaphyrin and Related Schiff-Base Macrocyclic Ligands

Formation of complexes of alaskaphyrin 1, bi-pyen 2 and bi-tpmd 3 ligands with actinyl ions AnO2(n+), An = U, Np, Pu and n = 1, 2, was studied using density functional theory (DFT) within the scalar relativistic four-component approximation. The alaskaphyrin complexes of the uranyl are predicted to have a bent conformation, in contrast to the experimentally available X-ray data. This deviation is likely due to crystal packing effects. Apart from these conformational differences, calculated geometry parameters and vibrational frequencies are in agreement with the available experimental data. The character of bonding in the complexes is investigated using bond order analysis and extended transition states (ETS) energy decomposition. Metal-to-ligand bonds can be described as primarily ionic although substantial charge transfer is observed as well. Based on ETS analysis, it is shown that steric and/or fit/misfit requirements of actinyl cations to the ligand cavities, among the studied complexes, are the most favorable for the bi-pyen ligand 2, because its flexibility allows for optimal metal-to-donor-atom distances. Planarity of the equatorial coordination sphere of the actinide atom is found to be less important than the ability of a ligand to provide optimal uranium-to-nitrogen bond lengths. Experimental differences in demetalation rates between similar alaskaphyrin, bi-pyen and bi-tpmd uranyl complexes are explained as a result of easier protonation of the Schiff-base nitrogen of the latter. Reduction potentials calculated for the uranium complexes show a good agreement with the experiment, both in relative and in absolute terms.

Two-dimensional nonclose-packed colloidal crystals formed by spincoating

We report a simple spin-coating technique for the production of monolayer nonclose-packed colloidal crystals. Dispersions of submicron silica spheres in triacrylate monomers are spincoated and polymerized to form two-dimensional colloidal crystal-polymer nanocomposites. By removing the polymer matrix, wafer-scale nonclose-packed colloidal crystals with high crystalline quality can be made. The technique is compatible with standard microfabrication and allows for the production of microstructures for potential devices. Normal-incidence reflectivity spectra in the visible and near-infrared regions show sharp peaks due to Bragg diffraction from the colloidal monolayers. The peak position matches with the theoretical prediction using scalar wave approximation.

All-solid silica-based photonic crystal fibers

An index-guiding all-solid photonic crystal fiber (PCF) composed entirely of silica material is proposed in this paper. The core of this optical fiber is composed of pure silica, and the cladding consists of doped silica rod in the background of pure silica. The dependence of confinement loss on the diameter of the doped rods, the number of doped-rod rings, and the doping level is investigated numerically. In addition, the proposed fiber possesses a shorter cutoff wavelength as compared with the air/silica PCF, which is directly confirmed by the V parameter, and explained based on a scalar approximation method. Furthermore, the bending loss for the fiber is predicted. A low-loss single-mode all-solid silica-based PCF with a large-mode-area is possible by the appropriate selection of configuration parameters.

The quadrupole moment of the Sb nucleus from molecular microwave data and calculated relativistic electric-field gradients

The recently determined accurate values of the nuclear quadrupole coupling constant of the Sb nucleus in SbN, SbP, SbF, and SbCl and the calculated electric-field gradients at Sb in these molecules are used to obtain the nuclear quadrupole moment of 121Sb and 123Sb. The calculation of the electric-field gradient has been carried out by using the infinite-order two-component relativistic method in the scalar approximation. The accompanying change of picture of the electric-field gradient operator has been accounted for by employing the shifted nucleus model of nuclear quadrupoles. The electron correlation effects are calculated at the level of the coupled cluster approximation. The present calculations give the "molecular" value of the nuclear quadrupole moment of 121Sb equal to -556+/-24 mb which is considerably different from the old "recommended" value of -360+/-40 mb and also differs from the recent "solid-state" result (-669+/-15 mb). The validation of the present data is comprehensively discussed.

The solution of the vector radiative transfer equation using the discrete ordinates technique: Selected applications

The paper is devoted to the presentation of a newly developed radiative transfer code SCIAPOL_1.0 for a plane-parallel turbid slab illuminated by the monodirectional wide beam. The SCIAPOL_1.0 is based on the discrete-ordinates solution of the vector radiative transfer equation. The code is applied to a number of problems, including studies of the applicability of the scalar approximation for the calculation of light reflectance from aerosols, clouds, and molecular atmospheres. We also study the accuracy of the single scattering approximation as applied to the calculation of light reflection from molecular and cloudy atmospheres and propose new approximations for the calculation of the reflection function and the degree of light polarization under unpolarized light illumination conditions.

Filter of optical vortices: highly twisted high-birefringence optical fibers

Modes and bandgap structure of highly twisted high-birefringence weakly guiding fibers are studied in the scalar approximation. It is shown that within the gap the system can serve as a filter of circular optical vortices.

Polarization and effective Mueller matrix for multiple scattering of light by nonspherical ice crystals

We investigated the errors associated with the scalar approximation (i.e., an approach that neglects polarization effects) for simulating the intensity of the radiation reflected by an ice cloud. In a case for an optical thickness of tau=1, the relative errors of the scalar approximation are typically between -0.5% and 0.1%. We also investigated the effect of the order of scattering on the degree of linear polarization. It is shown that substantial errors can be introduced by the first-order scattering approximation, and thus, the multiple-scattering effect is essential to an accurate simulation of the polarization configuration of a radiation field. Furthermore, we investigate the effective Mueller matrix pertaining to multiple scattering of light by ice clouds. The effective Mueller matrix is a 4x4 matrix that relates the incident and scattered Stokes parameters. This matrix implicitly contains the effects of all orders of scattering and absorbing events in the entire radiation transfer process. The sensitivity of the (2,1) and (3,1) elements of the effective Mueller matrix to ice crystal shape and size indicates that polarimetric information may be useful for inferring the microphysical properties of ice crystals within ice clouds.

Full-vectorial analysis of optical waveguides by the finite difference method based on polynomial interpolation

Based on the polynomial interpolation, a new finite difference (FD) method in solving the full-vectorial guided-modes for step-index optical waveguides is proposed. The discontinuities of the normal components of the electric field across abrupt dielectric interfaces are considered in the absence of the limitations of scalar and semivectorial approximation and the present FD scheme can be applied to both uniform and non-uniform mesh grids. The modal propagation constants and field distributions for buried rectangular waveguides and optical rib waveguides are presented. The hybrid nature of the vectorial modes is demonstrated and the singular behaviours of the minor field components in the corners are observed. Moreover, solutions are in good agreement with those published early, which tests the validity of the present approach.

Modal Analysis and Waveguide Dispersion of an Optical Waveguide Having a cross-section of the Shape of a Cardioid

In this paper, we choose a simple and practical analytical method based on scalar wave approximation to study the modal behaviour, cutoff condition of an unconventional optical waveguide having a cross section of the shape of a cardioid. We take the appropriate orthogonal coordinates for the proposed structure and impose the boundary conditions under the weak guidance approximation to get the modal eigen value equation. Using this equation we obtain numerical results in the form of dispersion curves and cutoff frequencies. Also the dependence, d(Vb′)/dV on V has been obtained and shown graphically, where V stands for normalized frequency parameter and b′ stands for normalized propagation constant. An attempt has been made to estimate how the modal behaviour and waveguide dispersion change as circular shape is changed to the shape of a cardioid.

Preaveraged Hydrodynamic Interaction Revisited via Boundary Element Computations.

The effect of preaveraging the Oseen tensor to yield a scalar approximation is examined for transport problems of rigid objects with stick boundary conditions using new very high accuracy computational codes. Nearly exact computations are compared to analytical results and preaveraged results for spheroids and, similarly, for a set of three globular proteins. In agreement with previous work, we find that the error in translational diffusion is less than 1%. However, in the case of rotational diffusion and intrinsic viscosity, the error is sensitively dependent on shape. In the case of the axial component of the rotational diffusion, the error is about -34% independent of shape, but for the perpendicular component, the error starts at -30% (sphere) and decreases as the axial ratio increases and then yields a similar but positive error. For the instrinsic viscosity, the errors are around 10% near spherical and decrease toward the needle or disk shape. For the globular proteins, the errors are similar to those found for the ellipsoids near the spherical shape. The calculations show that preaveraging is acceptable only for translational diffusion of rigid objects.