Slab Of Finite Thickness Research Articles

Simple and accurate expressions for diffuse reflectance of semi-infinite and two-layer absorbing and scattering media

We present computationally efficient and accurate semiempirical models of light transfer suitable for real-time diffuse reflectance spectroscopy. The models predict the diffuse reflectance of both (i) semi-infinite homogeneous and (ii) two-layer media exposed to normal and collimated light. The two-layer medium consisted of a plane-parallel slab of finite thickness over a semi-infinite layer with identical index of refraction but different absorption and scattering properties. The model accounted for absorption and anisotropic scattering, as well as for internal reflection at the medium/air interface. All media were assumed to be nonemitting, strongly forward scattering, with indices of refraction between 1.00 and 1.44 and transport single-scattering albedos between 0.50 and 0.99. First, simple analytical expressions for the diffuse reflectance of the semi-infinite and two-layer media considered were derived using the two-flux approximation. Then, parameters appearing in the analytical expression previously derived were instead fitted to match results from more accurate Monte Carlo simulations. A single semiempirical parameter was sufficient to relate the diffuse reflectance to the radiative properties and thickness of the semi-infinite and two-layer media. The present model can be used for a wide range of applications including noninvasive diagnosis of biological tissue.

Conjugate Mixed Convection Heat Transfer in Plane Laminar Wall Jet Flow

A numerical investigation of heat transfer from a uniformly heated slab of finite thickness by plane laminar wall jet flow under combined forced and natural convection, i.e., mixed convection, is presented. The problem has been solved for two classical cases such as Pr ≪ 1 and Pr ≫ 1. The effects of the Grashof number (Gr), Reynolds number (Re), Prandtl number (Pr), and thermal conductivity ratio (Rk) between the slab and fluid medium are investigated on the heat transfer characteristics, i.e., local Nusselt number, interface temperature, and average Nusselt number.

MULTI-LINE STOKES INVERSION FOR PROMINENCE MAGNETIC-FIELD DIAGNOSTICS

We present test results on the simultaneous inversion of the Stokes profiles of the He I lines at 587.6 nm (D_3) and 1083.0 nm in prominences (90-deg scattering). We created datasets of synthetic Stokes profiles for the case of quiescent prominences (B<200 G), assuming a conservative value of 10^-3 of the peak intensity for the polarimetric sensitivity of the simulated observations. In this work, we focus on the error analysis for the inference of the magnetic field vector, under the usual assumption that the prominence can be assimilated to a slab of finite optical thickness with uniform magnetic and thermodynamic properties. We find that the simultaneous inversion of the two lines significantly reduces the errors on the inference of the magnetic field vector, with respect to the case of single-line inversion. These results provide a solid justification for current and future instrumental efforts with multi-line capabilities for the observations of solar prominences and filaments.

New model for dwelling dose calculation using Monte Carlo integration

A new methodology and computer model using Monte Carlo simulation for indoor dose calculation are developed. A room model of six rectangular slabs of finite thickness with door or window in each slab was used. Point-kernel photon transport model with self-absorption correction was applied for dose calculations. New software was designed and programmed using Pascal programming language, which was evaluated for standard room design. The calculated dose due to natural radionuclides in the concert walls has differences from the average model results of 0.21% for (238)U, 12.3% for (232)Th and 13.9% for (40)K; and the variability of specific dose rate with changing position density and composition of walls was studied. The new model has more flexibility for real dose calculation of any room structure and tailing, which is not given in the published models.

Diffraction of electromagnetic plane wave by an infinitely long conducting strip on dielectric slab

Diffraction of electromagnetic plane wave by an infinitely long conducting strip which is placed on a dielectric slab of finite thickness is formulated rigorously. Both the principal polarizations have been considered. The method of analysis is Kobayashi potential. Imposition of boundary conditions result in dual integral equations. These dual integral equations are reduced to matrix equations with infinite number of unknowns. The elements of the matrix equations are given in terms of infinite integrals. These integrals are hard to solve analytically, so computed numerically. Diffracted far field patterns for different angle of incidence have been computed. Current distributions on the strip are also presented. We have compared our field patterns with those of obtained through physical optics. The agreement is good.

Analytical modelling of double-negative composites

Analytical model of metamaterials comprising lattices of small resonant scatterers and (optionally) infinite wires is developed for the case when the planar grids of magnetic dipoles alternate with those of electric dipoles (or those of wires) along the direction of the wave propagation. An important question on the possibility to extract material parameters from measurements or simulations of the plane-wave scattering matrix for finite-thickness slabs of left-handed metamaterials is revisited. It is shown that the class of Bloch lattices (for which this extraction makes sense) is broader than one could judge upon the previous works. Also, it is shown that the spatial dispersion that destroys the operation of double-negative media can arise for the oblique propagation with respect to crystal planes even if it is not revealed from the analysis of the normal propagation.

C-C 5H 5 on a Ni(1 1 1) surface: Theoretical study of the adsorption, electronic structure and bonding

In the present work the ASED-MO method is applied to study the adsorption of cyclopentadienyl anion on a Ni(1 1 1) surface. The adsorption with the centre of the aromatic ring placed above the hollow position has been identified to be energetically the most favourable. The aromatic ring remains almost flat, the H atoms are tilted 17° away from the metal surface. We modelled the metal surface by a two-dimensional slab of finite thickness, with an overlayer of c-C 5H 5 −, one c-C 5H 5 − per nine surface Ni atoms. The c-C 5H 5 − molecule is attached to the surface with its five C atoms bonding mainly with three Ni atoms. The Ni Ni bond in the underlying surface and the C C bonds of c-C 5H 5 − are weakened upon adsorption. We found that the band of Ni 5 d z 2 orbitals plays an important role in the bonding between c-C 5H 5 − and the surface, as do the Ni 6s and 6p z bands.

Influence of slab thickness on the Casimir force

We calculate the Casimir force between slabs of finite thickness made of intrinsic and doped silicon with different concentration of carriers and compare the results to those obtained for gold slabs. We use the Drude and the plasma models to describe the dielectric function for the carriers in doped Si. We discuss the possibility of experimentally testing the appropriateness of these models. We also investigate the influence of finite thickness on $VO_2$, which has recently been proposed for Casimir effect measurements testing the metal-insulator transition.

NUMERICAL SIMULATION OF PROPAGATION OF EM PULSE THROUGH LOSSLESS NON-UNIFORM DIELECTRIC SLAB USING CHARACTERISTIC-BASED METHOD

This paper demonstrates the one-dimensional computa- tional results of the propagation of Gaussian electromagnetic pulse through dielectric slabs of finite thickness with variation in permittiv- ity. The numerical approach used is the characteristic-based method solving the time-domain Maxwell curl equations involved with non- uniform permittivity. In the numerical model, all dielectric slabs are assumed to be isotropic, lossless, and linear. The permittivity of dielec- tric slab may increase or decrease linearly or sinusoidally. The numer- ical permittivity is finely discretized such that the variation between two adjacent grids is so small that the non-uniform permittivity is as- sumed to be piecewise continuous and consequently can be modeled as an individual block. The numerical results of various electric fields, both in the time- and frequency-domain, are presented and compared based on the dielectric slab of constant permittivity for close investi- gating the effects of the non-uniform permittivity distribution on the electromagnetic fields. It is also shown that under certain arrange- ment of Gaussian electromagnetic pulse and dielectric slab thickness the pattern of field propagation, reflection and transmission, can be reproduced in different time scales and frequency ranges.

Bloch material parameters of magneto-dielectric metamaterials and the concept of Bloch lattices

Metamaterials comprising lattices of small resonant scatterers and (optionally) infinite wires are considered. The crystal planes of these lattices contain magnetic dipoles and electric dipoles (or wires). The set of so-called Bloch material parameters is discussed. A class of lattices for which these parameters describe the transfer matrix of an individual monolayer is considered. These lattices are called as Bloch lattices. It is shown that for Bloch lattices and only for them the Bloch material parameters can be directly extracted from the S-parameters of a finite-thickness metamaterial slab. Material parameters retrieved in this way in the previous literature are either Bloch material parameters or senseless (not invariant with respect of the number of monolayers in the composite slab). Explicit examples of Bloch and non-Bloch lattices are presented. Some intermediate results (two definitions of the Bloch impedance, frequency bounds of the Lorentz–Lorenz formula for the local material parameters, etc.) having practical and theoretical importance are discussed.

Band structure and optical properties of wurtzite semiconductor nanotubes

We develop a comprehensive theoretical model for the band structure of single-crystal faceted nanotubes of wurtzite semiconductors based on the tight-binding approach. We focus on the GaN nanotube grown along the [0001] direction and surrounded by the equivalent surfaces ${1\overline{1}00}$. We first calculate the band structure of the wurtzite slab of finite thickness grown along the axis $[1\overline{1}00]$. We show that dangling bonds on two surfaces of the slab cause surface bands, which form the conduction and valence bands of the slab. Analyzing the symmetry of the single-crystal faceted nanotubes, we conclude that their band structure can be calculated from that of the slab with the help of cyclic boundary conditions. We show that the spectrum of the nanotubes depends both on the thickness of nanotube walls and on the radius. We further study the absorption coefficient of the nanotubes. We demonstrate that, with decreasing wall thickness, the contribution of surface states to the absorption spectrum becomes more pronounced.

Casimir force on real materials—the slab and cavity geometry

We analyse the potential of the geometry of a slab in a planar cavity for the purpose of Casimir force experiments. The force and its dependence on temperature, material properties and finite slab thickness are investigated both analytically and numerically for the slab and walls made of aluminium and teflon FEP respectively. We conclude that such a setup is ideal for measurements of the temperature dependence of the Casimir force. By numerical calculation it is shown that temperature effects are dramatically larger for dielectrics, suggesting that a dielectric such as teflon FEP whose properties vary little within a moderate temperature range, should be considered for experimental purposes. We finally discuss the subtle but fundamental matter of the various Green's two-point function approaches present in the literature and show how they are different formulations describing the same phenomenon.

Superprism effect in a metal-clad terahertz photonic crystal slab

We report an experimental demonstration of the superprism effect in a photonic crystal slab at terahertz frequencies. For a 10% frequency variation around 0.28 THz, the refraction angle at the output facet of a wedge-shaped photonic crystal varies by about 15 degrees. A comparison with the predictions of a band structure calculation demonstrates that a three-dimensional treatment, accurately modeling the finite slab thickness and the metallic boundary conditions, is required for even a qualitative agreement with the experimental observations.

A semi-analytical method to study the temperature evolutions of a slab and a semi-infinite target for plasma immersion ion implantation

The problems of heating a slab of finite thickness and a semi-infinite target with repetitive high negative bias voltage pulses in contact with a plasma are solved by using the two-dimensional Laplace integral transform technique. The plasma is composed of a collisionless presheath and sheath on an electrically negative biased wall, which partially reflects and secondarily emits ions and electrons. The heating of the workpiece from the plasma accounting for the presheath and sheath is determined by kinetic analysis. This work proposes a semi-analytical model to calculate the temperature evolutions and the melting times of the front surface of a slab and a semi-infinite target, and provides quantitative results applicable to control the temperature evolutions and the melting times. The predicted surface temperature of the slab as a function of time is found to agree well with experimental data. The effects of dimensionless pulse parameters, including the pulse duty cycle and pulse bias voltage, on the melting time and heating rate of the front surface are obtained. The results show that the temperatures and heating rates of the front surface of the slab and target increase with pulse parameters. The melting times to initiate the melting at the front surface are strongly dependent on the pulse parameters. The heat flux transport to workpiece from plasma is important to increase the surface temperature of the workpiece when the bias voltage is switched-off for low pulse duty cycle and low pulse bias voltage. The temperature of the workpiece is underestimated when not accounting for the heating effects during the pulse-off duration for low value of pulse parameters.

Resonant transparency of materials with negative permittivity

It is shown that the transparency of opaque material with negative permittivity exhibits resonant behavior. The resonance occurs as a result of the excitation of the surface waves at slab boundaries. Dramatic field amplification of the incident evanescent fields at the resonance improves the resolution of the the sub-wavelength imaging system (superlens). A finite thickness slab can be totally transparent to a \textit{p}-polarized obliquely incident electromagnetic wave for certain values of the incidence angle and wave frequency corresponding to the excitation of the surface modes. At the resonance, two evanescent waves have a finite phase shift providing non-zero energy flux through the non-transparent region.

On an integral equation arising in the transport of radiation through a slab involving internal reflection

In an earlier contribution to this journal [M.M.R. Williams, Eur. Phys. J. B 47 , 291 (2005)], we derived an integral equation for the transmission of radiation through a slab of finite thickness which incorporated internal reflection at the surfaces. Here we generalise the problem to the case when there is a source on each face and the reflection coefficients are different at each face. We also discuss numerical and analytic solutions of the equation discussed in [M.M.R. Williams, Eur. Phys. J. B 47 , 291 (2005)] when the reflection is governed by the Fresnel conditions. We obtain numerical and graphical results for the reflection and transmission coefficients, the scalar intensity and current and the emergent angular distributions at each face. The incident source is either a mono-directional beam or a smoothly varying distribution which goes from isotropic to a normal beam. Of particular interest is the philosophy of the numerical solution and whether a direct numerical approach is more effective than one involving a more elegant analytical solution using replication and the Hilbert problem. We also develop the solution of this problem using diffusion theory and compare the results with the exact transport solution.

Modal Analysis of Finite-Thickness Slab with Single-Negative Tensor Material Parameters

Eigenvalue equations and expressions of EM fields for volume modes in an anisotropic single-negative slab with tensor material parameters is presented. By the comparison with the eigenvalue equation of surface modes along single-negative slab with negative scalar permeability, the validity of the present study is confirmed. We have also made clear which elements of the material parameter tensors affect existence of TE and TM modes in the slab. Taking the dispersion of material parameters into consideration, we demonstrate in detail that TE modes propagate in a slab with one negative element of the permeability tensor numerically. These TE modes turn out to be the magnetostatic waves (MSWs), which is the first demonstration of the MSW in a nonmagnetic material.

The dynamic storage capacity of a periodically heated slab

The well-known problem of evaluating the dynamic heat storage capacity of a 1D slab is analysed extending the results to the more general case of periodic excitation profiles of any form. Equations in time and frequency domain to calculate the storage capacity are obtained and applied to some cases, showing that harmonic heating is not the most efficient way to store energy in finite and semi-infinite slabs. Quantitative comparisons show that, for slab of finite thickness, intermittent heating may yield up to 40% more heat storage capacity (and up to 52% for semi-infinite slab) than harmonic heating.

On the theory of domain structure in ferromagnetic phase of diluted magnetic semiconductors

We present a comprehensive analysis of domain structure formation in ferromagnetic phase of diluted magnetic semiconductors (DMS) of p-type. Our analysis is carried out on the base of effective magnetic free energy of DMS calculated by us earlier [Yu.G. Semenov, V.A. Stephanovich, Phys. Rev. B 67 (2003) 195203]. This free energy, substituting DMS (a disordered magnet) by effective ordered substance, permits to apply the standard phenomenological approach to domain structure calculation. Using coupled system of Maxwell equations with those obtained by minimization of above free energy functional, we show the existence of critical ratio ν cr of concentration of charge carriers and magnetic ions such that sample critical thickness L cr (such that at L < L cr a sample is monodomain) diverges as ν → ν cr . At ν > ν cr the sample is monodomain. This feature makes DMS different from conventional ordered magnets as it gives a possibility to control the sample critical thickness and emerging domain structure period by variation of ν. As concentration of magnetic impurities grows, ν cr → ∞ restoring conventional behavior of ordered magnets. Above facts have been revealed by examination of the temperature of transition to inhomogeneous magnetic state (stripe domain structure) in a slab of finite thickness L of p-type DMS. Our theory can be easily generalized for arbitrary temperature and DMS shape.

Line vortices in a three-dimensional ordered Josephson medium at a small pinning parameter

The structure and energy of a line vortex whose axis is aligned with the symmetry axis of a finite-thickness slab indefinitely long in two directions is calculated by solving a set of linear finite-difference equations. Fluxoid quantization conditions in cells near the center of the vortex serve as boundary conditions. An exact solution is approached by iterations in phase stepwise discontinuities that cannot be considered small. A close similarity between the configuration under study and a periodic sequence (chain) of vortices makes it possible to allow for the effect of the domain boundary on the structure and energy of the vortex. It is shown that, at any width of the slab, one can find a pinning parameter value so small that the vortex cannot be viewed as solitary and contributions from other vortices should be taken into account in calculation. Proceeding in this way, one can find the structure and energy of the vortex however small the pinning parameter is. The total energy of the vortex is its intrinsic energy plus the sum of its energies of interaction with other members of the chain. In turn, the intrinsic energy is the sum of the energies of the small discrete core and quasi-continuous outer shell. It is demonstrated that the energy of the core is a linear function of the pinning parameter and is comparable to the energy of the shell.