Scattering of light by polydisperse, randomly oriented, finite circular cylinders

We use the T-matrix method, as described by Mishchenko [Appl. Opt. 32, 4652 (1993)], to compute rigorously light scattering by finite circular cylinders in random orientation. First we discuss numerical aspects of T -matrix computations specific for finite cylinders and present results of benchmark computations for a simple cylinder model. Then we report results of extensive computations for polydisperse, randomly oriented cylinders with a refractive index of 1.53 + 0.008i, diameter-to-length ratios of 1/2, 1/1.4, 1, 1.4, and 2, and effective size parameters ranging from 0 to 25. These computations parallel our recent study of light scattering by polydisperse, randomly oriented spheroids and are used to compare scattering properties of the two classes of simple convex particles. Despite the significant difference in shape between the two particle types (entirely smooth surface for spheroids and sharp rectangular edges for cylinders), the comparison shows rather small differences in the integral photometric characteristics (total optical cross sections, single-scattering albedo, and asymmetry parameter of the phase function) and the phase function. The general patterns of the other elements of the scattering matrix for cylinders and aspect-ratio-equivalent spheroids are also qualitatively similar, although noticeable quantitative differences can be found in some particular cases. In general, cylinders demonstrate much less shape dependence of the elements of the scattering matrix than do spheroids. Our computations show that, like spheroids and bispheres, cylinders with surface-equivalent radii smaller than a wavelength can strongly depolarize backscattered light, thus suggesting that backscattering depolarization for nonspherical particles cannot be universally explained by using only geometric-optics considerations.     

Propagation of electromagnetic waves through a system of randomly placed cylinders: the partial scattering wave resonance

Propagation of electromagnetic waves through a system of randomly placed cylinders has been modelled. It was found that there is a dip in the ballistic transmission spectra for both the E and H polarizations, which is associated with scattering of the partial wave with angular momentum equal to zero by a single cylinder.     

Scattering of electromagnetic waves by a perfect electromagnetic conducting sphero

An exact solution to the problem of scattering of electromagnetic waves from a perfect electromagnetic conducting spheroid is presented, using the method of separation of variables. The formulation of the problem is realised by expanding the incident as well as the scattered electromagnetic fields in terms of appropriate spheroidal vector wave functions and imposing the appropriate boundary conditions at the surface of the spheroid. This generates a set of simultaneous equations, the solution of which yields the unknown coefficients associated with the expansion of the scattered electromagnetic field. Results are presented in the form of normalised bistatic and backscattering cross-sections for spheroids of different axial ratios, sizes and admittances, for both transverse electric and transverse magnetic polarisations of the incident wave.     

Incoherent intensities of electromagnetic waves in a random medium layer and radiative transfer theory

Abstract

Equations for incoherent intensities are obtained for electromagnetic waves in a random medium layer with plane parallel boundaries. These are based on the Bethe–Salpeter equation under the ladder approximation. These equations are then compared with the radiative transfer equations for this problem. Differences between these two approaches are pointed out and discussed. The Müller matrix is derived based on a first-order approximation to the equations for incoherent intensities which is then used to highlight the significance of the above-mentioned differences in radar cross-section computations.     

Scattering of electromagnetic radiation by a metal nanoparticle

The scattering cross section of electromagnetic radiation by a small spherical metal particle has been calculated in the framework of the standard kinetic theory in a dipole approximation. The calculation has been performed for relatively small (～10 nm) particles, which allows the skin effect to be ignored. A mechanism of mixed specular-diffuse reflection of conduction electrons from the particle surface is considered. It is established that, at certain angles of scattering, the mechanism of magnetic-dipole scattering becomes dominating. The influence of kinetic effects on the differential scattering cross section is analyzed.     

Magnetic shielding by superconducting simple and coaxial cylinders: a comparison

The attenuation of external magnetic fields by superconducting simple and coaxial cylinders are given. It is shown that inserting a superconducting rod into a simple superconducting cylinder of radius r reduces the attenuation of fields normal to the z-axis from exp (— 1.84 z/r) to exp (— 1.0 z/r) in the narrow gap limit.     

Scattering of electromagnetic plane wave from a perfect electric conducting strip located in topological insulator medium

In this article, scattering from a perfectly electric conducting strip located in an infinitely extended topological insulator (IT) medium is investigated using the Kobayashi potential method. For solving mixed boundary value problem, KP method is a fast and semi-analytical technique. In this method, edge conditions and boundary conditions are incorporated simultaneously. The scattered field is calculated from the strip geometry embedded in IT medium. The far zone scattered field is investigated with respect to different parameters of the geometry, i.e. topological parameter of the IT medium, size of the strip etc. It has been observed that the scattered field can be enhanced by increasing topological parameter of the IT medium. On the other hand, size of strip, permittivity of IT medium may also be used to enhance the main lobe of the scattering width/scattered field.     

Scattering by a dense layer of infinite cylinders at normal incidence

The solution for scattering by a layer of densely distributed infinite cylinders is presented. The layer is irradiated by an arbitrarily polarized plane wave that propagates in the plane perpendicular to the axes of the cylinders. The theoretical formulation utilized the effective field and quasi-crystalline approximation to treat the multiple scattering interactions in the dense finite medium. Governing equations for the propagation constants and amplitudes of the effective fields are derived for TM and TE mode incident waves, from which the scattered intensity distribution and scattering cross section for arbitrary polarization are obtained. The dense medium gives rise to coherent and incoherent scattered radiation that propagates in the plane normal to the axes of the cylinders. The coherent scattered radiation includes the forward component in the direction of the incident wave and the backward component in the direction of specular reflection. The incoherent scattered intensity distribution shows a pronounced forward peak that coincides with the angle of refraction of the effective waves inside the medium. Numerical results are presented to illustrate the scattering characteristics of a dense layer of cylinders as a function of layer thickness for a given solid volume fraction.     

Optical extinction by closely spaced parallel cylinders inside a finite dielectric slab

The formulation for the extinction and scattering cross sections of closely spaced parallel infinite cylinders in a dielectric medium of finite thickness is presented. We consider the general case of dissimilar refractive indices for the half-spaces on both sides of the slab, and the diameter and refractive index of each cylinder can be different. The formulation accounts for the coherent scattering between the cylinders and scattering of the multiply reflected internal waves inside the slab. Discontinuity in the refractive index across the dielectric slab interfaces results in boundary reflections that modify the angular distribution of the scattered intensity in both forward and backward directions. The extinction cross section, which is derived by a formal application of the optical theorem, is shown to consist of both a forward and a backward component. The general solution is applied to obtain the formulas for the cases of cylinders in front of a reflecting plane, cylinders inside a semi-infinite dielectric medium, and cylinders in free space.     

Scattering of plane electromagnetic waves by a chiral-metal cylinder

The problem of scattering of E-and H-polarized plane electromagnetic waves by a metal cylinder covered with a chiral layer is solved by the method of partial regions. The scattering field is studied in the near and far zones. The correlation between the type of polarization of the incident electromagnetic wave and the magnitude of the depolarized component of the scattered field is considered.     

Polychromatic reflectance and transmittance of a slab with a randomly rough boundary

We investigated four different approximation models for describing the polychromatic reflectance and transmittance of a slab with a randomly rough boundary while taking into account the coherent and the incoherent scattering of the rough boundary. Comparisons with experiments (an etched-silicon wafer) show that approximation models that apply a two-scale roughness to the randomly rough boundary and that take into account the coherent and the incoherent scattering yield better agreement and extend the range of validity of the approximation to shorter wavelengths.     

Scattering by a dense finite layer of infinite cylinders at oblique incidence

This paper presents the scattering solution for a finite dense layer of cylinders irradiated by an arbitrarily polarized plane wave at a general incident direction. The theoretical formulation utilizes the effective field approach and quasi-crystalline approximation to derive the governing equations for the propagation constant and amplitudes of the effective waves. The finite layer thickness gives rise to effective waves propagating in both the forward and backward directions inside the dense medium. Formulas are developed for the far-field coherent and incoherent scattered intensities, as well as the extinction and scattering cross sections of the dense layer. The forward peak of the incoherent scattered intensity is shown to be shifted to the propagating direction of the effective waves. The influence of incident direction, layer thickness, and solid volume fraction on the scattering properties is illustrated by means of a numerical example.     

Relationship between the Kubelka-Munk scattering and radiative transfer coefficients

The relationship between the Kubelka-Munk (K-M) and the transport scattering coefficient is obtained through a semi-empirical approach. This approach gives the same result as that given by Gate [Appl. Opt.13, 236 (1974)] when the incident beam is diffuse. This result and those given by Star et al. [Phys. Med. Biol.33, 437 (1988)] and Brinkworth [Appl. Opt.11, 1434 (1972)] are compared with the exact solution of the radiative transfer equation over a large range of optical properties. It is found that the latter expressions, which include an absorption component, do not give accurate results over the range considered. Using the semi-empirical approach, the relationship between the K-M and the transport scattering coefficient is derived for the case where the incident light is collimated. It is shown that although the K-M equation is derived based on diffuse incident light, it can also represent very well the reflectance from a slab of infinite thickness when the incident light is collimated. However, in this case the relationship between the coefficients has to include a function that is dependent on the anisotropy factor. Analysis indicates that the K-M transform achieves the objective of obtaining a measure that gives the ratio of absorption to scattering effects for both diffuse and collimated incident beams over a large range of optical properties.     

Calculation of radiative transfer in nongray gas using a narrow-band model and Monte Carlo simulation

Radiation transfer is treated by the application of a narrow-band statistical model (NBSM) that takes emission and absorption gas spectral structures into account. A Monte Carlo method (MCM) using a net exchange technique was developed to integrate the radiative-transfer equation in nongray gas. The proposed procedure is based on a net-exchange formulation (NEF). This formulation provides an efficient way of systematically fulfilling the reciprocity principle, which avoids some of the major problems usually associated with the Monte Carlo method; the numerical efficiency becomes independent of the optical thickness, highly nonuniform grid sizes can be used with no increase in computation time, and configurations with small temperature differences can be treated with very good accuracy. It is shown that the radiative term is significant compared to the conductive term in just two specific regions in the emitting and absorbing gas in the immediate vicinity of the wall and in the external part of the boundary layer. The exchange Monte Carlo method (EMCM) is described in detail for a one-dimensional slab.     

Reflectance of pigmented polymer coatings: comparisons between measurements and radiative transfer calculations

Solar reflectance spectra of pigmented coatings have been obtained from spectroscopic measurements involving integrating sphere attachments. We demonstrate that measured and computed reflectances of an extended four-flux model [Appl. Opt. 37, 2615 (1998)] whose average path-length parameters (APP's) and forward-scattering ratios (FSR's) are explicitly evaluated from a multiple-scattering approach at the front or back interface of the particulate coatings display fairly good agreement. The agreement of these properties in a standard four-flux model [Appl. Opt. 23, 3353 (1984)], which neglects the spectral dependence of the APP and FSR, is found in the near infrared. Good agreement between these two four-flux approaches over the solar spectral range is obtained when the mean values of the APP's and FSR's are used in the standard model.     

Scattering of electromagnetic spherical waves by a buried spheroidal perfect conductor

We examine the electromagnetic scattering of spherical waves by a buried spheroidal perfect conductor. The proposed analysis is based on the integral equation formalism of the problem and focuses on the establishment of a multiparametric model describing analytically the scattering process under consideration. Both the theoretical and the numerical treatment are presented. The outcome of the analysis is the determination of the scattered field in the observation environment along with its multivariable on several physical and geometric parameters of the system.     

Scattering of electromagnetic waves by a coated not perfectly conducting sphere

We consider the low-frequency scattering problem of a plane electromagnetic wave by a sphere, which is covered by a penetrable concentric spherical shell. The medium, occupying the shell, is lossless while on the surface of the core an impedance boundary condition is satisfied. The impedance boundary condition was introduced by Leontovich (Investigations of Radiowave Propagation. Part II, Academy of Science, Moscow, 1948) and it accounts for situations where the obstacle is not perfectly conducting but the exterior field will not penetrate deeply into the scatterer. For the near electromagnetic field we obtain the low-frequency coefficients of the zeroth and the first orders while in the far field we derive the leading non-vanishing terms for the scattering amplitude and the scattering cross-section. Spherical coated obstacles are very important in applications. Small particles in biological suspensions, cells, some human organs, atmospheric particles and granules within composite materials are only a few examples of applied interest in science and technology.     

Scattering of electromagnetic radiation by multilayered spheroidal particles: recursive procedure

A formalism is developed for the calculation of the electromagnetic field scattered by a multilayered spheroidal particle. The suggested formalism utilizes the recursive approach with respect to passing from one layer to the next; thus it does not require an increase in the size of the equation matrices involved as the number of layers increases. The equations operate with matrices of the same size as for a homogeneous spheroid. The special cases of extremely prolate and weakly prolate spheroids are considered in more detail. It is shown that in such cases one can avoid the matrix calculations by instead using the iterative scalar calculations.