Isotropic scattering by penetrable cylinders

Isotropic scattering is considered for infinite cylinders thin in the sense that ka < 1, although ?k'a? and cross-sectional shape can be arbitrary within limits (k and k' are, respectively, free-space and interior propagation constants, and a is a characteristic dimension of the cylinder). For circular cylinders, scattering width is found to saturate at its perfectly conducting value, and absorption width is found to peak, when skin depth becomes comparable with cylinder diameter. For a variety of cylinders with and without edges, both scattering and absorption widths are then found to be effectively identical to those of the circular cylinder with equal cross-sectional area. A new analytical formula is obtained for high but not infinite conductivity, and the connection with scattering cross sections of corresponding finite cylinders is discussed.     

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.     

Electric line source illumination of a chiral cylinder placed in another chiral background medium

An electric line source illumination of a chiral cylinder embedded in a chiral background medium is considered. The field expressions inside and outside of a chiral cylinder have been derived using the wave field decomposition approach. The effects of various chiral cylinders, chiral background media and source locations upon the scattering gain pattern have been investigated. It is observed that the chiral background reduces the backward scattering gain as compared to the free space background for a dielectric cylinder. It is also studied that by moving a line source away from a cylinder reduces the backward scattering gain for a chiral cylinder placed in a chiral background under some specific conditions. A unique phenomenon of reduced scattering gain has been observed at a specific observation angle for a chiral cylinder placed in a chiral background having an electric line source location of unity free space wavelength. An isotropic scattering gain pattern is observed for a chiral nihility background provided that if cylinder is chiral or chiral nihility type. It is also observed that this isotropic behaviour is independent of background and cylinder chirality.     

Scattering of elastic P- and SV-waves by a circular coated nanofiber based on Gurtin–Murdoch model of surface elasticity: Scattering cross section results

In this article, an analytical study of elastic P- and SV-wave scattering by a circular nanofiber is presented. The nanofiber is assumed to be surrounded by an inhomogeneous interphase layer, and Gurtin–Murdoch's model of surface elasticity is utilized to study the surface/interface effects in the regions between the fiber and interphase and also interphase and matrix. The simultaneous effects of surface elasticity and interphase inhomogeneity are considered here; by taking the inhomogeneous interphase to be composed of several sublayers, a transfer matrix approach is used to find the unknown field variables and, consequently, the scattering cross sections. The results indicate that considering the effects of surface elasticity and interphase inhomogeneity has a considerable impact on the calculated scattering cross sections.     

An integral equation approach to eddy-current calculations

An integral-equation approach has been used to solve eddy current problems. The conducting material is represented by a network of current-carrying line elements. Consequently, Maxwell's field equations can be replaced by Kirchhoff's circuit rules. The loop equations for voltages, supplemented by the node equations for the currents, comprise a set of linear equations that can be solved repeatedly to give the time development of the eddy currents. Currents, magnetic fields, and power are calculated at each step. For a two-dimensional geometry, either thin plates or infinite cylinders can be calculated. Rectangular and circular cross sections have been calculated with good agreement to analytical expressions. Thin curved shells have also been calculated.     

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.     

The scattering of water waves by an array of circular cylinders in a channel

The full linear problem of the scattering of water waves by an array of N bottom-mounted vertical circular cylinders situated in a channel of constant depth and width is solved using the method of multipoles. A simple formula is derived for the velocity potential in the vicinity of a cylinder, and in particular on the cylinder surfaces, which allows hydrodynamic quantities such as forces to be easily evaluated. The simplicity of the solution makes the evaluation of quantities of interest straightforward and extensive results are given. An approximate solution for the forces on the cylinders, based on the assumption that the wavelength of the incident wave is long compared with the cylinder radii, is also given, and this is compared with results from the exact linear solution.     

Light scattering by a coated infinite cylinder in an absorbing medium

The scattering formulation for a coated infinite cylinder in an absorbing medium is presented in this paper. The cylinder is subjected to an arbitrarily polarized plane wave propagating in a general direction at the cylinder. The refractive index and magnetic permeability of the host medium, as well as those for the core and coating of the cylinder, can be real or complex. The scattering and extinction efficiencies and the scattering amplitudes are derived for both the near field and the far field. As the medium is absorbing, the "true" extinction and scattering efficiencies are derived based on the radiative energy outflow at the surface of the cylinder. The radiative efficiencies in the far field are denoted as "apparent" properties because they include absorption by the intervening medium. The influence of the refractive index and permeability of the host medium on the scattering properties of a coated cylinder is illustrated by numerical examples.     

Use of circular cylinders as surrogates for hexagonal pristine ice crystals in scattering calculations at infrared wavelengths

We investigate the errors associated with the use of circular cylinders as surrogates for hexagonal columns in computing the optical properties of pristine ice crystals at infrared (8-12-microm) wavelengths. The equivalent circular cylinders are specified in terms of volume (V), projected area (A), and volume-to-area ratio that are equal to those of the hexagonal columns. We use the T-matrix method to compute the optical properties of the equivalent circular cylinders. We apply the finite-difference time-domain method to compute the optical properties of hexagonal ice columns smaller than 40 microm. For hexagonal columns larger than 40 microm we employ an improved geometric optics method and a stretched scattering potential technique developed in previous studies to calculate the phase function and the extinction (or absorption) efficiency, respectively. The differences between the results for circular cylinders and hexagonal columns are of the order of a few percent. Thus it is quite reasonable to use a circular cylinder geometry as a surrogate for pristine hexagonal ice columns for scattering calculations at infrared (8-12-microm) wavelengths. Although the pristine ice crystals can be approximated as circular cylinders in scattering calculations at infrared wavelengths, it is shown that optical properties of individual aggregates cannot be well approximated by those of individual finite columns or cylinders.     

Light scattering at oblique incidence on two coaxial cylinders

A solution for the problem of a plane wave at oblique incidence on two coaxial cylinders is presented. The solution of the wave equation is determined for various geometric regions, and boundary conditions are applied at the material interfaces. The resulting solution consists of a system of eight equations in eight unknown coefficients. Expressions for two of the Mueller-scattering matrix elements (S(11) and S(12)) and the extinction, scattering, and backscattering cross sections are derived. A numerical algorithm for the solution is developed and implemented. The algorithm is tested for several limiting cases: homogeneous, hollow, and metal-core cylinders at various angles of incidence for TM and TE waves. Comparisons of the results of the algorithm with the results of studies reported in the literature are made. The comparisons are favorable, achieving good agreement with published work. For two coaxial cylinders, the numerical calculations show that if one is to use light scattering as a diagnostic tool, both of the Mueller-scattering matrix elements S(11) and S(12) must be measured simultaneously. In addition, the backscattering cross section is very sensitive for monitoring change in the radii of the cylinders.     

Scattering of antiplane shear wave by a piezoelectric circular cylinder with an imperfect interface

Summary We present analytical solutions for the scattering of an antiplane shear wave by a piezoelectric circular cylinder with an imperfect interface. We first consider the simple case in which the imperfection is homogeneous along the interface. Two typical imperfect interfaces are addressed: 1) mechanically compliant and dielectrically weakly conducting interface, and 2) mechanically compliant and dielectrically highly conducting interface. The expressions for the directivity pattern and scattering cross-section of the scattered shear waves are derived. We then investigate the more difficult problem in which the imperfection is circumferentially inhomogeneous along the interface. A concise expression for an inhomogeneously compliant and weakly conducting interface is derived by means of matrix notation. Numerical examples are presented to demonstrate the effect of the imperfection and the circumferential inhomogeneity of the interface on the directivity patterns and scattering cross-sections of the scattered shear wave. The circumferentially inhomogeneous interface is also utilized to model the interface where an arbitrary number of cracks exist. Results show that when every part of the interface is rather compliant, large low-frequency peaks of the scattered cross-sections, which correspond to the resonance scattering, can be observed no matter if the interface is homogeneous or inhomogeneous. The appearance of large low-frequency peaks can be well explained by estimating the natural frequency of the corresponding reduced mass-spring system where the cylinder is assumed as a rigid body. Peaks of the scattered cross-sections spanning from low frequencies to high frequencies can be observed for a cylinder with a partially debonded interface.     

Scattering of elastic P and SV waves by a rigid elliptic cylindrical inclusion

The 2-dimensional problem of scattering of obliquely incident $\text{P}$ and SV waves by an infinite rigid elliptic cylinder embedded in an infinite, isotropic and homogeneous elastic medium is solved. Approximate formulas are derived for the displacement field, stress tensor, far-field amplitudes and the scattering cross section when the wave lengths are large compared to the distance between the two focii of the elliptic cylinder.     

Application of the sinc basis moment method to the reconstruction of infinite circular cylinders

A solution of the ultrasonic scattering and inverse scattering problem has been obtained by solving the inhomogeneous Helmholtz wave equation by the sinc basis moment method. In this numerical study, the algorithm of S.A. Johnson and M.L. Tracy (1983) has been applied to the reconstruction of an infinite circular cylinder that is subject to an incident cylindrical wave of ultrasound and is surrounded by a homogeneous coupling medium. For weak scattering cylinders, successful reconstructions have been obtained using the known exact solution for the scattered field as the input data for the algorithm. A detailed discussion of sampling requirements for this algorithm is presented, and the threshold derived correlates well with results of a numerical study of variation of the sampling density. Effects of varying object contrast, object size, grid size, sampling density, and method of iteration are investigated. Because the algorithm is slow, optimization of computation is described.     

Generalized Lorenz-Mie theory for an arbitrarily oriented, located, and shaped beam scattered by a homogeneous spheroid

The theory of an arbitrarily oriented, shaped, and located beam scattered by a homogeneous spheroid is developed within the framework of the generalized Lorenz-Mie theory (GLMT). The incident beam is expanded in terms of the spheroidal vector wave functions and described by a set of beam shape coefficients (G(m)(n),(TM),G(m)(n),(TE)). Analytical expressions of the far-field scattering and extinction cross sections are derived. As two special cases, plane wave scattering by a spheroid and shaped beam scattered by a sphere can be recovered from the present theory, which is verified both theoretically and numerically. Calculations of the far-field scattering and cross sections are performed to study the shaped beam scattered by a spheroid, which can be prolate or oblate, transparent or absorbing.     

S approximation for light scattering by an infinitely long cylinder

We obtain a simple expression for the scattering functions for perpendicular incidence in the main form of the S approximation for light scattered by an infinitely long, circular, dielectric cylinder. We numerically validate resulting expressions for extinction efficiency and scattered intensity against exact results.     

Near zone scattering and extinction properties of a left handed material cylinder buried in a semi infinite medium with rough interface

A solution utilizing the spectral plane wave representation of fields (SPRF) combined with the extended boundary condition method (EBCM) is presented to study the scattering and extinction properties of a left handed material cylinder buried in a semi infinite medium with a rough interface. The EBCM is used to evaluate the field transmitted through the interface, which excites the cylinder. The SPRF is used to study the interaction of scattered field from the cylinder with the rough interface. The effect of the negative permittivity and permeability of the cylinder on the far zone scattered field is observed. Further, the near zone scattered field is investigated, which is very helpful to characterize the scenario in which object detection is a challenging task. It is also observed that the electrical size is an important factor affecting the near zone scattered field since the extinction cross section depends upon size.     

Electromagnetic scattering by an infinite cylinder of material or metamaterial coating eccentrically a dielectric cylinder

The electromagnetic scattering by an infinite cylinder of dielectric material or metamaterial, coating eccentrically another infinite dielectric cylinder, is treated in this work. The problem is solved using classical separation of variables techniques. No use is made of the translational addition theorem. For small eccentricities h = d/a(? 1), where d is the distance between the axes of the cylinders and a the radius of the outer cylinder, we use instead the cosine and the sine laws to satisfy the boundary conditions at the surface of the outer cylinder. Keeping terms up to the order h2 we finally obtain exact, closed-form expressions for the expansion coefficients g(1) and g(2) in the relation S(h) = S(0)[1 + g(1)h + g(2)h2 + O(h3)], giving the scattered field and the scattering cross sections of the problem, where S(0) corresponds to the coaxial geometry, with h = 0 (d = 0). Both polarizations are considered for normal incidence. Numerical results are given for various values of the parameters, corresponding to materials or metamaterials. Our method is an alternative of the one using the translational addition theorem in the case of small eccentricities h.     

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.     

Application of the exact solution for scattering by an infinite cylinder to the estimation of scattering by a finite cylinder

A new algorithm for cylindrical Bessel functions that is similar to the one for spherical Bessel functions allows us to compute scattering functions for infinitely long cylinders covering sizes ka = 2πa/λ up to 8000 through the use of only an eight-digit single-precision machine computation. The scattering function and complex extinction coefficient of a finite cylinder that is seen near perpendicular incidence are derived from those of an infinitely long cylinder by the use of Huygens's principle. The result, which contains no arbitrary normalization factor, agrees quite well with analog microwave measurements of both extinction and scattering for such cylinders, even for an aspect ratio p = l/(2a) as low as 2. Rainbows produced by cylinders are similar to those for spherical drops but are brighter and have a lower contrast.     

A Rigorous Theory for Problems of Scattering: The Delta Boundary Operator Method

Abstract

A rigorous approach for solving a large class of scattering problems is presented and implemented for the classical problem of scattering by a perfectly conducting circular cylinder. This method is characterized by the preliminary calculations of a ψ distribution, deduced from a new kind of boundary value problem. This ψ distribution allows us to express the surface current density in the form of the integral of a known function, valid for any kind of incident wave. Numerical comparisons with the classical method are performed. A numerical study of ψ allows us to deal with cylinders having diameters larger than 100 wavelengths on a HP 1000 F minicomputer.