Parallel Infinite Cylinders Research Articles

A general solution for scattering by infinite cylinders in the presence of an interface

A general solution for scattering by multiple parallel infinite cylinders in the presence of a half space interface is presented in this paper. The cylinders are located in either or both half spaces, which are irradiated by a homogeneous or evanescent source wave traversing in a direction inclined from the axes of the cylinders. The theoretical approach is an exact analytical treatment that accounts for depolarization at oblique incidence, near-field scattering between cylinders, interaction with reflected waves from the interface, and coupling of cylinders across the interface. The electromagnetic fields are formulated using Hertz potenials that are expanded in terms of cylindrical wave functions. The unknown expansion coefficients are determined by boundary matching. Analytical formulas are derived for the electromagnetic fields and Poynting vector of scattered radiation in the far field. Application of the present solution to all scenarios of scattering by cylinders in the presence of a half space interface is illustrated analytically and by numerical examples.

Scattering by multiple cylinders located on both sides of an interface

The solution for scattering by multiple parallel infinite cylinders located in adjacent half spaces with dissimilar refractive index is presented in this paper. The incident radiation is an arbitrarily polarized plane wave propagating in the upper half space in the plane perpendicular to the axis of the cylinders. The formulation of the electromagnetic field vectors utilized Hertz potentials that are expressed in terms of an expansion of cylindrical wave functions. It accounts for the near-field multiple scattering, Fresnel effect at the interface, and interaction between cylinders in both half spaces. Analytical formulas are derived for the electromagnetic field and Poynting vector in the far-field. The present solution provides the theoretical framework for deducing the solutions for scattering by cylinders located on either side of an interface irradiated by a propagating or an evanescent incident wave. Deduction of these solutions from the present formulation is demonstrated. Numerical results are presented to illustrate the frustration of total internal reflection and scattering of light beyond the critical angle by nanocylinders located in either or both half spaces.

Scattering at oblique incidence by multiple cylinders in front of a surface

This paper presents a theoretical solution for scattering by multiple parallel infinite cylinders located on top of a dielectric substrate. The incident plane wave is arbitrarily polarized and propagates in a general direction inclined from the axis of the cylinders. The scattered waves become depolarized at oblique incidence, which are reflected from the surface of the substrate to become incident waves at the cylinders. An exact solution of Maxwell׳s equations is developed that rigorously treats the depolarization of scattered waves and the angular spectrum of reflected and transmitted waves from the surface. Numerical results are presented for different configurations of perfectly conducting and coated cylinders at perpendicular and oblique incidence to illustrate plasmonic resonances in the near-field and scattering characteristics in the far-field.

Scattering of evanescent wave by multiple parallel infinite cylinders near a surface

This paper presents an exact analytical solution for the scattering of evanescent wave by an arbitrary collection of parallel infinite cylinders located near the surface of an optically denser substrate. The evanescent wave is generated by total internal reflection of the source wave propagating within the substrate at greater than the critical angle. The source wave is arbitrarily polarized and propagates in the plane perpendicular to the axes of the cylinders. The theoretical formulation utilizes Hertz potentials, which accounts for the near-field scattering between the cylinders and Fresnel reflection of angular distribution of scattered waves from the surface. Analytical formulas are derived for the electric and magnetic fields and Poynting vector of the scattered radiation in the near field, as well as their asymptotic forms in the far-field. Numerical results are presented to illustrate the scattering of evanescent wave by several configurations of cylinders located near the surface.

Scattering by multiple perfectly conducting cylinders buried in a lossy half space

The analytical solution for scattering of electromagnetic wave by an arbitrary configuration of parallel infinite cylinders buried in a lossy half space is presented in this paper. The cylinders are perfectly conducting and the incident wave is arbitrarily polarized that propagates in the plane perpendicular to the axes of the cylinders. The formulation accounts for the Fresnel effect at the half space interface, absorption of electromagnetic wave by the lossy medium, and near-field interaction between the cylinders. Near-field and far-field formulas are derived for the electric and magnetic fields and Poynting vector of radiation emerging from the half space. Numerical results are shown for scattering by two different configurations of perfectly conducting cylinders buried in a lossy half space.

Supersonic rarefied gas flow through a wire grid

The direct simulation Monte Carlo method is used to study a plane-parallel supersonic gas flow through a grid formed by a series of parallel infinite cylinders. Characteristic features of the shock disturbance formation during the interaction of a supersonic flow with a permeable grid and the effect of this disturbance on the flow parameters behind the grid are revealed. The boundaries of the domain of supersonic flow breakup ahead of the grid and the laws of the total momentum loss on the grid are obtained. Kinetic and energetic characteristics of the flow behind the grid are determined.

Scattering by multiple parallel radially stratified infinite cylinders buried in a lossy half space

The theoretical solution for scattering by an arbitrary configuration of closely spaced parallel infinite cylinders buried in a lossy half space is presented in this paper. The refractive index and permeability of the half space and cylinders are complex in general. Each cylinder is radially stratified with a distinct complex refractive index and permeability. The incident radiation is an arbitrarily polarized plane wave propagating in the plane normal to the axes of the cylinders. Analytic solutions are derived for the electric and magnetic fields and the Poynting vector of backscattered radiation emerging from the half space. Numerical examples are presented to illustrate the application of the scattering solution to calculate backscattering from a lossy half space containing multiple homogeneous and radially stratified cylinders at various depths and different angles of incidence.

Developing a new form of the Kozeny–Carman parameter for structured porous media through lattice-Boltzmann modeling

The semi-empirical Kozeny–Carman (KC) equation is a commonly-used relationship for determining permeability as a function of porosity for granular porous materials. This model features a material-specific fitting parameter, CKC, which is generally treated as a constant coefficient. Recent studies, however, have shown that CKC is not constant and could be a varying function of porosity. We used lattice-Boltzmann (LB) modeling to calculate the absolute permeability of two simulated porous structures: periodic arrays of (a) staggered parallel infinite cylinders and (b) spheres. We then identified various functional forms of CKC, and for each form, we performed a regression analysis in order to fit the function to the permeability values determined from the LB simulations. From this analysis, we extracted optimal fitting parameters for each function that minimized the error between permeability values obtained from the KC model and the LB simulations. All linear and non-linear functional forms proposed in this work improve the predictability of the KC model. An algebraic function for CKC provided the most accurate prediction of the KC porosity–permeability relationship for the geometries examined.

Scattering of electromagnetic waves by many thin cylinders: Theory and computational modeling

Electromagnetic (EM) wave scattering by many parallel infinite cylinders is studied asymptotically as a→0, where a is the radius of the cylinders. It is assumed that the centers of the cylinders x^m are distributed so that N(Δ)=ln(1/a)∫ΔN(x)dx[1+o(1)], where N(Δ) is the number of points x^m=(xm1,xm2) in an arbitrary open subset of the plane xOy, the axes of cylinders are parallel to z-axis. The function N(x)≥0 is a given continuous function. An equation for the self-consistent (limiting) field is derived as a→0. The cylinders are assumed perfectly conducting. Formula for the effective refraction coefficient of the new medium, obtained by embedding many thin cylinders into a given region, is derived. The numerical results presented demonstrate the validity of the proposed approach and its efficiency for solving the many-body scattering problems as well as the possibility to create media with negative refraction coefficients.

SCATTERING BY CLOSELY SPACED INFINITE CYLINDERS IN AN ABSORBING MEDIUM

Scattering by closely spaced parallel infinite cylinders in an absorbing medium is considered in this paper. The source wave is arbitrarily polarized and propagates in a general direction at the cylinders. The formulation utilizes the Hertz potential approach, and the scattering cross section and intensity distribution in the far-field are developed. Numerical results are presented to illustrate the influence of the absorbing medium on the scattering properties of two configurations of closely-spaced cylinders.

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.