The excitation of the surface plasmon resonances on a graphene strip and a disk in free space is studied numerically as a 2D and 3D electromagnetic wave-scattering problem, respectively. The associated mathematical model is based on the Maxwell equations with resistive boundary conditions on the surface of a zero-thickness strip or disk, where the graphene electron conductivity is included as a parameter and determined from the Kubo formalism. It is shown that plasmon resonance frequencies in the terahertz range shift with variation of the chemical potential of the graphene. Far-field and near-field patterns are plotted at several resonance frequencies.

Abstract-The scattering of an arbitrary electromagnetic wave by a thin disk located in free space is formulated rigorously in terms of coupled dual integral equations (CDIEs) for the unknown images of the jumps and average values of the normal to the disk scattered-field components. Considered are three cases of the disk: (1) Zero-thickness perfectly electrically conducting (PEC) disk, (2) thin electrically resistive (ER) disk and (3) dielectric disk. Disk thickness is assumed much smaller than the disk radius and the free space wavelength, in ER and dielectric disk cases, and also much smaller than the skinlayer depth, in the ER disk case. The set of CDIEs are "decoupled" by introduction of the coupling constants. Each set of DIEs are reduced to a Fredholm second kind integral equation by using the semi-inversion of DIE integral operators. The set of "coupling" equations for finding the coupling constants is obtained additionally from the edge behavior condition. Thus, each problem is reduced to a set of coupled Fredholm second kind integral equations. It is shown that each set can be reduced to a block-type three-diagonal matrix equation, which can be effectively solved numerically by iterative inversions of the two diagonal blocks and 2 × 2 matrix.

Considered are the problems of electromagnetic wave scattering, absorption and emission by several types of twodimensional and three-dimensional dielectric and metallic objects: arbitrary dielectric cylinder, thin material strip and disk, and arbitrary perfectly electrically conducting surface of rotation. In each case, the problem is rigorously formulated and reduced to a set of boundary integral equations with smooth, singular and hyper-singular kernel functions. These equations are further discretized using Nystrom-type quadrature formulas adapted to the type of kernel singularity and the edge behavior of unknown function. Convergence of discrete models to exact solutions is guaranteed by general theorems. Practical accuracy is achieved by inverting the matrices of the size that is only slightly greater than the maximum electrical dimension of corresponding scatterer. Sample numerical results are presented.

Considered is the plane-wave scattering from and absorption by a thin circular dielectric disk. The analysis uses a set of the singular integral equations for the effective electric and magnetic currents, derived using the generalized boundary conditions on the disk median section. Following the recently developed analytical preconditioning procedure, these equations are discretized by the Galerkin technique with judiciously chosen expansion functions, which provide for the Fredholm second-kind nature of the resulting matrix equations. This guarantees the code convergence and high efficiency. It is demonstrated that the developed technique delivers the most important features of thin dielectric disksthe resonances on the natural modes. In the resonances on the slab modes, the disk can be well-transparent and the shadow is created only by its rim; in the whispering gallery mode resonances, the scattering occurs mainly in the disk plane.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

In this paper, the analysis of the electromagnetic scattering from a thin dielectric disk is formulated as two sets of one-dimensional integral equations in the vector Hankel transform domain by taking advantage of the revolution symmetry of the problem and by imposing the generalized boundary conditions on the disk surface. The problem is further simplified by means of Helmholtz decomposition, which allows to introduce new scalar unknows in the spectral domain. Galerkin method with complete sets of orthogonal eigenfunctions of the static parts of the integral operators, reconstructing the physical behavior of the fields, as expansion bases, is applied to discretize the integral equations. The obtained matrix equations are Fredholm second-kind equations whose coefficients are efficiently numerically evaluated by means of a suitable analytical technique. Numerical results and comparisons with the commercial software CST Microwave Studio are provided showing the accuracy and efficiency of the proposed technique.