Light scattering by dielectric particles with axial symmetry

A new method is suggested for solving the problem of scattering of a plane electromagnetic wave by dielectric particles with the axial symmetry. The method is based on the separation of fields into two parts: the axially symmetric part, which is independent of the angle of rotation, and the part that is not axially symmetric, which vanishes upon averaging over this angle. The scattering problem is solved separately for each of the parts. In the first case, scalar potentials related to the azimuthal components of electromagnetic fields are used, and in the second case, superpositions of the Debye potentials and vertical components of the Hertz vectors are used. The surface integral equations for these potentials are obtained. They are represented as expansions in the spherical wave functions. The infinite systems of linear algebraic equations are obtained for unknown expansion coefficients. Our calculations demonstrated the high efficiency of the new method.     

Surface waves at the interface between a dielectric and a topological insulator

Surface waves that propagate along the interface between an isotropic linear or nonlinear (of the Kerr type) dielectric and a topological insulator have been studied theoretically. A dispersion relation for surface waves, which are represented by superpositions of TE and TM waves, has been obtained. This hybridization occurs because, upon passage through the interface, the polarization of a surface wave changes, which is caused by an induced surface current (which is transverse to the electric field vector of the wave). The surface current of this kind is characteristic of topological insulators. Expressions for the energy flux transferred by a surface wave have been given.     

Enhancement of cross-polarized beam components at a metamaterial surface

Beam-interface interactions under incidence of a TE polarized elegant Hermite–Gaussian beam are considered in order to obtain efficient excitation of higher-order beam modes at a homogeneous, isotropic metamaterial surface. It is shown by numerical simulations that two transmitted TE and TM polarization beam components are enhanced more efficiently at a metamaterial surface than in the case of a dielectric interface. The mixed Poynting vector contribution to the incident energy flux is evaluated to explain this enhancement. The numerical results obtained are verified against energy balance at the interface.     

Effect of dielectric interface on vector field mapping using gold nanoparticles as a local probe: Theory and experiment

We investigate the influence of an air–dielectric interface on evanescent field vector detections using a gold nanoparticle as a local probe. In particular, we are interested in how the reflected field from the interface modifies the scattered signal, both in its strength and polarization direction depending on the detection angle. Dielectric–air or dielectric–water interface is a most widely used platform to perform single molecule spectroscopy. Knowing the electric field direction that the single molecule experiences is prerequisite for obtaining precise information on that molecule. The far-field scattered signal is derived by solving self-consistently the polarization induced on the gold nanoparticle by the local field and its radiated field in the Green function formalism. The scattered light intensity for each detector polarization direction is obtained by varying the dielectric constant, the distance from the gold nanoparticle to the interface, and the detection angle. The gold nanoparticle is modeled by a single dipole and coupled dipoles, respectively, and comparisons are given. Detection angle dependent far-field measurements are compared with theory, and they are in good agreements. Our study shows that for vector-field mapping on dielectric-interface, an ideal detector angle exists whereby the horizontal and vertical field components can be readily deduced without further correction. For any other detector angles, a correction factor should be taken into consideration to determine local field polarization direction.     

Parameters Extraction of Millimeter Wave Circuits by Hybrid Vector Finite Element and Moment Method Combined with SOC Technique

This paper presents a hybrid method, which couples the vector finite element method (FEM) and method of moment (MOM) for analyzing the field and current distribution of the millimeter wave circuits. The FEM is applied to handle the interior region of dielectric bodies and MOM is used to solve surface integral equations. Then, These integral expressions are coupled into the FEM equations through the continuity of the tangential fields across the connection boundaries. Simultaneously, the short-open calibration (SOC) technique is used for predicting accurately the scattering parameters of the circuits. Numerical results are well compared with those published in the previous literatures.     

Green's function for arbitrarily shaped dielectric bodies of revolution

In this paper, a solution is developed to calculate the electric field at one point in space due to an electric dipole exciting an arbitrarily shaped dielectric body of revolution (BOR). Specifically, the electric field is determined from the solution of coupled surface integral equations (SIE) for the induced surface electric and magnetic currents on the dielectric body excited by an elementary electric current dipole source. Both the interior and exterior fields to the dielectric BOR may be accurately evaluated via this approach. For a highly lossy dielectric body, the numerical Green's function is also obtainable from an approximate integral equation (AIE) based on a surface boundary condition. If this equation is solved by the method of moments, significant numerical efficiency over SIE is realized. Numerical results obtained by both SIE and AIE approaches agree with the exact solution for the special case of a dielectric sphere. With this numerical Green's function, the complicated radiation and scattering problems in the presence of an arbitrarily shaped dielectric BOR are readily solvable by the method of moments.     

Reflected and refracted electromagnetic fields in a semi-infinite body

We compute the reflected and refracted electromagnetic fields for an ideal semi-infinite body (either a plasma or a dielectric), as well as the reflection coefficient, by using a general approach based on the polarization equation of motion and electromagnetic potentials. The method consists of representing the charge disturbances by a displacement field in the positions of the moving charges. The propagation of an electromagnetic wave in matter is treated by means of the retarded electromagnetic potentials, and the resulting integral equations are solved. Generalized Fresnel’s relations are thereby obtained for any incidence angle and polarization and the angles of total polarization and total reflection are derived (the latter for the plasma). Bulk and surface plasmon–polariton modes are also identified for the plasma. As it is well known, the field inside the plasma is either damped (evanescent) or propagating (transparency regime), and the reflection coefficient exhibits an abrupt enhancement on passing from the propagating regime to the damped one (total reflection).     

The surface plasmon polariton dispersion relations in a nonlinear-metal-nonlinear dielectric structure of arbitrary nonlinearity

The analytic surface plasmon polaritons(SPPs) dispersion relation is studied in a system consisting of a thin metallic film bounded by two sides media of nonlinear dielectric of arbitrary nonlinearity is studied by applying a generalised first integral approach.We consider both asymmetric and symmetric structures.Especially,in the symmetric system,two possible modes can exist:the odd mode and the even mode.The dispersion relations of the two modes are obtained.Due to the nonlinear dielectric,the magnitude of the electric field at the interface appears and alters the dispersion relations.The changes in SPPs dispersion relations depending on film thicknesses and nonlinearity are studied.     

Static dielectric properties of Stockmayer fluids

Dielectric constants for the Stockmayer fluid are computed both from the equilibrium fluctuations of the polarization and from the polarization response to an applied field in a molecular dynamics simulation with periodic boundary conditions and with the dipole interactions treated by the Ewald method. The dielectric constant at finite wavelength is obtained from a Kirkwood-like expression, while for uniform polarization fluctuations a different expression applies due to the absence of surface effects in the Ewald calculation. The results are nearly independent of the number (up to 500) of particles investigated, even at large values of the dipole moment. The dielectric constants obtained from the approximate solution of the hypernetted chain integral equation are considerably larger than the molecular dynamics results except at low dielectric constants. The external field simulation permits study of the non-linear dependence of the dielectric constant on the magnitude of the applied electric field.     

Spinless particles in the field of unequal scalar vector Yukawa potentials

We present analytical bound state solutions of the spin-zero Klein-Gordon (KG) particles in the field of unequal mix- ture of scalar and vector Yukawa potentials within the framework of the approximation scheme to the centrifugal potential term for any arbitrary l-state. The approximate energy eigenvalues and unnormalized wave functions are obtained in closed forms using a simple shortcut of the Nikiforov-Uvarov (NU) method. Further, we solve the KG-Yukawa problem for its exact numerical energy eigenvalues via the amplitude phase (AP) method to test the accuracy of the present solutions found by using the NU method. Our numerical tests using energy calculations demonstrate the existence of inter-dimensional degeneracy amongst the energy states of the KG-Yukawa problem. The dependence of the energy on the dimension D is numerically discussed for spatial dimensions D = 2-6.     

支撑介质对平面型电磁带隙结构带隙特性的影响

运用直线法对含有不同参数支撑介质的平面型电磁带隙（EBG）结构进行了分析.概述了算法的实现过程,使用周期边界条件隔离出一个结构单元作为计算区域,并利用直线法得到了位函数在各层介质界面间的传输方程.通过联立场分量与位函数的变换关系和界面处切向场分量的连续性条件,建立了本征方程, 得到了表征该EBG 结构表面波带隙的本征模频带图.同时,使用该方法对含有不同介电常数、不同厚度支撑介质的表面波带隙进行了计算.通过对计算结果的分析,得到了支撑介质对平面型EBG 结构带隙特性影响的六条结论,为平面型EBG 结构的设计 关键词： 超媒质 光子带隙 周期结构 表面波     

Exact Solutions of Klein-Gordon Equation with Exponential Scalar and Vector Potentials

We obtain the exact analytical solution of the Klein-Gordon equation for the exponential vector and scalar potentials by using the asymptotic iteration method. For the scalar potential greater than the vector potential case, the exact bound state energy eigenvalues and corresponding eigenfunctions are presented. The bound state eigenfunction solutions are obtained in terms of the confluent hypergeometric functions.     

Makarov势的Dirac方程的束缚态解

给出了Makarov型标量势与矢量势相等条件下的Dirac方程的束缚态解. Dirac方程的角向方程用因子分解方法求解，在得出角向波函数的过程中，自然地得到了属于同一本征值的不同角向波函数间的递推操作. 径向束缚态波函数用合流超几何函数表示，束缚态的能量方程可由径向波函数满足的边界条件得到. 关键词： Makarov势 Dirac方程 束缚态 因子分解方法     

Capacitance of an elliptical disk on a semi-infinite dielectric material

Using an integral transform, the mixed boundary value problem of a conducting, elliptical disk on a dielectric half-space in an electric field is reduced to the solution of an integral equation. An analytical expression of the electric system capacitance is derived, which is a function of the eccentricity of the elliptical disk. The electric charge and electric stress distribute non-uniformly over the surface of the elliptical disk and display local singularities at the edge of the elliptical disk. The square root singularity of the electric field at the edge of the elliptical disk leads to the divergent of the resultant force on the elliptical disk, which is physically unrealistic. There likely exist geometrical constraint and/or field constraint to limit the presence of the square root singularity of the electric field. For any symmetric conductor in an infinite space that consists of air (vacuum) and a semi-infinite dielectric material with symmetric plane being in the interface between the air and the dielectric material, the electric potential in the space is independent of the dielectric constant of the dielectric material.     

Study of MPI based on parallel MOM on PC clusters for EM-beam scattering by 2-D PEC rough surfaces

This paper firstly applies the finite impulse response filter (FIR) theory combined with the fast Fourier transform (FFT) method to generate two-dimensional Gaussian rough surface. Using the electric field integral equation (EFIE), it introduces the method of moment (MOM) with RWG vector basis function and Galerkin's method to investigate the electromagnetic beam scattering by a two-dimensional PEC Gaussian rough surface on personal computer (PC) clusters. The details of the parallel conjugate gradient method (CGM) for solving the matrix equation are also presented and the numerical simulations are obtained through the message passing interface (MPI) platform on the PC clusters. It finds significantly that the parallel MOM supplies a novel technique for solving a two-dimensional rough surface electromagnetic-scattering problem. The influences of the root-mean-square height, the correlation length and the polarization on the beam scattering characteristics by two-dimensional PEC Gaussian rough surfaces are finally discussed.     

Exact Solutions of the Klein-Gordon Equation for the Scarf-Type Potential via Nikiforov-Uvarov Method

In this paper we present the exact solutions of the one-dimensional Klein-Gordon equation for the Scarf-type potential with equal scalar and vector potentials. Exact solutions and corresponding energy eigenvalues equation are obtained using Nikiforov-Uvarov mathematical method for the s-wave bound state. The PT-symmetry and Hermiticity for this potential are also considered. It will be shown that the obtained results of the Scarf-type potential are reduced to the results of the well-known potentials in the special cases.     

A new integral equation method for direct electromagnetic scattering in homogeneous media and its numerical confirmation

In this paper, we derive a new integral equation method for direct electromagnetic scattering in homogeneous media and present a numerical confirmation of the new method via a computer simulation. The new integral equation method is based on a paper written by DeSanto [1], originally for scattering from an infinite rough surface separating homogeneous dielectric half-spaces. Here, it is applied to a bounded scatterer, which can be an ohmic conductor or a dielectric, with some simplification of the continuity conditions for the fields. The new integral equation method is developed by choosing the electric field and its normal derivative as boundary unknowns, which are not the usual boundary unknowns. The new integral equation method may provide significant computational advantages over the standard Stratton-Chu method [2] because it leads to a 50% sparse, rather than 100% dense, impedance (collocation) matrix. Our theoretical development of the new integral equation method is exact.     

Moment method analysis of charge distribution & capacitance for the dielectric coated tilted plates isolated in free space

This paper presents a method for the evaluation of the capacitance of the dielectric coated metallic plates forming a corner using the method of moments based on the pulse basis function and the point matching. Two integral equations are formed based on the boundary conditions for the potential on the conductor surface and continuity of the normal component of the displacement flux density at the dielectric-free space interface. A set of simultaneous equations are formed from the two integral equations using the method of moments. The total free charge on the conductor surface is found from the solution of the set of simultaneous equations. Numerical data on the capacitance and the charge distribution are presented. The validity of the analysis has been justified by comparing the data on the capacitance that is available in the literature for a metallic structure with the data on the capacitance computed with the present method for a similar structure considering a very low dielectric constant as well as a very thin dielectric coating. Further validation has been carried out by comparing the capacitance data of the specific case when the angle between two metallic plates is 180° forming a dielectric coated metallic rectangular plate for which the capacitance data are available in the literature.     

均匀外电场中无限长介质圆柱壳的场分布的计算和讨论

用圆柱坐标系中的分离变量法计算了位于均匀外电场中的无限长介质圆柱壳各区域的电势和电场,由计算结果分析了无限长介质圆柱壳对外电场的屏蔽效果,并指出均匀外电场中的无限长导体圆柱壳、无限长介质圆柱体、无限长导体圆柱及无限大均匀电介质中开有一无限长的圆柱形空腔的电势和电场都可以由均匀电场中的无限长介质圆柱壳电势及电场给出.