An improved perfectly matched layer for the eigenmode expansion technique

When performing optical simulations for rotationally symmetric geometries using the eigenmode expansion technique, it is necessary to place the geometry under investigation inside a cylinder with perfectly conducting walls. The parasitic reflections at the boundary of the computational domain can be suppressed by introducing a perfectly matched layer (PML) using e.g. complex coordinate stretching of the cylinder radius. However, the traditional PML suffers from an artificial field divergence limiting its usefulness. We show that the choice of a constant cylinder radius leads to mode profiles with exponentially increasing field amplitudes resulting in numerical instability. As a remedy we propose an improved PML based on a mode-dependent cylinder radius and mode profiles with stable field amplitudes. The new PML formulation eliminates the artificial field divergence and ensures numerical stability.     

Scattering of a plane electromagnetic wave by an infinite wedge with a truncated circular cylinder coated coaxially with a magnetodielectric layer

We formulate and solve the problem of scattering of a plane electromagnetic wave by an infinite, perfectly conducting wedge with a truncated, perfectly conducting circular cylinder which is coated coaxially with a magnetodielectric layer and located along the wedge edge. The rigorous solution is obtained and reduced to a system of linear algebraic equations of the second kind for unknown coefficients of Fourier expansions of the scattered field. The results of calculating the scattered field in the far zone with a specified accuracy are presented for the case of an H-polarized wave. It is shown that for certain values of the electric radius of the cylinder, the backscattering cross section of such a structure has pronounced maxima.     

Analysis of scattering wave for a conducting cylinder coated with eccentric plasma

Object coated with plasma has stimulated great interests of many people because of its stealth capability. The study on a conducting cylinder coated with coaxial plasma is very much, but there are little works on a conducting cylinder coated with eccentric plasma. In this article, a model for a conducting cylinder coated with eccentric unmagnetized plasma is set up, the scattering cross section of the object cylinder is studied by adopting the superposition of cylindrical wave functions and the coordinate transformation, where these wave functions are the solutions of Maxwell's equations with boundary conditions in cylindrical coordinates. The results show that the radar cross section for a conducting cylinder coated with eccentric plasma in every direction decrease obviously with an increase of the distance between two eccentric axes, but is almost not impacted by electron–neutral collision frequency of plasma, and the backscattering cross section of the target reduce with the increase of electron density. Comparing with the coaxial model, the backscattering cross section of the eccentric model has a smaller value in a wide frequency band. This is of significance for the target plasma stealth technology in practice.     

强非局域非线性介质中复宗量厄米一高斯光束的传输

利用Snyder-Mitchell模型讨论了笛卡儿坐标系下(1+1)维和(1+2)维光束的传输过程,得到了强非局域非线性介质中传输光束的复宗量厄米-高斯型解.该解为抛物线柱函数对高斯光束的调制.给出了复宗量厄米-高斯光束共线传输情况.在一定条件下共线传输的复宗量厄米-高斯型光束演化为涡旋光束.给出了单束复宗量和涡旋复宗...     

外包壳对具有氧化孔径层的圆柱形VCSEL阈值增益的影响

采用矢量场模型,对具有诱人应用前景的圆柱形垂直腔面发射半导体激光器（VCSEL）的模式阈值增益进行了数值模拟;为减弱金属圆柱的反射以使理论计算更接近实际,采用两种方案,将外加金属包壳视为非理想导体,或在此基础上,将金属包壳与激光器主体结构隔开. 从模式的阈值增益与顶Bragg反射镜层周期数的关系方面,与理想金属外包壳情况进行了比较. 结果表明,高阶贝塞耳函数模式的阈值增益变化规律基本相同,而0阶贝塞耳函数模式的阈值增益变化规律相差较大.     

Energy levels and states of parabolic cylindrical lens shaped quantum dots

The parabolic cylindrical lens shaped quantum dot is investigated theoretically. The Schrǒdinger equation for an electron confined in this structure is solved in the parabolic cylindrical coordinate system. The wavefunctions for the electron are presented in terms of confluent hypergeometric functions, and the electron energy spectra are also obtained.     

Barut-Girardello Coherent States for the Parabolic Cylinder Functions

The Barut-Girardello coherent states for the parabolic cylinder functions are constructed. It is shown that the resolution of unity condition is satisfied for the coherent states. In the Hilbert space spanned by the parabolic cylinder eigenstates, the appropriate measure is also obtained.     

Integral equation for a strip coil antenna located on a dielectric cylinder

The problem about the distribution of the surface current density in a narrow circular strip antenna as an infinitely thin perfectly conducting ribbon folded in a circle and positioned on the surface of a dielectric cylinder is reduced to a one-dimensional integral equation (IE). A method for solving the obtained IE is proposed. Complex distributions of the azimuthal component of the surface current density over the circular conductor are presented for different values of the dielectric permittivity of the cylinder.     

Diffraction of Electromagnetic Waves by an Anisotropic Cylindrical Inhomogeneity in a Planar Waveguide

We consider diffraction of electromagnetic waves by an anisotropic cylindrical inhomogeneity located in a planar waveguide with perfectly conducting walls. Anisotropy is allowed for by using the uniaxial-crystal approximation. A rigorous analytical solution is represented in the form of double sums over eigenfunctions of a planar waveguide with perfectly conducting walls and azimuthal eigenfunctions of a cylinder. Different components of the intensity of the electric field scatttered by an anisotropic inhomogeneity are numerically calculated. The influence of the anisotropy and sizes of the inhomogeneity on the scattered field is analyzed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 7, pp. 605–615, July 2005.     

Theoretical and experimental validation of UTD applied to electromagetic-wave scattering by circular cylinders

The scattering of obliquely incident electromagnetic waves by a perfectly conducting circular cylinder is analyzed. In this paper the accuracy of a high-frequency asymptotic model based on the Uniform Theory of Diffraction (UTD) is investigated by comparing UTD simulations with results obtained from the exact eigenfunction solution for plane-wave incidence.UTD results are also compared with results from experiments carried out at 50 GHz, for various cylinder radii and for different linear wave polarizations. Excellent agreement between the measurement results and the theoretical ones is obtained.     

Scattering of a Plane Electromagnetic Wave by an Infinite Dihedral Wedge with a Slotted Cylinder at the Apex

The problem of scattering of a plane electromagnetic wave by a perfectly conducting dihedral wedge with a slotted cylinder at the apex in rigorous formulation is reduced to solving a system of linear algebraic equations for unknown coefficients of the Fourier expansion of the scattered field. The results of calculation of the far-zone field with a given accuracy are presented in the case of an E-polarized incident wave. It is shown that for a slot with a large opening angle, the radiation patterns of the field in the long-wavelength far zone has a shape similar to a cardioid and does not depend on the incident-wave direction and the dielectric permittivity of the cylinder. In the case of a narrow slot, the radiation-pattern shape depends significantly on the incidence angle of the wave.     

Uniform asymptotics of the wave diffracted by a cone of arbitrary cross section

In this paper, inspired by V. A. Borovikov’s pioneering work, we study a wave diffracted by a convex cone of arbitrary cross section. Our analysis is focused on the shadow boundary of the wave reflected by the cone surface, where geometric optics yields nonphysical weak singularity. The uniform asymptotic expansion constructed here, which is expressed in terms of the parabolic cylinder functions, is regular at the geometric shadow boundary. Outside the penumbra region, it perfectly matches the ray expansions of the reflected wave, yielding in addition a regular spherical wave, would-be scattered by the cone vertex. Dedicated to the memory of Vladimir Borovikov     

Screening of low-frequency electric fields by a set of screens: A thin unclosed ellipsoidal sheath plus a thin-walled penetrable cylinder

The problem of penetration of a low-frequency electric field into a thin-walled infinitely long conducting cylinder with an ideally thin unclosed ellipsoidal perfectly conducting sheath on its axis is solved by the method of paired equations, which is combined with addition theorems and relevant averaged boundary conditions. The effect of the vertex angle of the unclosed ellipsoidal sheath on the coefficient of field attenuation inside the sheath is numerically evaluated for different screen geometries.     

Analysis of Electromagnetic Waves Scattering by a Finite Size Dielectric and Metal Cylinder in a Rectangular Waveguide

The paper presents a rigorous solution of the scattering problem by a circular dielectric and perfectly conducting cylinders of any radius and any height in the rectangular waveguide oriented perpendicularly to a wall. The method is based on the representation of fields in waveguide and dielectric medium by cylindrical eigenfunctions and application of boundary conditions on surfaces of the cylinder to evaluate the fields inside and outside the cylinder. The reflection and transmission coefficients are expressed through the fields. As an example the reflection and transmission coefficients versus frequency for various dielectric and metallic cylinders are computed. The comparison of numerical with experimental data is presented.     

Scattering characteristics of conducting cylinder coated with nonuniform magnetized ferrite

An analytical technique, referred to as the scattering matrix method （SMM）, is developed to analyse the scattering of a planar wave from a conductolution for the nonuniform fering cylinder coated with nonuniform magnetized ferrite. The SMM srite coating can be reduced to the expressions for the scattering and penetrated coefficients in four particular cases： nonuniform magnetized ferrite cylinder, uniform magnetized ferrite-coated conducting cylinder, uniform ferrite cylinder as well as homogeneous dielectric-coated conducting cylinder. The resonant condition for the nonuniform ferrite coating is obtained. The distinctive differences in scattering between the nonuniform ferrite coating and the nonuniform dielectric coating are demonstrated. The effects of applied magnetic fields and wave frequencies on the scattering characteristics for two types of the linear profiles are revealed.     

Theory of electromagnetic wave propagation in a longitudinally periodic cylinder

Thinking of photonic crystals, we investigate the theory of electromagnetic wave propagation in a perfectly conducting semi-cylinder endowed with a periodic permittivity along its axis while its circular base is illuminated by an harmonic Bessel beam, symmetric around the cylinder axis. We prove that the Floquet-Bessel expansions of electromagnetic fields whose Floquet parts are solutions of a Mathieu equation. is a suitable tool to handle this kind of problems.     

On the representations of the groups SO(3), O(2, 1), and M(2) defined in terms of Lamé, Mathieu,and parabolic functions

Products of Mathieu, parabolic-cylinder and Lamé functions appear as basis functions for the irreducible representations of the groups M(2), O(2,1) and SO(3). Addition formulas concerning the Mathieu functions, parabolic cylinder functions, and Lamé polynomials are recovered or obtained.     

Scattering of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces – study with the curvilinear coordinate method

We present a method giving the bi-static scattering coefficient of two-dimensional (2-D) perfectly conducting random rough surface illuminated by a plane wave. The theory is based on Maxwell's equations written in a nonorthogonal coordinate system. This method leads to an eigenvalue system. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the scattering amplitudes to be determined. The Monte Carlo technique is applied and the bi-static scattering coefficient is estimated by averaging the scattering amplitudes over several realizations. The random surface is represented by a Gaussian stochastic process. Results are compared to published numerical and experimental data. Comparisons are conclusive.     

Scattering of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces - study with the curvilinear coordinate method

We present a method giving the bi-static scattering coefficient of two-dimensional (2-D) perfectly conducting random rough surface illuminated by a plane wave. The theory is based on Maxwell's equations written in a nonorthogonal coordinate system. This method leads to an eigenvalue system. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the scattering amplitudes to be determined. The Monte Carlo technique is applied and the bi-static scattering coefficient is estimated by averaging the scattering amplitudes over several realizations. The random surface is represented by a Gaussian stochastic process. Results are compared to published numerical and experimental data. Comparisons are conclusive.