Cylindrical Vector Wave Functions Research Articles

Scattering characteristics of a perfect electromagnetic conducting cylindrical object covered with a general Bi-isotropic layer

Abstract An analytic theory has been developed for the scattering of electromagnetic plane wave from a perfect electromagnetic conducting (PEMC) cylindrical object coated with a general bi-isotropic (BI) material. The proposed problem has been solved using cylindrical vector wave function expansion approach along with the application of tangential boundary conditions. Analytic expressions of the scattering coefficients have been derived in their simplest forms. It is seen that by proper selection of admittance of PEMC core, electromagnetic parameters of BI coating, and coating thickness, one can optimize the scattering characteristics for specific applications. It is shown that the specific types of BI and strong chiral-coated PEMC cylinders having certain coating thicknesses can be used to significantly enhance the co-polarized forward scattering while keeping the cross-polarized forward scattering very small. Such types of enhanced co-polarized forward scattering are preferred in point-to-point communication. Some interesting features have been discussed where co-polarized and cross-polarized backscattering may be suppressed, which find applications in radar engineering problems and stealth technology.

Vibration characteristics of eccentric annular plates

An effective theoretical method for investigating the vibration characteristics of eccentric annular plates is developed. The vibration equation of eccentric annular plates is solved by utilizing the Bessel function as the vibration mode function and combining it with the translational addition theorem for cylindrical vector wave functions. Substituting the boundary conditions into the vibration mode function yields the frequency equation. The natural frequencies and corresponding vibration modes of the plate are obtained by determining the natural frequency coefficients. Compared with the results obtained from the finite element method (FEM) and vibration experiment, the correctness of the mode shapes and natural frequencies of the plate obtained by the present method are validated. The influences of several parameters such as the eccentric distance, the structural parameters, and various boundary conditions on the vibration characteristics of the plates are discussed. An analysis on the mode composition of the eccentric annular plates is also presented. The research results are useful for the practical engineering applications of the eccentric annular plates.

Light scattering by an infinitely long circular cylinder above a plane interface

An exact analytical method is presented to calculate light scattering by an infinitely long circular cylinder above a plane interface. The transformation relations of rectangular and cylindrical vector wave functions are used to deal with the coupling scattering between the circular cylinder and plane interface. By applying the boundary conditions over the cylindrical surface, the unknown expansion coefficients of the scattered field by the circular cylinder in terms of cylindrical vector wave functions are determined. Mueller matrix elements are computed, and also compared with those measured for a plane wave with normal incidence.

Transmission characteristics of terahertz Bessel vortex beams through a multi-layered anisotropic magnetized plasma slab

The transmission of terahertz (THz) Bessel vortex beams through a multi-layered anisotropic magnetized plasma slab is investigated by using a hybrid method of cylindrical vector wave functions (CVWFs) and Fourier transform. On the basis of the electromagnetic boundary conditions on each interface, a cascade form of expansion coefficients of the reflected and transmitted fields is obtained. Taking a double Gaussian distribution of the plasma density as an example, the influences of the applied magnetic field, the incident angle and polarization mode of the incident beams on the magnitude, OAM mode and polarization of the transmitted beams are analyzed in detail. The results indicate that the applied magnetic field has a major effect upon the polarization state of the transmitted fields but not upon the transmitted OAM spectrum. The incident angle has a powerful influence upon both the amplitude profile and the OAM spectrum of the transmitted beam. Furthermore, for multiple coaxial vortex beams, an increase of the maximum value of the plasma density causes more remarkable distortion of both the profile and OAM spectrum of the transmitted beam. This research makes a stable foundation for the THz OAM multiplexing/demultiplexing technology in a magnetized plasma environment.

Electromagnetic wave beam propagation through a chiral slab

A general scheme for investigating the electromagnetic wave beam reflection by and transmission through a chiral slab is proposed. The electromagnetic wave beams within different regions are described by appropriate cylindrical vector wave function expansions, and their expansion coefficients are determined by using the boundary conditions and projection method. Under illumination by a fundamental Gaussian beam, a Hermite–Gaussian beam and a doughnut mode beam, numerical results of the normalized field intensity distributions are provided and discussed briefly.

Dyadic Green’s function for the graphene–dielectric stack with arbitrary field and source points

In this paper, the dyadic Green’s function for a graphene–dielectric stack is formulated based on the scattering superposition method. To this end, the scattering Green’s function in each layer is expanded in terms of cylindrical vector wave functions with unknown coefficients. Using the Kronecker delta function in the field expansion, it is considered that the field and source points lie in the arbitrary layers. Afterward, recurrence relations to calculate the unknown expansion coefficients are derived by applying the impedance boundary condition at the interface of a graphene sheet surrounded by two adjacent dielectric layers. The verification of the calculated coefficients is conducted by using them in the analysis of graphene-based structures with different numbers of layers, including (1) free-standing frequency-selective surfaces and (2) parallel plates with graphene walls. A potential application of our proposed structure is investigating the interaction of donor–acceptor pairs residing in the arbitrary layers of the graphene–dielectric stack with a desired number of layers.

Cutoff Wavenumbers of Multilayered Gyrotropic Circular Waveguides

A coupled-field volume integral equation (CFVIE) method is developed for the calculation of the normalized cutoff wavenumbers of circular metallic walled waveguides having concentric continuously varying highly inhomogeneous gyrotropic (i.e., gyroelectric and gyromagnetic) infill. The normalized cutoff wavenumbers are obtained as the roots of a determinantal equation formed by solving the CFVIEs using the cylindrical Dini series expansion (CDSE) method where the unknown fields inside the waveguide are expanded by entire domain orthogonal Dini-type vectorial basis functions. To account for the electric boundary condition (BC) on waveguide's circular perfect electric conducting (PEC) surface, two modified 2-D tensorial Green's functions (GFs), expanded in cylindrical vector wave functions (CVWFs), are employed in the kernels of the CFVIEs. These modified 2-D tensorial GFs are constructed by enforcing, on their dyadic form, the satisfaction of the electric BC. The CDSE, along with the modified 2-D tensorial GFs, allow for the analytical integration of the volumetric-type integrals and the reduction of the CFVIEs to a set of algebraic equations. We exhaustively demonstrate the validity of the CFVIE-CDSE by a series of comparisons on the normalized cutoff wavenumbers: we first construct the solutions for obtaining the normalized cutoff wavenumbers in homogeneous gyrotropic waveguides by the separation of variables method (SVM), and second, we employ HFSS commercial software for two-layered isotropic and three-layered gyroelectric loaded waveguides. We characterize the type of modes, i.e., TE/TM or hybrid HE/EH, for each configuration presented, and discuss the efficiency of the CFVIE-CDSE method.

Complex WGM frequencies of gyroelectric cylindrical resonators

Asymptotic closed-form expressions for calculating complex transverse electric (TE)/transverse magnetic (TM) whispering gallery mode (WGM) frequencies in homogeneous gyroelectric circular cylindrical resonators of infinite length are derived. In addition, a volume integral equation (VIE)-cylindrical Dini series expansion method is extended to support the prediction of complex WGMs for continuously varying highly inhomogeneous gyroelectric circular cylindrical resonators. To this end, the entire domain orthogonal vectorial basis of VIE is extended to support very large indices of the involved Dini-type cylindrical vector wave functions via asymptotic closed-form expressions. This way, the eigenbasis required to solve the VIE becomes free of numerical instabilities arising when very large orders of the involved Bessel functions are employed. The complex frequencies obtained by the asymptotic closed-form expressions for the case of the homogeneous gyroelectric resonator, as well as those obtained by the VIE when the multilayered gyroelectric resonator is reduced to one layer, are validated by comparisons with the complex roots extracted by numerically solving the TE/TM characteristic equations obtained from the separation of variables method, using complex root finding techniques. We demonstrate the calculation of very high-order WGM frequencies for cylindrical resonators composed of homogeneous and highly inhomogeneous permittivity profiles. This asymptotic theory constitutes a rigorous tool that may serve for verifying method of analytical regularisation–based numerical solutions for other non-circular inhomogeneous cylinders, and for interpreting experimental data for applications such as WGM lasing, refractometric sensing, and magneto-optic coupling.

Electromagnetic beam propagation through a gyrotropic anisotropic circular cylinder

A general scheme is proposed for investigating the propagation of an incident electromagnetic beam through a gyrotropic anisotropic circular cylinder. The electromagnetic fields in different regions are expanded in terms of appropriate cylindrical vector wave functions, and the unknown expansion coefficients are determined by using the boundary conditions and projection scheme. For incidence of a fundamental Gaussian beam, Hermite–Gaussian beam and zero-order Bessel beam, normalized field intensity distributions are evaluated and discussed briefly.

Propagation of a terahertz Bessel vortex beam through a homogeneous magnetized plasma slab

This paper provides an analytic method to study propagation characteristics of a linearly polarized Bessel vortex beam through a homogeneous magnetized plasma slab. The incident Bessel vortex beam, as well as the reflected, transmitted and internal fields are expanded in terms of cylindrical vector wave functions (CVWFs). The effects of plasma thickness, electron density and magnetic induction strength on the contour profiles of the reflected and transmitted beams and orbital angular momentum (OAM) spectra are analyzed and discussed in detail. In particular, the magnetic induction strength has a significant impact on the polarization of the transmitted beam, but not on OAM state distribution. The channel capacity of THz OAM multiplexing decreases with an increase of plasma thickness and electron density.

An Entire Domain CFVIE-CDSE Method for EM Scattering on Electrically Large Highly Inhomogeneous Gyrotropic Circular Cylinders

A coupled-field volume integral equation (CFVIE) method for electromagnetic (EM) scattering on electrically large, highly inhomogeneous gyrotropic circular cylinders, under normal incidence, is developed in this work. The CFVIEs are solved by the cylindrical Dini series expansion (CDSE) method where the unknown fields are expanded by entire domain orthogonal vectorial basis functions. The main advantage of the present method is that it permits the scatterer to have continuously varying highly inhomogeneous gyrotropic characteristics, i.e., the constitutive parameters of the cylinder can be highly inhomogeneous in both gyroelectric and gyromagnetic tensors. Initially, the 2-D Green's function (GF) is expanded in a tensorial form using the cylindrical vector wave functions (CVWFs). Then, by employing the CDSE for the unknown fields, the 2-D volumetric integrals are carried out analytically, reducing the CFVIEs to a set of algebraic equations. The method is validated by comparisons with the exact solution based on the separation of variables method (SVM) for homogeneous gyroelectric/gyromagnetic cylinders, with HFSS commercial software for three-layered gyroelectric cylinders, as well as with the recently developed hybrid projection method (HPM) for electrically large continuously varying highly inhomogeneous isotropic cylinders. Results for combined gyroelectric-continuously varying highly inhomogeneous isotropic cylinders are presented and discussed.

Gaussian beam propagation through a biaxial anisotropic circular cylinder

Based on the electromagnetic field expansions over appropriate cylindrical vector wave functions, the scattering features of a Gaussian beam by a biaxial anisotropic circular cylinder are analyzed. The unknown expansion coefficients are determined from a system of linear equations derived by using continuous boundary conditions. For a TE and TM polarized Gaussian beam with different propagation directions, the normalized near-surface and internal field intensity distributions are evaluated. The propagation properties are compared and discussed briefly.

Propagation of shaped beam through uniaxially anisotropic chiral slab* *Project supported by the National Natural Science Foundation of China (Grant No. 61771385), the Science Foundation for Distinguished Young Scholars of Shaanxi Province, China (Grant No. 2020JC-42), the Fund from the Science and Technology on Solid-State Laser Laboratory, China (Grant No. 6142404180301), and the Science and Technology Research Plan of Xi’an

A general solution is obtained to a canonical problem of the reflection and refraction of an arbitrary shaped beam by using a uniaxially anisotropic chiral slab. The reflected, internal as well as refracted shaped beams are expanded in terms of cylindrical vector wave functions, and the expansion coefficients are determined by using the boundary conditions and method of moments procedure. As two typical examples, the normalized field intensity distributions are evaluated for a fundamental Gaussian beam and Hermite–Gaussian beam, and some propagation properties, especially the negative refraction phenomenon, are discussed briefly.

Reflection and transmission of a Bessel vortex beam by a stratified uniaxial anisotropic slab

The reflection and transmission of a Bessel vortex beam incident on a stratified uniaxial anisotropic slab are analytically solved by use of the expansion of cylindrical vector wave functions (CVWFs). This work is an extension of our previous paper, in which the reflection and transmission of a Bessel vortex beam incident on a homogeneous uniaxial anisotropic slab were studied. A closed form of the expansion coefficients of the reflected and transmitted beams for a stratified slab is derived. Taking a three-layered uniaxial anisotropic slab as an example, the characteristics of the reflected and transmitted beams and its influencing factors are numerically analyzed, including the magnitude profiles of the electric field components, the energy conversion between the two transverse electric components, and the distortion of orbital angular momentum (OAM) states. The results indicate that the effects of the dielectric properties of each layer on the magnitude profiles of the reflected field components are prominent, while those of the transmitted beams are opposite, which could be applied in the design of optical devices. Compared with other polarization modes, the polarization perturbation for the circularly polarized caseis very slight. As for the oblique incidence, an increase of the incident angle can obtain a high-quality reflected beam with fewer derived OAM states, and the lossy media can also do the same. Since the uniaxial anisotropic media has many applications in optical communication, radar detection, microwave device manufacture, etc., and vortex beams are proved to increase the channel capacity of an optical communication systems, these numerical results are of use in optical communications, for example, reducing the crosstalk in optical communication.

Gaussian beam scattering by an infinite cylinder with a spherical inclusion

An analytical method of analyzing the electromagnetic scattering of a Gaussian beam by an infinitely long circular cylinder with a spherical inclusion is presented. The fields within different regions are expanded in terms of appropriate cylindrical or spherical vector wave functions. By applying the integral representation of spherical vector wave functions over cylindrical ones, boundary conditions and projection procedure, the unknown expansion coefficients are determined. For a localized beam model, numerical results of the total scattered field and normalized field intensity distribution are shown, and the scattering properties are discussed briefly.

Propagation of light beam through a uniaxially anisotropic chiral cylinder

A general scheme is proposed for investigating a canonical problem of light beam scattering by a uniaxially anisotropic chiral cylinder. The light beams within different regions are expanded in terms of appropriate cylindrical vector wave functions, and their expansion coefficients are determined by using the boundary conditions and projection method. For incidence of a fundamental Gaussian beam and Hermite–Gaussian beam, numerical results of normalized field intensity distributions are provided and discussed briefly.

Characteristics of electromagnetic wave transmission and reflection from isotropic plasma coated circular nihility cylinder

Theoretical investigation has been carried out to study the scattering and transmission of electromagnetic energy from isotropic plasma coated circular nihility cylinder. The physical modeling of the problem is done in frame work of classical scattering theory. All the fields are expanded in terms of cylindrical vector wave functions (CVWFs). The analytical as well as numerical solution for both Transverse Electric (TE) and Transverse Magnetic (TM) polarizations is presented. The unknown scattering coefficients are computed by implementing the boundary conditions at each interface (free space/plasma and plasma/nihility). The influence of plasma parameters i.e., plasma density (ND) and effective collision frequency (v) on the bistatic echo width is analyzed and it is concluded that the plasma coating can be used to control and tune the scattering amplitude. Further it is also concluded that for the case ω > ωp the scattering amplitude is much less than for the case ω < ωp. Under special conditions, the results of present work compared with the published literature and good agreement is found.

Transmission of electromagnetic beam through a uniaxial anisotropic slab

We present a general theoretical scheme to investigate the propagation characteristics of a focused electromagnetic beam in a uniaxial anisotropic slab. The reflected, internal as well as transmitted waves are expanded in terms of cylindrical vector wave functions, and the unknown expansion coefficients are determined by virtue of the boundary conditions and the projection method. For incidence of a fundamental Gaussian beam, Hermite–Gaussian beam and doughnut mode beam, normalized field intensity distributions are evaluated and discussed briefly.

Internal and near-surface electromagnetic fields for a chiral cylinder with arbitrary monochromatic illumination

A semi-analytical solution is proposed to the electromagnetic scattering by an infinite chiral circular cylinder with arbitrary monochromatic illumination. The scattered and internal fields are expanded in terms of appropriate cylindrical vector wave functions, and their expansion coefficients are determined by virtue of the boundary conditions and the projection method. As a demonstration of the theoretical procedure, the normalized internal and near-surface field intensity distributions are evaluated for a fundamental Gaussian beam, and the scattering properties are discussed briefly for different chirality parameters.

Fast Analysis of Parallel-Plate Cylindrical Luneberg Lens Antennas Through Dyadic Green’s Functions

An accurate analytic and computationally efficient method based on dyadic Green's function (DGF) is presented for the analysis of parallel-plate cylindrical Luneberg lens antennas. DGFs for electric and magnetic current sources are rigorously derived for an infinite parallel-plate waveguide filled with radially stratified media, which is the ideal model of cylindrical Luneberg lens antennas. The DGF for the electric current source is constituted of cylindrical vector wave functions and their associated coefficients, which is developed from the scattering superposition and the corresponding matching of boundary conditions, respectively. The DGF for the magnetic current source is proved to be directly related to the DGF for the electric current source by applying the second-kind vector Green's theorem. The proposed DGFs and the aperture field method are then applied to analyze the radiation characteristics of parallel-plate cylindrical Luneberg lens antennas with equivalent sources. Numerical results of several large-sized parallel-plate cylindrical Luneberg lens antennas show that the results of the proposed approach are in good agreement with those from commercial software simulations. The proposed approach has much less computational costs and can be used for the fast analysis of large-sized cylindrical Luneberg lens antennas.