Dielectric Circular Cylinder Research Articles

Scattering of electromagnetic plane wave from a low contrast circular cylinder buried in non-integer dimensional Half Space

The objective of this paper is to study ‘scattering of electromagnetic waves from a dielectric circular cylinder buried in non-integer dimensional dielectric half-space’. To achieve this objective first two auxiliary problems are solved. The problem of reflection and transmission of electromagnetic waves for an interface between two dielectric mediums is studied first. The dimension normal to the interface is non-integer. Secondly, radiated fields from a buried current carrying line source in an non-integer dimensional half-space have been derived. By using the results of these auxiliary problems, scattering from a low contrast dielectric cylinder buried in non-integer dimensional half-space is studied using perturbation technique. Special cases are also considered when one of the two or both half-spaces are taken to be of integer dimension

Persistence of photonic nanojet formation under the deformation of circular boundary

A photonic nanojet is a highly focused optical beam with a subwavelength waist on the shadow side of the dielectric microsphere or microcylinder. In this paper, photonic nanojets resulting from corrugated cylinders (with irregular boundaries) under normally incident plane-wave illumination are studied. Different levels of corrugations induced at the boundaries of the dielectric microcylinders produce strong light focusing as well as a photonic nanojet with unique performance compared to perfectly smooth cylinders. The spectral element method is utilized in this study for the sake of high accuracy. Interestingly, we found that under some geometrical/material parameters one may not need a highly perfect cylinder in order to obtain a photonic nanojet. In addition, resonance behavior is reported and examined under larger variations in the parameters defining corrugated cylinders when compared with circular dielectric cylinders.

Evaluation of a graphene-covered dielectric microtube as a refractive-index sensor in the terahertz range

We studied the scattering and absorption of the H-polarized plane wave by a graphene-covered circular dielectric cylinder and a hollow tube with a graphene cover on the outer boundary in the terahertz range. The analytical solution of the wave-scattering problem was based on the Maxwell equations and the use of the separation of variables in the polar coordinates. We assumed the resistive boundary conditions on the zero-thickness graphene cover where the graphene electron conductivity was included as a parameter and was determined from the Kubo formalism. The computed spectra of the total scattering cross section and the absorption cross section displayed several types of resonances: the localized-surface-plasmon (LSP) resonances of the graphene cover and the resonances on the whispering-gallery modes of a dielectric cylinder or dielectric tube. The computed data can be useful for the design of graphene-based sensors of the changes in the refractive index of the host medium. For this purpose, the sensitivities and the figure-of-merit values of the LSP resonances were computed; their comparison demonstrated advantages of a thin-tube configuration.

Calculating the resonance radius of a dielectric cylinder under illumination by a plane TE-wave

When a dielectric circular cylinder of specific radius is illuminated by a plane wave, a whispering gallery mode (WGM) is generated in the cylinder. This resonance radius of the cylinder can be derived numerically on the assumption of the maximal value of the coefficient in a Bessel series expansion of the E-field amplitude of the TE-wave. Equations composed of cylindrical functions are obtained, allowing the cylinder's resonance radius to be calculated approximately. For instance, based on the equations, one can determine eight initial significant digits of the cylinder resonance radius for a WGM with mode number 26 to be generated. In a cylinder with refractive index 1.59 and resonance radius 3.469239 λ (λ is wavelength), a WGM with mode number 30 is excited. Such a cylinder can generate an external focal spot of size 0.15 λ, with its maximal intensity being 1500 times larger than that of incident light.

Effect of a magnetic field on the circulation of a conductive medium within a rotating cylinder in the presence of a retarding end surface

Within the framework of the magnetohydrodynamic approach, the rotational flow of an electrically conducting fluid within a rectangular circular dielectric cylinder in the presence of an asynchronously rotating upper end surface and external axial magnetic field B is investigated. The radial profiles of the azimuthal and axial medium velocity components inside the rotating volume bounded in the axial and radial directions are calculated approximately, using the analytical solutions of the system of nonlinear differentialMHD equations for boundary layers on an unbounded disk.

Nonlinear standing waves on a periodic array of circular cylinders.

A periodic array of parallel and infinitely long dielectric circular cylinders surrounded by air can be regarded as a simple two-dimensional periodic waveguide. For linear cylinders, guided modes exist continuously below the lightline in various frequency intervals, but standing waves, which are special guided modes with a zero Bloch wavenumber, could exist above the lightline at a discrete set of frequencies. In this paper, we consider a periodic array of nonlinear circular cylinders with a Kerr nonlinearity, and show numerically that nonlinear standing waves exist continuously with the frequency and their amplitudes depend on the frequency. The amplitude-frequency relations are further investigated in a perturbation analysis.

Standing waves on two-dimensional periodic dielectric waveguides

Guided modes of a periodic waveguide usually exist below the light line, if the minimum period of the waveguide is used in the definition, but for some periodic waveguides, there are standing waves with the same period as the waveguide. These non-propagating waves localized around the waveguide core are special guided modes above the light line with a zero wavenumber, and they are related to transmission anomalies and other resonant phenomena. In this paper, we analyze the standing waves on two periodic waveguides: a periodic array of circular dielectric cylinders, and a dielectric slab with a periodic array of circular air-holes. Based on an efficient semi-analytic method, the frequencies of standing waves are calculated as functions of the dielectric constant and the radius of cylinders. Our work provides a basis for further studies on these waves and for realizing their potential applications.

Well-conditioned algorithm for scattering by a few eccentrically multilayered dielectric circular cylinders

The new regularization of the well-known analytical formulation of the monochromatic electromagnetic wave scattering by a few eccentrically multilayered homogenous circular cylinders is presented. It is found out that a regularization of this formulation is absolutely necessary. The two-sided regularization that we made is based on the integral formulation of the mentioned problem. The polarization of the fields are parallel to the longitudinal axes of the cylinders; thus, a two dimensional problem for each both polarizations are under consideration. The condition number of the resulting algebraic system is uniformly bounded while its truncation number increases. The numerical results are validated by existing results such as near and far fields obtained under various geometrical and electrical parameters of the scattering problem. Numerical results including the condition numbers of the regularized and nonregularized systems show that only regularized system gives numerically stable results with any desired accuracy in a wide range of frequencies from quasistatic to rather high-frequency range, limited only by the capabilities of the computer with the guarantee of the physical reliability of the solution.

Cutoff Properties of a Circular Waveguide Loaded with Two Eccentric Dielectric Cylinders

An exact closed-form technique is employed to calculate the cutoff wavenumbers of a conducting circular waveguide loaded with two circular dielectric cylinders. An analytical expression of the hybrid modes is derived in terms of cylindrical coordinates of the geometry. The addition theorem of Bessel functions is used to transfer the electromagnetic fields from one coordinate system to another to apply the boundary conditions. A MATLAB (The MathWorks, Natick, Massachusetts, USA) code is developed to solve the system of equations and produce the cutoff wavenumbers for different geometrical parameters. The present problem can be extended to model a circular waveguide loaded with multiple dielectric cylinders that resembles a petroleum-carrying pipeline. A professional High Frequency Structure Simulator (HFSS; ANSYS, Inc., Canonsburg, PA, USA) is used to solve this model and to determine the ratio of the multi-phase fluid.

Calculation of the resonant radius of a dielectric cylinder illuminated by a plane TE-wave

When a dielectric circular cylinder of specific radius is illuminated by a plane wave, a whispering gallery mode (WGM) is generated in the cylinder. This resonant radius of the cylinder can be derived numerically on the assumption of the maximal value of the coefficient in a Bessel series expansion of the E-field amplitude of the TE-wave. Equations composed of cylinder functions are obtained, allowing the cylinder’s resonant radius to be calculated approximately. For instance, based on the equations, one can accurately determine eight initial significant digits of the cylinder resonant radius for a WGM with mode number N = 26 to be generated. In a cylinder with refractive index n = 1.59 and resonant radius R = 3.469239λ (λ is wavelength), a WGM with mode number N = 30 is excited. Such a WGM cylinder can generate an external focal spot of size 0.15λ, with its maximal intensity being 1500 times higher than that of incident light.

Extremely Low Numerical Dispersion FDTD Method Based on H(2, 4) Scheme for Lossy Material

This paper expands a previously proposed optimized higher order (2, 4) finite-difference time-domain scheme (H(2, 4) scheme) for use with lossy material. A low dispersion error is obtained by introducing a weighting factor and two scaling factors. The weighting factor creates isotropic dispersion, and the two scaling factors dramatically reduce the numerical dispersion error at an operating frequency. In addition, the results confirm that the proposed scheme performs better than the H(2, 4) scheme for wideband analysis. Lastly, the validity of the proposed scheme is verified by calculating a scattering problem of a lossy circular dielectric cylinder.

Excitation of cyclic Sommerfeld waves and Wood's anomalies in plane wave scattering from a dielectric cylinder at oblique incidence

An analysis is presented of the scattering of a plane electromagnetic wave in the case of oblique incidence from a circular dielectric cylinder. Under certain conditions, this scattering process involves the excitation of cyclic surface Sommerfeld waves (SWs) capable of propagating over large distances along the cylinder. It is shown that the interaction of SWs of low azimuthal order with the cylinder continuous (radiation) modes gives rise to cyclic Sommerfeld resonances (SRs), analogous to well-known Wood's anomalies in a plane wave scattering from one-dimensional metallic diffraction gratings. Conditions necessary for the effective excitation of SWs and SRs are established and the SW and SR contributions to mode formation in microstructured optical fibers are discussed.

Two-Dimensional Simulation of EM Scattering from a Rotating Circular Dielectric Cylinder

The computational results of the scattered electromagnetic (EM) fields from a rotating circular dielectric cylinder were presented in this paper. The method of characteristics (MOC) was applied in a two dimensional modified O-type grid system to the solutions of the time-dependent Maxwell equations. To accurately model the rotating cylinder under the illumination of EM pulse, the passing center swing back grids (PCSBG) technique is employed in cooperation with MOC to overcome the difficulty of grid distortion due to the rotational movement of the cylinder. A number of electric and magnetic field distributions over the whole computational space were demonstrated in a side-by-side fashion for the comparison of the scattered EM fields from rotating circular dielectric cylinder with those from the stationary one. The numerical results exhibit feasible trends.

Improving the integral equation in the hybrid FEM‐RBCI method for scalar electromagnetic scattering problems

Purpose – The purpose of this paper is to improve the accuracy of the integral equation of the hybrid FEM‐RBCI (Finite Element Method‐Robin Boundary Condition Iteration) method for the numerical solution of two‐dimensional electromagnetic (or acoustic) scattering problems.Design/methodology/approach – This accuracy improvement is achieved by selecting the integration curve as straight segments lying in the middle of the triangular finite elements. An accuracy improvement is obtained as compared with selecting the integration curve as constituted by element sides.Findings – The improved FEM‐RBCI method described in this paper leads to accuracies of the numerical results which are better than those obtained by selecting the integration curve by element sides.Originality/value – The paper presents results for a simple two‐dimensional structure: a dielectric circular cylinder.

Diffraction of an electromagnetic pulse at a finite-length dielectric gradient cylinder

Effects accompanying the propagation of an electromagnetic pulse with a nanosecond edge length in a finite-length dielectric gradient circular cylinder are studied within a three-dimensional model based on Maxwell’s equations. The pulse-edge length is commensurate with the dimensions of the dielectric body being considered. The effect of the direction of electric-vector polarization on the distribution of regions of electric-field enhancement is explored. The effect of the dielectric-cylinder length on special features of the formation of electric fields both within the body and in the surrounding medium is considered.

Propagation Characteristics of Dielectric Waveguides with Arbitrary Inhomogeneous Media along the Middle Layer

In this paper, we apply an improved method for the guiding problem of dielectric waveguide with arbitrary inhomogeneous media along the middle layer introduced the defect layers, and analyzed the propagation characteristics of dielectric waveguide composed of dielectric circular cylinders and the arbitrary inhomogeneous media in the middle layer by using a combination of the improved Fourier series expansion method and multilayer method. Numerical results are given for the propagation constants in the first stop band regions, and the distribution of energy flow for both TE0 and TM0 modes. The influence of permittivity and the shape variation of arbitrary inhomogeneous media are discussed in the first stop band regions.

A generalized transformation to convert an arbitrary perfect electric conductor into another arbitrary dielectric object

A generalized transformation is proposed to design an illusion device. The device can reshape an arbitrarily shaped perfect electrical conductor (PEC) into another dielectric object with arbitrary geometry. Such a device can evolve into an ideal invisibility cloak with non-conformal boundaries if the virtual space is filled with air. Furthermore, the validity of our proposed transformation is confirmed by two specific devices. One is to convert a regular polygonal PEC cylinder into a circular dielectric cylinder. Another one is to reshape a circular PEC cylinder into a regular polygonal dielectric cylinder.

ELECTROMAGNETIC SCATTERING FROM A CORN CANOPY AT L AND C BANDS

ELECTROMAGNETIC SCATTERING FROM A CORN CANOPY AT L AND C BANDS

Source-model technique analysis of transient electromagnetic scattering by dielectric cylinders

This study considers the application of the source-model technique to the solution of the problem of electromagnetic scattering by an arbitrarily shaped dielectric cylinder illuminated by a transient plane wave. The technique is utilised to study the scattering from a dielectric cylinder of circular cross-section and from a cylindrical void of the same cross-section lying in a dielectric medium. The effect of numerical parameters on accuracy and stability is studied and guidelines as to the choice of source location and their number are given. The scattering from a dielectric circular cylinder is then compared with the scattering by a cylinder of a rectangle capped by semi-circles cross-section, and the results are interpreted from a physical point of view.

Low-threshold lasing eigenmodes of an infinite periodic chain of quantum wires

We study the lasing eigenvalue problems for a periodic open optical resonator made of an infinite grating of circular dielectric cylinders standing in free space, in the E- and H-polarization modes. If possessing a "negative-absorption" refractive index, such cylinders model a chain of quantum wires made of the gain material under pumping. The initial-guess values for the lasing frequencies are provided by the plane-wave scattering problems. We demonstrate a new effect: the existence of specific grating eigenmodes that have a low threshold of lasing even if the wires are optically very thin.