Thin Dielectric Disks Research Articles

Electromagnetic characterization of a metasurface composed of thin circular dielectric disk under normal incidence

Electromagnetic characterization of a metasurface composed of circular dielectric disks under normal incidence is presented. A dielectric disk is assumed to be infinitesimally thin with moderate values of the relative permittivity so that it can be modeled as an electric dipole. Thus, for the considered infinitesimally thin metasurface, normal electric surface polarization current is negligible. An analytic expression of electric polarizability of a thin circular dielectric disk has been derived for completeness. For most of the presented results, it is assumed that dielectric disk is made of realistic materials. Some interesting applications of realistic metasurfaces as a transparent sheet and a perfect reflector have also been discussed.

A Wideband High-Gain Circularly-Polarized Dielectric Horn Antenna Equipped With Lamé-Axicon Stacked-Disk Lens for Remote Sensing, Air Traffic Control and Satellite Communications

A wideband high-gain circularly polarized (CP) shaped dielectric horn-lens antenna (SDHLA) operating in the frequency band between 6.7 and 18.2 GHz [fractional impedance bandwidth (FIBW) of 92.4%] with a 3-dB axial-ratio in the frequency range from 8.1 to 16.3 GHz [fractional axial-ratio bandwidth (FARBW) of 67.2%], is presented. The antenna, composed of a suitably shaped dielectric horn, integrated with a super-ellipsoidal-axicon dielectric lens made out of stacked thin dielectric disks, is mounted on a printed circuit board (PCB) where a broadband microstrip line terminated with a radial stub is used to excite a S-shaped slot through which the circular polarization is achieved. Parameterized 3D Lamé curves describe the optimal geometries of horn and lens profiles. The antenna features a peak realized gain exceeding 13.1 dBi that is beneficial in a variety of applications, such as digital video broadcasting (DVB), remote sensing, weather monitoring, satellite communications, and air traffic control. The full-wave electromagnetic solver CST Studio Suite™, based on a locally conformal finite integration technique (FIT), was employed to design and characterize the antenna. The antenna characteristics estimated by FIT were found to be in good agreement with the experimental measurements performed on an antenna prototype.

Terahertz-range plasmon and whispering gallery mode resonances in the plane wave scattering from thin microsize dielectric disk with graphene covers

We analyse the scattering and absorption of a terahertz-range plane wave by a thin circular dielectric disk with two graphene covers. Assuming that the thickness of the whole composite disk is much smaller than the free-space wavelength, we reduce the complexity of the problem with the aid of the generalized boundary conditions. This yields a set of singular integral equations for the effective electric and magnetic currents, induced on an equivalent zero-thickness disk. The adopted advanced numerical solution technique is a version of the method of analytical preconditioning, which uses weighted polynomials as expansion functions in the discretization of the integral equations. Then, the resulting matrix equation has Fredholm second-kind property that enables us to control the computational error by the matrix size and reduce it to the desired level. This accurate analysis reveals resonances on several types of natural modes, best understood via visualization of in-resonance near-fields. They are the plasmon-mode resonances of the graphene disk, perturbed by the presence of the dielectric filler, and the dielectric disk modes, perturbed by the graphene covers. Additionally, quasi-full disk transparency is observed if the transverse resonance condition is fulfilled. Special attention is paid to the tunability of the found effects with the aid of graphene's chemical potential.

Plane wave scattering from thin dielectric disk in free space: Generalized boundary conditions, regularizing Galerkin technique and whispering gallery mode resonances

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 disks–the 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.

Back-scattered cross section from a sparse distribution of tilted thin dielectric disks

The back-scattered cross section from a sparse distribution of tilted thin circular dielectric disks have been investigated using numerical simulations. Three widely known scattering approximations from a dielectric disk such as Rayleigh–Gans, Koh–Sarabandi and volumetric integral physical optics have been used for the proposed theory. The influences of the various parameters including incident angle, size parameter of the disk, relative permittivity of the disk and spacing among disks upon the back-scattered cross sections have been studied for incident horizontal and vertical polarizations. Some conditions are discussed where a pair of sparsely located tilted low loss Gallium Arsenide disks can be used to significantly reduce the back-scattered cross section as a compared to a single tilted Gallium Arsenide disk. This type of reduced back scattering for both types of incoming horizontally and vertically polarized waves is desired in the stealth technology.

A Class of Lightweight Spherical-Axicon Dielectric Lenses for High Gain Wideband Antennas

A class of lightweight spherical-axicon-like dielectric lenses suitable for enhancing broadband antennas performances is presented. The proposed lenses, sized according to a reference massive lens, are formed by thin dielectric sheets spaced equiangularly on the azimuth plane (petal-shaped lens), or regularly orthogonally arranged along the lens axis (disks-shaped lens), thus yielding construction simplicity and significant weight reduction. While petal-shaped dielectric lenses are shown to yield mild gain increase, lenses made by thin dielectric disks, orthogonally periodically arranged along the lens optical axis, offer performances much closer to those achieved by comparable massive refractive spherical-axicon dielectric lenses. The time-domain and the focusing characteristics of the proposed lenses are investigated. Then, a Floquet’s mode-based model is proposed to describe the stop-band characteristics of stacked-disk lenses, illustrating the mechanism underpinning their sudden performance degradation observed at the stop-band onset frequency. Full-wave analyses, based on a locally conformal finite integration technique (FIT), implemented in CST Studio Suite™ and validated by measurements or highly accurate FEM simulations, illustrate the excellent characteristics of the proposed lenses to operate with narrowband as well as ultra-wideband (UWB) waveforms.

A Fast-Converging Scheme for the Electromagnetic Scattering from a Thin Dielectric Disk

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.

Scattering of electromagnetic waves from a thin triangular dielectric disk

An analytic theory for the scattering of electromagnetic waves from a thin dielectric triangular disk is presented. The proposed theory is based on the Koh–Sarabandi approximation for the electromagnetic wave scattering from a thin dielectric disk along with the spectral representation of the dyadic Green's function. The validity of the proposed formulation is justified by comparing it with the numerical method such as method of moments. For completeness, the scattering cross sections of a triangular disk for horizontal and vertical incident polarizations are compared with their respective scattering cross sections of elliptical, circular, semi-circular and square disks having same electromagnetic and geometrical parameters. It is studied that the back scattering cross sections for a low loss Gallium Arsenide triangular disk at a specific incidence angle can be made almost zero for both types of incident polarizations. This type of almost zero back scattering has applications in the stealth technology and remote sensing.

Method of analytical regularization in the analysis of axially symmetric excitation of imperfect circular disk antennas

This work presents accurate numerical method and computational results in the modeling of the axisymmetric radiation of resistive and thin-dielectric circular disk-on-substrate antennas. To simulate resistive and thin-dielectric disk features, we use two-side Generalized Boundary Conditions (GBC). The analysis is based on the singular integral equations (IEs) and the Method of Analytical Regularization (MAR) exploiting a Galerkin Method (GM) with judicious basis functions, which convert IEs into the Fredholm second-kind infinite matrix equations. Unlike previously known numerical techniques, this guarantees convergence and enables us to compute the solution with controlled accuracy even in sharp resonances. Numerical results demonstrate the effect of disk losses and transparency on the fundamental radiation phenomena and help improve antenna characteristics such as radiation efficiency.

Back-scattering cross section from a tilted thin circular dielectric disk

An analysis about the back-scattering cross section from a tilted thin circular dielectric disk is presented. The proposed formulation is based upon the widely used scattering techniques from a dielectric disk such as Rayleigh–Gans, Koh–Sarabandi and volumetric integral physical optics. It is investigated that by varying the orientation of the disk, the back-scattering cross section can be enhanced or diminished as compared to the disk having no tilt. It is further studied that for the specific tilt and size parameter of a low loss Gallium Arsenide disk, the back-scattering cross sections can be made almost equal to zero for both types of incident polarizations, i.e., horizontal and vertical. Such type of almost zero back-scattering cross section find applications in the stealth technology.

EXPERIMENTAL CONDITIONS FOR THE EXCITATION OF THIN DISK WHISPERING-GALLERY-MODE RESONATORS

Measurements of mm-wave excitation spectra of highorder whispering gallery modes in free-space cylindrical disk resonators as functions of resonator thickness have been made. Resonators in the form of tight stacks of thin dielectric disks excited via dielectric waveguides have been used in the experiment. Experimental conditions for the excitation of thin-disk resonators have been found. A simple approach for the modeling of resonator spectra and recovery of dielectric parameters has been proposed.

Channel Simulator for Land Mobile Satellite Channel Along Roadside Trees

We study the signal fading for the land mobile satellite channel caused by roadside trees. A channel simulator is developed which takes into account the signal fading caused by position-dependent tree scattered fields and by swaying tree components. In the model, the tree canopy is modeled as a vertically oriented cylindrical volume containing randomly distributed and oriented leaves and branches. The tree trunk is modeled as a finite lossy dielectric cylinder. Leaves are modeled as thin lossy dielectric disks and branches as finite lossy dielectric cylinders. The scattering pattern of the new model has a narrow forward lobe with an isotropic background which is comparable to the one found using the radiative energy transfer theory. In addition, the variation of the specific attenuation with frequency of the model is fairly similar to the one given in the ITU Recommendation. The model is validated using measurements at 2 GHz in terms of the cumulative distribution functions of the received signal and the Ricean K-factor, average fade duration and level crossing rate. Good agreement is found between the measured and simulated statistics.

ELECTROMAGNETIC SCATTERING FROM A CORN CANOPY AT L AND C BANDS

ELECTROMAGNETIC SCATTERING FROM A CORN CANOPY AT L AND C BANDS

A new approximate solution for scattering by thin dielectric disks of arbitrary size and shape

In this paper, an approximate solution for electromagnetic scattering by a very thin planar homogeneous dielectric object is presented. This solution is obtained from a volumetric integral equation using Fourier transform and is shown to be uniformly valid from low to high frequencies at all incidence angles including edge-on incidence. Validity of the solution is demonstrated through a comparison with canonical objects such as an infinite dielectric slab, and a number of two-dimensional (2-D) and three-dimensional (3-D) dielectric scatterers. For 2-D, and 3-D scatterers, the approximate solution is compared with a method of moments solution. In all cases examined the approximate formulation provides very accurate results except for situations where the dielectric constant is very high.

Polarimetric channel characterization of foliage for performance assessment of GPS receivers under tree canopies

The attenuation, depolarization, and fluctuation of a microwave signal going through a tree canopy are investigated by developing a Monte Carlo based coherent scattering model. In particular, the model is used to analyze the performance of Global Positioning System (GPS) receivers under tree canopies. Also the frequency and time-domain channel characteristics of a forest are investigated when a transmitter is outside and a receiver is inside a forest. A fractal algorithm (Lindenmayer system) is used to generate the structure of coniferous or deciduous trees whose basic building blocks are arbitrarily oriented finite cylinders, thin dielectric needles, and thin dielectric disks. Attenuation and phase change of the mean field through foliage is accounted for using Foldy's approximation. Scattering of the mean field from individual tree components and their images in the underlying ground plane are computed analytically and added coherently. Since tree trunks and some branches are large compared to the wavelength and may be in the close proximity of the receiver, a closed-form and uniform expression for the scattered near-field from dielectric cylinders is also developed. Monte Carlo simulation of field calculation is applied to a cluster of trees in order to estimate the statistics of the channel parameters, such as the probability density function (pdf) of the polarization state of the transmitted field, path loss, and the incoherent scattered power (the second moment of the scattered field), as a function of the observation point above the ground.

Particle acceleration by laser fields in a dielectric disk-loaded waveguide

A new method is proposed for accelerating relativistic charged particle beams in a vacuum by a laser. The laser propagates in an overmoded waveguide interrupted periodically by thin dielectric disks spaced many wavelengths apart. The particle beam travels along the waveguide axis, passing through irises in the disks. The disks correct for slippage of the particle phase relative to the laser wave. This concept exploits the inverse of familiar radiation processes (transition radiation, diffraction radiation). Several practical accelerator issues are incorporated in a systems analysis. Acceleration gradients in the GeV/m range are projected using lasers with ∼100 GW power. This represents more than an order of magnitude stronger coupling of the laser energy compared to other laser acceleration schemes.

Microwave propagation constant for a vegetation canopy at X band

An equivalent‐medium model is developed for vegetation media to relate the propagation constant γ, associated with propagation of the mean field through a vegetation canopy, to the geometrical and dielectric parameters of the canopy constituents at high frequencies. The model is intended for media containing vertical dielectric cylinders, representing the stalks, and randomly oriented, arbitrary shaped thin dielectric disks, representing the leaves. The formulation accounts for absorption and scattering losses by both stalks and leaves. A resistive sheet model in conjunction with the physical optics approximation is used to model scattering by the canopy leaves, which is valid when the leaf dimensions are larger than a wavelength. The model is found to be in good agreement with experimental results at 10.2 GHz. The experimental component of the study included measurements of the attenuation loss for horizontally polarized and vertically polarized waves transmitted through a fully grown corn canopy. The measurements were made at incidence angles of 20°, 40°, 60°, and 90° relative to normal incidence. The proposed model is suitable for cornlike canopies, provided the leaves are larger than λ in size.

Polarization utilization in the microwave inversion of leaf angle distributions

The inverse problem of deducting the inclination angle distribution of leafy vegetation has been investigated using L-band multipolarization backscattered data. The modeling procedure replaces canopy leaves with thin circular dielectric disks. The Born approximation is then used to establish a linear relationship between the radar backscattering coefficients and the leaf inclination angle distribution. The inversion of the leaf angle distribution is carried out for horizontal, vertical, and cross-polarized data. It is shown that the results of the inversion using vertical and cross-polarized data are comparable to the inversion results of horizontally polarized data obtained previously (R. Lang and H. Saleh, 1985).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Scattering from thin dielectric disks

A solution for scattering from thin dielectric disks has been obtained by approximating the currents induced inside the disk with the currents which would exist inside a dielectric slab of the same thickness, orientation and dielectric properties. This procedure yields an electrostatic approximation when the disk thickness <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</tex> is small compared to the wavelength of the incident radiation and yields a conventional physical optics approximation when the dimension <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</tex> , characteristic of the geometrical cross section of the disk, is large compared to wavelength. When the ratio <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A/T</tex> is sufficiently large one or the other of these approximations applies, regardless of the frequency of the incident radiation. Consequently, the solution provides a conventional approximation for the scattered fields at all <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">kA</tex> . As a check on this conclusion, a comparison has been made between measurements of the radar cross section of thin dielectric disks and the cross sections predicted using this theory. Agreement was found for thin disks with both large and small values of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">kA</tex> .

Integral equation method for scattering and absorption of electromagnetic radiation by thin lossy dielectric discs

An integral equation for the current induced in a dielectric body by incident electromagnetic radiation is solved for the case of a thin flat circular disc of homogeneous lossy dielectric material. The equation is reduced by using the method of moments to a linear algebraic matrix equation for the coefficients in an expansion of the current density as a linear combination of basis functions. The matrix elements consist of integrals involving the basis functions. The novel computational aspects of this work lie in the choice of basis functions and in the techniques which this choice enabled to handle singularities in the integrands when evaluating the matrix elements, to reduce the matrix size and to rigorously preserve symmetries in the matrix. Expressions are given for the scattering and absorption cross sections in terms of the expansion coefficients. The results are most suitable in the resonance range of wavelengths when the disc radius and free-space wavelength are of the same order of magnitude.