Method Of Analytical Regularization Research Articles

Performance of Hemielliptic Dielectric Lens Antennas With Optimal Edge Illumination

The role of edge illumination in the performance of compact-size dielectric lens antennas (DLAs) is studied in accurate manner using a highly efficient algorithm based on the combination of the Muller boundary integral equations and the method of analytical regularization. The analysis accounts for the finite size of the lens and directive nature of the primary feed placed close to the center of the lens base. The problem is solved in a two-dimensional formulation for both E- and H-polarizations. It is found that away from internal resonances that spoil the radiation characteristics of DLAs made of dense materials, the edge illumination has primary importance. The proper choice of this parameter helps maximize DLA directivity, and its optimal value depends on the lens material and feed polarization. Index Terms: Beam collimation, dielectric lens antenna, directivity improvement, edge illumination, edge taper, hemielliptic lens.

Exact off-resonance near fields of small-size extended hemielliptic 2-D lenses illuminated by plane waves

The near fields of small-size extended hemielliptic lenses made of rexolite and isotropic quartz and illuminated by E- and H-polarized plane waves are studied. Variations in the focal domain size, shape, and location are reported versus the angle of incidence of the incoming wave. The problem is solved numerically in a two-dimensional formulation. The accuracy of results is guaranteed by using a highly efficient numerical algorithm based on the combination of the Muller boundary integral equations, the method of analytical regularization, and the trigonometric Galerkin discretization scheme. The analysis fully accounts for the finite size of the lens as well as its curvature and thus can be considered as a reference solution for other electromagnetic solvers. Moreover, the trusted description of the focusing ability of a finite-size hemielliptic lens can be useful in the design of antenna receivers.

Analytical regularization method for electromagnetic wave diffraction by axially symmetrical thin annular strips

A new mathematically rigorous and numerically efficient method based on the combination of Orthogonal Polynomials Method, and Analytical Regularization Method, for electromagnetic wave diffraction by a model structure for various antennae such as Fresnel zone plates is proposed. It can be used as validation tool for the other (more general or less accurate) numerical methods and physical approaches. The initial boundary value problem is equivalently reduced to the infinite system of the linear algebraic equations of the second kind, i.e. to an equation of the type (I + H)x = b in the space l2 with compact operator H . This equation can be solved numerically by means of truncation method with, in principle, any required accuracy. Numerical results show that physical optics approximation may not be valid, especially in diffraction by sources other than plane wave, as it does not take into account the contribution of strip edges and interaction of strips by means of traveling slow waves.

Plane wave scattering and absorption by flat gratings of impedance strips

The problem of the plane wave scattering by a flat impedance-strip grating located in free space is considered. The formulation involves a set of generalized boundary conditions relating limiting values of the fields to effective electric and magnetic currents. We develop an accurate numerical solution to this problem using the dual series equations and the method of analytical regularization (MAR) based on the main part inversion. This guarantees a fast convergence and controlled accuracy of computations. Reflected, transmitted, and absorbed power fractions as a function of the frequency and the grating parameters are analyzed. Sharp resonances are revealed in the H-polarized scattering near to the grazing of the higher-order modes; these resonances are absent for the perfect electrically conducting strip grating. Low-frequency asymptotics for the reflectance and transmittance in the single-mode regime are presented and compared with numerical solutions.

Vacuum Effects on Massive Spinor Fields: S 1× R 3 Topology

The aim of this work was to investigate the role played by an external field on the Casimir energy density for massive fermions under S1× R3 topology. Both twisted- and untwisted-spin connections are considered and the calculation in a closed form is performed using an alternative approach based on the combination of the analytic regularization method and the Euler–Maclaurin summation formula. It is shown that no mass scale appears in the final result and, therefore, Casimir effect arises only from the boundary conditions and vacuum fluctuations induced by the coupling with the external field.

Analysis of aperture illumination and edge rolling effects for parabolic reflector antenna design

The radiation from parabolic reflector antennas for different amplitude and phase aperture illumination patterns is treated and the minimizations of the edge diffraction effects by edge rolling techniques are investigated in an accurate manner. The analytical regularization method (ARM) is used to solve the problem of E-polarized wave diffraction by parabolic shaped perfectly electrical conductive (PEC) cylindrical reflector with finite thickness. The initial boundary value problem is reduced to the infinite algebraic system of the second kind, which is an equation that can in principal be solved with any predetermined accuracy by means of the truncation procedure. The parabolic reflector is illuminated by a fictive feeder antenna which produces the desired phase and amplitude field distributions over the antenna aperture. Some edge rolling structures are analyzed to suppress the side and back lobes and to improve the aperture efficiency. The ARM procedure is verified by the analytical solutions and the calculated field patterns are presented for typical antenna configurations.

MAR Analysis of a Spherical-Circular Printed Antenna With Finite Ground Excited by an Axially Symmetric Probe

The paper deals with an accurate mathematical and numerical analysis of a spherical-circular antenna printed over a coaxial spherical-circular ground conductor. A coaxial probe simulated by a radial driving current placed between two conductors excites the antenna. Consideration is done in terms of the spherical vector wave function expansions of the field in each partial domain. The problem is cast into a coupled set of the dual-series equations for the expansion coefficients, and then to an infinite-matrix equation having favorable features. This is achieved by following the Method of Analytical Regularization developed earlier for the analysis of spherical reflectors.

Time domain theory of open waveguide resonators: Canonical problems and a generalized matrix technique

In this paper, we consider new solutions and algorithms for initial boundary‐value problems in the electromagnetic theory of open waveguide resonators. The approaches are based on a description of the scattering properties of such resonators in terms of the transform operators for an evolutionary basis of the non‐stationary signal, that have the same significance in the course of analyses in time domain as generalized scattering matrixes in frequency domain. All suggested approaches imply using mathematically correct computational procedures at the key stages of forming the solution, in particular, the analytical regularization method—the semi‐inversion method.

Highly efficient design of spectrally engineered whispering-gallery-mode microlaser resonators

We present an accurate, reliable and versatile method for studying the effect of deformations on the characteristics of the high-Q whispering gallery (WG) modes supported by two-dimensional dielectric resonators (DR). An eigenvalue problem is formulated in terms of contour integral equations and further discretised with the method of analytical regularisation. Such a procedure significantly reduces the number of unknowns whilst providing high and controllable accuracy. Natural frequencies, Q-factors and field patterns of elliptical, flower- and egg-shaped DRs are calculated. Methods to enhance the Q-factors, provide directional light output, and parasitic mode suppression are discussed. The identification of WG modes is simplified by the symmetrical/asymmetrical mode separation included into the formulation of the problem and solution algorithm.

Method of analytical regularization based on the static part inversion in wave scattering by imperfect thin screens

Method of analytical regularization based on the static part inversion in wave scattering by imperfect thin screens

A note on the method of analytical regularization

Many problems of electromagnetics are governed by singular integral equations of the first kind. As discussed by Nosich (1999), it is often possible to obtain a different equation describing the problem by applying the method of analytical regularization, and analytically inverting part of the original equation. The transformed equation is of the second kind. Therefore, as a rule, it is usually preferable to apply a numerical method to the transformed equation than to the original one. What appears to be an exception to that rule is discussed in the present paper: under proper conditions, and for a particular numerical method, results obtained by application to the transformed equation are shown to be identical to those obtained by application to the original equation. Some consequences of this equivalence are discussed.

E-Polarized Scalar Wave Diffraction by Perfectly Conductive Arbitrary Shaped Cylindrical Obstacles with Finite Thickness

The Analytical Regularization Method is applied to the problem of E-polarized wave diffraction by arbitrary shaped cylindrical obstacle which is perfectly conductive and homogeneous in longitudional direction. The initial electromagnetic boundary value problem is reduced to the infinite algebraic system of the second kind by means of constructed analytical regularization procedure. As it is well-known, an equation of such a kind, in principal, can be solved with any predetermined accuracy by means of truncation procedure. Numerical implementation of corresponding analytical regularization procedure is suggested. Numerical results thus obtained show high quality of the algorithm, including relatively small values and uniform boundness of condition number of truncated algebraic systems when their size tends to infinity. By the qualitative property of infinite algebraic system of the second kind, it guarantees the stability of numerical process of truncated solving as well as the convergence of solution of truncated system to the solution of infinite system. Relevant numerical results, including condition number behaviour, current density, field space distribution and far field pattern for a few different resonant and non-resonant obstacles are presented.

Accurate computation of a circular-disk printed antenna axisymmetrically excited by an electric dipole

Galerkin's method, combined with the method of analytical regularization in the Hankel-transform domain, is used to analyze a circular-disk metallic printed antenna. The fundamental effects are investigated, such as the surface-wave and space-wave powers and the radiation efficiency. The validity of the cavity (magnetic-current) model is studied. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 25: 211–216, 2000.

A conformal spherical-circular microstrip antenna: Axisymmetric excitation by an electric dipole

ABSTRACT: A mathematically accurate method of analysis of a spheri - cal-disk antenna conformally printed on a dielectric-co ¤ ered metallicsphere is presented. The antenna is fed by a radial coaxial probesimulated by an electric dipole. The solution consists of reducing theboundary- ¤ alue problem to the dual-series equations, and further to aregularized infinite-matrix equation. This procedure is based on theanalytical in ¤ ersion of the static part of the problem of a disk in freespace, and results in a stable and fast algorithm with a guaranteedcon ¤ ergence. Numerical data on the basic antenna characteristics arepresented. Q 2000 John Wiley & Sons, Inc. Microwave Opt TechnolLett 26: 176]182, 2000. Key words: spherical disk; conformal antenna; dual-series equations;analytical regularization; directi ¤ ity 1. INTRODUCTION Metallic circular disks printed on dielectric substrates areused frequently in patch antenna technology. Conformalprinted antennas are necessary in automotive and airbornecommunications and radar due to their low profile and lightweight. In this paper, the problem of modeling of aspherical-disk conformal printed antenna is considered as-suming an excitation by a coaxial probe. The probe is mod-eled by a radial electric dipole RED located at the surface.of the metal sphere covered with dielectric. From a theoreti-cal point of view, such a geometry is a canonical one for awide class of conformal patch antennas. Previously, similarproblems have been analyzed by direct applications of themethod of moments 1, 2 . However, convergence of thesewxnumerical approximations is not uniformly guaranteed, espe-cially if narrow resonances are present 3 . Patch antennaswxare essentially resonant devices; hence, this must be kept inmind when developing an accurate simulation software. Wepropose an exact mathematical method based on the analyti-cal inversion of the free-space static problem for a sphericaldisk 4, 5 that has been used previously in the analysis ofwxcavity-backed apertures and reflector antennas 6wx]8 . Thismethod belongs to the broad family of techniques collectivelycalled the method of analytical regularization 9 that arewxremarkable for stable and fast numerical solutions.

The method of analytical regularization in wave-scattering and eigenvalue problems: foundations and review of solutions

We discuss the foundations and state-of-the-art of the method of analytical regularization (MAR) (also called the semi-inversion method). This is a collective name for a family of methods based on conversion of a first-kind or strongly-singular second-kind integral equation to a second-kind integral equation with a smoother kernel, to ensure point-wise convergence of the usual discretization schemes. This is done using analytical inversion of a singular part of the original equation; discretization and semi-inversion can be combined in one operation. Numerous problems being solved today with this approach are reviewed, although in some of them, MAR comes in disguise.

Numerical optimization of a cylindrical reflector-in-radome antenna system

Accurate numerical optimization based on rigorous solution of the integral equation using the method of analytical regularization is performed for a cylindrical reflector antenna in a dielectric radome. It is shown that the multiple scattering in this system is more significant for the optimum radome design than any nonplane-wave effects or the curvature of the radome. We claim that, although the common half-wavelength design is a good approximation to avoid negative effects of the radome (such as the loss of the antenna directivity), one can, by carefully playing with the radome thickness, its radius, reflector location, and the position of the feed, improve the reflector-in-radome antenna performance (e.g., increase the directivity) with respect to the same reflector in free-space.

Finite deformations of conformal field theories using analytically regularized connections

We study some natural connections on spaces of conformal field theories using an analytical regularization method. The connections are based on marginal conformal field theory deformations. We show that the analytical regularization preserves conformal invariance and leads to integrability of the marginal deformations. The connections are shown to be flat and to generate well-defined finite parallel transport. These finite parallel transports yield formulations of the deformed theories in the state space of an undeformed theory. The restrictions of the connections to the tangent space are curved but free of torsion.

The stress tensor conformal anomaly and analytic regularizations

In this paper the stress tensor conformal anomaly of a conformally coupled scalar field defined in a d dimensional Riemannian manifold is derived with or without a boundary, using the zeta function analytic regularization method. It is found that the scalar anomaly is independent of any massless limit. In an odd dimensional manifold with a boundary, the anomaly is not zero owing the boundary condition dependent term. After briefly discussing the cutoff method, it is proven that the zeta function method is equivalent to the cutoff method with a subtraction of the polar terms.

ANALYTIC EVALUATION OF LANDSHOFF TYPE INTEGRALS FOR AXIAL GAUGES

It is demonstrated that it is possible to expand Feynman Integrals in axial gauges to arbitrary orders in a small mass-like parameter, and in so doing, replace ad hoc prescriptions by the limit of a gauge-fixing term imposed within the Lagrangian. Both the Landshoff and Principle Value prescriptions are related to the canonical form of the integrals and the expansions associated with them, and the values for a subset of the Landshoff Integrals are tabulated to second order in the mass-like parameter. The expansion technique relies 011 the method of Analytic Regularization, which includes Dimensional Regularization as one of a number of limiting cases.

DOES STOCHASTIC ANALYTIC REGULARIZATION PROVIDE QUANTUM FIELD THEORIES?

We analyze whether the so-called method of stochastic analytic regularization is suitable as an intermediate step for constructing perturbative renormalized quantum field theories. We choose a λϕ3 in six dimensions to prove that this regularization method does not in general provide a quantum field theory. This result seems to apply to any field theory with a quadratically UV-divergent stochastic two-point function, for instance λϕ4 and gauge theories in four dimensions.