Nikolaos L. Tsitsas

On the Resonance and Radiation Characteristics of Multi-Layered Spherical Microstrip Antennas

Abstract The resonance and radiation characteristics of a spherical microstrip with its circular metallic patch located inside a coating, possessing an arbitrary number of layers, are investigated. The developed methodology combines the Legendre transform with a T-matrix method. The appropriate basis functions for the surface current on the patch are chosen according to the cavity model. The complex resonant frequencies are the singular points of a homogeneous linear system, resulting by following a Galerkins technique. The numerical results of this article propose novel multi-layered spherical microstrip configurations. More precisely, a new type of excitation that concerns an amplifying layer located between core and patch is proposed. The control mechanism of the amplifying capability via the layers thickness and dielectric constant is reported. Moreover, the behavior of a microstrip with two airgaps that are surrounded by a zero-index material is analyzed. Finally, a coatings continuous distribution, following a “shifted” Luneburg law, is treated by a step approximation of the radial function of its dielectric constant, and the achieved high quality factor of such a microstrip is discussed.

A recursive algorithm for the inversion of matrices with circulant blocks

We investigate the recursive inversion of matrices with circulant blocks. Matrices of this type appear in several applications of Computational Electromagnetics and in the numerical solution of integral equations with the boundary-element method. The inversion is based on the diagonalization of each circulant block by means of the discrete Fourier transform and the application of a recursive algorithm for the inversion of the matrix with diagonal blocks, determined by the eigenvalues of each block. The efficiency of the recursive inversion is exhibited by determining its computational complexity. An implementation of the algorithm in MATLAB is given and numerical results are presented to demonstrate the efficiency in terms of CPU time of our approach.

Vector solitons in nonlinear isotropic chiral metamaterials

Starting from the Maxwell equations, we used the reductive perturbation method to derive a system of two coupled nonlinear Schrodinger (NLS) equations for the two Beltrami components of the electromagnetic field propagating along a fixed direction in an isotropic nonlinear chiral metamaterial. With single-resonance Lorentz models for the permittivity and permeability and a Condon model for the chirality parameter, in certain spectral regimes, one of the two Beltrami components exhibits a negative-real refractive index when nonlinearity is ignored and the chirality parameter is sufficiently large. We found that, inside such a spectral regime, there may exist a subregime wherein the system of the NLS equations can be approximated by the Manakov system. Bright–bright, dark–dark, and dark–bright vector solitons can be formed in that spectral subregime.

Short pulse equations and localized structures in frequency band gaps of nonlinear metamaterials

Abstract We consider short pulse propagation in nonlinear metamaterials characterized by a weak Kerr-type nonlinearity in their dielectric response. Two short-pulse equations (SPEs) are derived for the high- and low-frequency “band gaps” (where linear electromagnetic waves are evanescent) with linear effective permittivity ϵ 0 and permeability μ > 0 . The structure of the solutions of the SPEs is also briefly discussed, and connections with the soliton solutions of the nonlinear Schrodinger equation are made.

Finding a source inside a sphere

A sphere excited by an interior point source or a point dipole gives a simplified yet realistic model for studying a variety of applications in medical imaging. We suppose that there is an exterior field (transmission problem) and that the total field on the sphere is known. We give analytical inversion algorithms for determining the interior physical characteristics of the sphere as well as the location, strength and orientation of the source/dipole. We start with static problems (Laplace’s equation) and then proceed to acoustic problems (Helmholtz equation).

Hiding a bump on a PEC plane by using an isotropic lossless dielectric layer

An infinite perfect electric conducting (PEC) plane on top of which lies a 2-D PEC object (bump) is excited by a plane wave. The main purpose of this work concerns the determination of the appropriate permittivity εr and thickness H of a lossless dielectric superstrate slab layer, placed on top of the overall structure of the PEC bump and the PEC plane, such that two objectives are fulfilled: 1) the plane wave reflection by the grounded slab configuration in the absence of the bump resembles closely that by the infinite PEC plane, and simultaneously 2) the contribution due to the presence of the bump itself on the scattered far-field radiated over all directions becomes as small as possible. A semianalytic integral equation methodology is developed to determine the field scattered by the bump configuration. Numerical results are presented demonstrating that indeed for certain regions of values of the superstrates parameters both objectives 1) and 2) are met within significant numerical accuracy. Particularly, it is shown that may offer optimal cloaking characteristics. Finally, the results of the analysis as well as of the developed two objectives strategy are verified by appropriate computational simulations.

On the Nature of Oscillations in Discretizations of the Extended Integral Equation

Using analytical methods, previous studies have shown that it is possible for oscillations to occur in the auxiliary surface current determined by applying the method of auxiliary sources (MAS) to problems of scattering by perfect conductors of a very simple shape. Such oscillations are inherent to MAS and would occur even in a hypothetical computer with ideal hardware and software. Because the integral equation relevant to MAS very much resembles the “extended integral equation” (in which the unknown is the actual surface current on the conductor), one might surmise that similar oscillations also occur in discretizations of the latter equation. In this communication, we use analytical means to show that this is not the case. Therefore, any oscillations that do occur in discretizations of the extended integral equation are-at least for “sufficiently simple” problems-likely to be due to matrix ill-conditioning, which magnifies errors that would otherwise be unimportant.

Rigorous integral equation analysis of nonsymmetric coupled grating slab waveguides

A rigorous integral equation formulation in conjunction with Greens function theory is used to analyze the waveguiding and coupling phenomena in nonsymmetric (composed of dissimilar slabs) optical couplers with gratings etched on both slabs. The resulting integral equation is solved by applying an entire-domain Galerkin technique based on a Fourier series expansion of the unknown electric field on the grating regions. The proposed analysis actually constitutes a special type of the method of moments and provides high numerical stability and controllable accuracy. The singular points of the systems matrix accurately determine the complex propagation constants of the guided waves. The results obtained improve on those derived by coupled-mode methods in the cases of large grating perturbations and highly dissimilar slabs. Numerical results referring to the evolution of the propagation constants as a function of the gratings characteristics are presented. Optimal grating parameters with respect to minimum coupling length and maximum coupling efficiency are reported. The couplers efficient operation as an optical bandpass filter is thoroughly investigated.

Green’s-function method for the analysis of propagation in holey fibers

A Greens-function method is employed to provide a rigorous analysis to the propagation and coupling phenomena in holey fibers. The analysis is carried out for an arbitrary grid of circular air holes of the fiber guide, while the electromagnetic field is taken to be a vector quantity. Application of the Greens-function concept leads to a coupled system of equations incorporating as unknowns the field expansion coefficients to cylindrical wave functions within the air holes. The propagation constants of the guided waves are computed accurately by determining the singular points of the corresponding systems matrix. Field distribution and dispersion properties of guided modes as well as coupling phenomena between parallel-running holey fibers are investigated, and numerical results are presented.

Field Enhancement in a Grounded Dielectric Slab by Using a Single Superstrate Layer

The addition of a dielectric layer on a slab configuration is frequently utilized in various electromagnetic devices in order to give them certain desired operational characteristics. In this work, we consider a grounded dielectric film-slab, which is externally excited by a normally-incident Gaussian beam. On top of the film-slab, we use an additional suitably selected single isotropic superstrate layer in order to increase the field concentration inside the slab and hence achieve optimal power transfer from the external source to the internal region. We define a quantity of interest, called “enhancement factor,” expressing the increase of the field concentration in the film-slab when the superstrate is present compared to the case that it is absent. It is shown that large enhancement factor values may be achieved by choosing properly the permittivity, the permeability, and the thickness of the superstrate. In particular, it is demonstrated that the field in the film-slab is significantly enhanced when the slab is composed by an ϵ-near-zero (ENZ) or low-index metamaterial.