Grigorios P. Zouros

Electromagnetic Scattering by an Inhomogeneous Gyroelectric Sphere Using Volume Integral Equation and Orthogonal Dini-Type Basis Functions

The electromagnetic scattering by an inhomogeneous gyroelectric sphere is studied in this work. The solution is constructed using the well-known electric field volume integral equation (EFVIE). The kernel that incorporates the Greens function is expanded in spherical vector wave functions, and the unknown electric field and electric displacement is expanded in spherical vector wave functions using fully orthogonal Dini-type basis functions. The permittivity tensor of the spherical object supports a continuously varying radial inhomogeneity, while its permeability is that of free space. This approach allows a fully analytical computation of the unknown matrix coefficients in special cases of homogeneous permittivity tensors. The validation of our method is performed by comparisons with published results in the literature. New numerical results are given for various continuously varying permittivity tensors.

Electromagnetic plane wave scattering by arbitrarily oriented elliptical dielectric cylinders

The electromagnetic scattering by an arbitrarily oriented elliptical cylinder having different constitutive parameters than those of the background medium is treated in this work. The separation of variables method is used to solve this problem, but, due to the oblique incidence of the source fields, hybrid waves for the scattered and induced fields are generated, thus making the formulation complicated. Moreover, because of the different wavenumbers between the scatterer and the background medium, the orthogonality relations for Mathieu functions do not hold, leading to more complicated systems, compared to those of normal incidence, which should be solved in order to obtain the solution for the scattered or induced fields. The validation of the results reveals the high accuracy of the implementation, even for electrically large scatterers. Both polarizations are considered and numerical results are given for various values of the parameters. The method is exact and can be used for reference as an alternative validation for future methods involving scattering problems.

Oblique electromagnetic scattering from lossless or lossy composite elliptical dielectric cylinders

The oblique electromagnetic scattering by a dielectric elliptical cylinder which is coated eccentrically by a nonconfocal dielectric elliptical cylinder is examined in this work. The problem is solved using the separation of variables in terms of Mathieu functions, in combination with the addition theorem for Mathieu functions, a complicated procedure due to the following three factors: the nonexistence of the orthogonality relations for Mathieu functions due to the different constitutive parameters between the two cylinders and the background medium, the complex expressions due to the oblique incidence that leads to hybrid waves for both the scattered and induced fields, and the use of the addition theorem, which introduces a cross relation between even and odd terms. The method described here is exact, its solution is validated compared with other published results from the literature, and the high accuracy is revealed. Both polarizations are examined and numerical results are given for the scattering cross sections, including lossless and lossy materials.

Transverse Electric Scattering on Inhomogeneous Objects: Spectrum of Integral Operator and Preconditioning

The domain integral equation method with its FFT-based matrix-vector products is a viable alternative to local methods in free-space scattering problems. However, it often suffers from the extremely slow convergence of iterative methods, especially in the transverse electric (TE) case with large or negative permittivity. We identify very dense line segments in the spectrum as being partly responsible for this behavior and the main reason why a normally efficient deflating preconditioner does not work. We solve this problem by applying an explicit multiplicative regularizing operator, which on the operator level transforms the system to the form “identity plus compact.” On the matrix level this regularization reduces the length of the dense spectral segments roughly by a factor of four while preserving the ability to calculate the matrix-vector products using the FFT algorithm. Such a regularized system is then further preconditioned by deflating an apparently stable set of eigenvalues with largest magnitudes, which results in a robust acceleration of the restarted GMRES under constraint memory conditions.

Electromagnetic Scattering by a General Rotationally Symmetric Inhomogeneous Anisotropic Sphere

In this work, the electromagnetic scattering in general rotationally symmetric inhomogeneous anisotropic spheres is investigated. A rigorous full-wave solution is presented based on the volume integral equation. The solution is achieved by expanding the unknown fields in fully orthogonal Dini-type spherical vector wave functions. This formulation allows the study of general rotationally symmetric gyrotropic spheres with varying permittivity and permeability tensors. We investigate the validity of the developed method, which is next applied on the computation of the scattering cross sections of inhomogeneous rotationally symmetric gyroelectric and gyromagnetic spheres.

Electromagnetic Scattering on Inhomogeneous Gyroelectric Bodies of Revolution

The volume integral equation (VIE) method with Dini series expansion (DSE) technique is extended for solving electromagnetic scattering problems by inhomogeneous gyroelectric bodies of revolution (BoRs). The permittivity tensor of the BoR supports continuously varying inhomogeneity, while its permeability is that of free space. The VIE-DSE is tested exhaustively by numerous comparisons for various geometrical configurations. The robustness and limitations of the VIE-DSE are discussed for its application on scattering problems beyond the sphericity.

Exact Cutoff Wavenumbers of Composite Elliptical Metallic Waveguides

The cutoff wavenumbers of eccentric nonconfocal elliptical metallic waveguides are calculated in this paper. The solution is obtained using expansions in terms of the elliptical wave functions, in combination with the related addition theorem. The method presented here is exact, and allows the study of more complex elliptical waveguide geometries, like rotated elliptical interfaces arbitrarily placed inside the outer elliptical interface, or studies for possible change of the operational bandwidth. The solution is validated compared with other published results from the literature. The known problem of an elliptical metallic waveguide loaded by a concentric nonconfocal strip is revisited and discrepancies noticed by other authors are justified. Numerical results are presented for the cutoff wavenumbers for various composite elliptical waveguides for both TM and TE modes.

Green’s function of radial inhomogeneous spheres excited by internal sources

Greens function in the interior of penetrable bodies with inhomogeneous compressibility by sources placed inside them is evaluated through a Schwinger-Lippmann volume integral equation. In the case of a radial inhomogeneous sphere, the radial part of the unknown Greens function can be expanded in a double Dinis series, which allows analytical evaluation of the involved cumbersome integrals. The simple case treated here can be extended to more difficult situations involving inhomogeneous density as well as to the corresponding electromagnetic or elastic problem. Finally, numerical results are given for various inhomogeneous compressibility distributions.

CCOMP: An efficient algorithm for complex roots computation of determinantal equations

Abstract In this paper a free Python algorithm, entitled CCOMP (Complex roots COMPutation), is developed for the efficient computation of complex roots of determinantal equations inside a prescribed complex domain. The key to the method presented is the efficient determination of the candidate points inside the domain which, in their close neighborhood, a complex root may lie. Once these points are detected, the algorithm proceeds to a two-dimensional minimization problem with respect to the minimum modulus eigenvalue of the system matrix. In the core of CCOMP exist three sub-algorithms whose tasks are the efficient estimation of the minimum modulus eigenvalues of the system matrix inside the prescribed domain, the efficient computation of candidate points which guarantee the existence of minima, and finally, the computation of minima via bound constrained minimization algorithms. Theoretical results and heuristics support the development and the performance of the algorithm, which is discussed in detail. CCOMP supports general complex matrices, and its efficiency, applicability and validity is demonstrated to a variety of microwave applications. Program summary Program Title: CCOMP Program Files doi: http://dx.doi.org/10.17632/x6fx4zssft.1 Licensing provisions: GPLv3 Programming language: Python Nature of problem: The determination of the resonances of a physical system, arising from determinantal type equations. These resonances arise from the non trivial solution of a homogeneous system of equations, whose system matrix depends on a parameter z , which can be either real or complex depending on the application. The values of z for which the determinant of the aforementioned system matrix is zero, are the resonances of the physical system. Solution method: An open-source software is developed for the efficient detection of all complex roots inside a prescribed complex domain D . The program is written in Python programming language [1] in conjunction with NumPy [2], SciPy [3], and Matplotlib [4]. The key to the method presented is the efficient determination of the candidate points inside D which in their close neighborhood the existence of a minimum is guaranteed. Once these points are detected, the algorithm proceeds to a two-dimensional minimization problem with respect to the minimum modulus eigenvalue of the system matrix, which is a positive function inside D . If the minimization yields global minima (near zero), the roots are found. For local minima (values of minimum modulus eigenvalue function away from zero), no roots exist. For all other points which have not been flagged as candidates, the algorithm does not proceed to the minimization problem. Additional comments including restrictions and unusual features: Python library psutil is used to compute memory consumption. [1] The Python programming language, https://www.python.org/ . [2] NumPy, http://numpy.org/ . [3] SciPy, http://scipy.org/ . [4] Matplotlib, http://matplotlib.org/ .

Eigenfrequencies and Modal Analysis of Uniaxial, Biaxial, and Gyroelectric Spherical Cavities

The normalized eigenfrequencies in spherical cavities filled with uniaxial, biaxial, and gyroelectric medium are calculated, and the corresponding modal analysis is performed. A discrete eigenfunction approach is employed that permits the direct calculation of the normalized eigenfrequencies. First, a discrete basis that depends on the tensorial permittivity elements is constructed for expansion of the unknown electric field inside the cavity. Then, the boundary condition is applied on the perfect electric conductor at the cavity’s surface, which leads to two infinite sets of homogeneous equations. It is found that the uniaxial/biaxial cavities maintain quasi-TMr, quasi-TEr, as well as hybrid modes, but when the medium becomes gyroelectric, the modes are purely hybrid. The proposed approach is validated against other eigenmode solvers, up to the biaxial anisotropy. The normalized eigenfrequencies of uniaxial, biaxial, and gyroelectric filled cavities are presented and the corresponding eigenmodes are discussed.