Christos S. Lavranos

Eigenvalue Analysis of Curved Waveguides Employing an Orthogonal Curvilinear Frequency-Domain Finite-Difference Method

An eigenvalue analysis numerical technique for curved closed waveguiding structures loaded with inhomogeneous and/or anisotropic materials is presented. For this purpose, a frequency-domain finite-difference method is developed for a general orthogonal curvilinear coordinate system. The main strength of the technique is the accurate modeling of curved transverse boundaries, as well as curved geometries along the propagation direction, under certain limitations for the latter. This feature avoids the necessity of a fine mesh, while it retains a high accuracy and it is free of any staircase effects. In general, the proposed method shares the finite-element technique capabilities in modeling complex boundaries, while it preserves the finite-difference convenience in handling inhomogeneous and anisotropic material loadings. The resulting eigenvalue-based problem is solved using the Arnoldi algorithm, which exploits the system matrix sparcity and the overall technique is robust, unconditionally stable with minimal computational and memory requirements. Numerical results are validated against analytical results and results from 3-D commercial electromagnetic simulators. Finally, novel results are also given.

Eigenvalue Analysis of Curved Open Waveguides using a Finite Difference Frequency Domain Method Employing Orthogonal Curvilinear Coordinates

Eigenvalue analysis of open curved geometries is performed by using a two dimensional (2-D) Finite Difference Frequency Domain (FDFD) eigenvalue method employing orthogonal curvilinear coordinates, in conjunction with a perfectly matched layer (PML) tensor. This method can be used to compute the dispersion characteristics of open curved structures such as open microstrip lines printed on curved substrates. Numerical results for the eigenvalues of several geometries are presented, and compared against already published results, so as to validate the accuracy of the method.

Periodic structures eigenanalysis incorporating the Floquet Field Expansion

The current work elaborates on the study of periodic structures loaded either with anisotropic or isotropic media. An eigenanalysis methodology is adopted using Finite Difference in Frequency Domain (FDFD) in order to evaluate the Floquet wavenumbers. An eigenvalue problem is addressed and solved with Arnoldi iterative Algorithm. The periodicity of the structure is accounted in two alternative approaches. Initially Periodic Boundary Conditions (PBCs) are imposed on the periodic surfaces whose results found to be in a very good agreement with analytical ones. However, there is a deviation when the phase difference between periodic surfaces rise above 150 degrees. In order to get more accurate results, a Floquet Field Expansion is incorporated into the FDFD formulation. Also, adaptive meshing is employed for the accurate study of very fine discontinuities. In turn certain periodic structures loaded with anisotropic media are simulated in order to reveal the so-called Frozen Modes.

Investigation of Nonreciprocal Dispersion Phenomena in Anisotropic Periodic Structures Based on a Curvilinear FDFD Method

The aim of this paper is the investigation of nonreciprocal phenomena in anisotropically loaded 2-D periodic structures. For this purpose, our well-established 2-D curvilinear finite difference frequency domain method is combined with periodic boundary conditions and extended toward the eigenanalysis of periodic structures loaded with both isotropic and general anisotropic materials. The periodic structures are simulated in a 2-D domain, while uniformity is considered along the third axis. The propagation constant along the third axis can either be zero (in-plane-propagation) or nonzero (out-of-plane propagation). Particular effort was devoted to the identification of the appropriate irreducible Brillouin zone to be scanned during the eigenanalysis. It was herein realized that similar to geometrically artificial crystal anisotropy, the wave propagation directional asymmetries modify the irreducible Brillouin zone in the microwave regime as well. Both gyrotropic and particularly magnetized ferrite as well as full tensor anisotropic (arbitrarily biased ferrite) material loadings are investigated through the eigenanalysis of different periodic structures, including strip grating. Interesting nonreciprocal backward wave and unidirectional phenomena are justified as expected.

A three dimensional finite element eigenanalysis of reverberation chambers

A study of reverberation chambers based on a three dimensional finite element eigenanalysis is elaborated. For this purpose the electric field vector wave equation is transformed into its weak form using the Galerkin procedure and discretized with the aid of tetrahedral edge elements. The resulting system of equations is then formulated into a generalized eigenproblem for a complex frequency (ω). When losses are ignored this eigenproblem is linear but is highly singular resulting to spurious solutions, a characteristic common to all numerical methods when analyzing lossless cavities. Including wall and material losses the singularity is reduced but the eigenproblem becomes nonlinear. Herein, the lossless case is considered first with an attempt to reject spurious solutions. Artificial air losses are then introduced to handle the singularity and the effects of these losses are checked against analytical solutions for a simple cavity. The rigorous non — linear eigenproblem including the realistic conducting walls and materials losses is currently under consideration.

Eigenvalue analysis of planar or curved shielded or open printed transmission lines loaded with full tensor anisotropic materials

An eigenvalue analysis of curved shielded or open waveguides and planar transmission lines loaded with full tensor anisotropic materials is presented. This analysis is based on our previously established two-dimensional Finite Difference Frequency Domain eigenvalue method formulated in orthogonal curvilinear coordinates. This method is used herein in order to accurately handle closed or open curved geometries filled or partially loaded with full tensor anisotropic materials. Numerous investigations are carried out involving all type of propagating modes.

Numerical techniques for the eigenanalysis of arbitrary curved and open waveguiding structures.

A review of our research effort on the eigenanalysis of open and curved waveguiding structures is presented herein. A hybrid finite element in conjunction with a cylindrical harmonics expansion is established for the analysis of open waveguides. The transparency of the fictitious circular contour truncating the finite element mesh is ensured by enforcing the field continuity conditions according to a vector Dirichlet-to-Newmann mapping. The eigenanalysis of curved waveguides is confronted by a finite difference frequency domain method in orthogonal curvilinear coordinates. The latter eliminates the usually encountered stair case effects by making the grid conformal to the material boundaries. Additionally it supports multi-coordinate systems and inhomogeneous grids enabling fine mesh around current carrying conductors and coarse mesh in the area of low field variations. These features offer high accuracy with minimum computer resources. Finally, both methods are validated against published analytical, numerical and experimental results.

Eigen-analysis of composite radiating structures with emphasis on characteristic modes: A review

Eigenanalysis of canonically shaped structures served as an indispensable tool the conception and establishment of a plethora of electromagnetic structures from filters to cavities and antennas. However, the recent evolution of radio systems and wireless communications ask for the design of multifunctional rf front-ends in compact form and conformally integrated on mobile devices. The eigen-analysis features could again support this evolution but could only be performed numerically. It is toward this ambitions aims that our research effort is directed during the last years. This article presents an overview of the related work, which is based on finite difference, finite element, mode matching and moment method. The applications elaborated include closed as well as open-radiating structures loaded with inhomogeneous and/or anisotropic media. Particular effort is devoted to external eigenmodes and characteristic modes, especially for antenna design.

Eigenanalysis of a tuneable two-dimensional radiating array of wires covered with magnetized ferrite using a curvilinear FDFD method

Computing of wave propagation and radiation through periodic band gap structures and their unique electromagnetic features attracted a huge research interest during the last decades. These features enabled the development of novel metamaterials and were exploited in frequency selective surfaces, phased arrays and numerous electromagnetic bandgap applications. Moreover, the metamaterials including photonic crystals are extensively investigated in the fields of optics, microwave, and antenna engineering due to their inherent possibility to develop novel devices that may not be found until now, [Huan Xie and Ya Yan Lu, J. Opt. Soc. Am. A 26, 2009, pp. 1606–1614]. Thus, the analysis and design of such structures have received particular attention which is almost exclusively directed toward the deterministic numerical simulations. Even though this analysis served as a very useful tool, it does not offer the required physical insight, while it does not provide any means to devise novel structures.

FDFD eigenanalysis of non-reciprocal periodic structures

A two dimensional Finite Difference Frequency Domain (2D-FDFD) eigenanalysis of an array consisting of periodically located strips printed on axially magnetized ferrite film is presented. The main interest in these structures arises from our previous study which revealed their support of backward surface and possibly backward leaky waves. Moreover these structures exhibit non-reciprocal phenomena. These phenomena are studied thoroughly by using our two - dimensional curvilinear frequency domain finite difference (2D-FDFD) method, modified appropriately for the eigenanalysis of periodic structures. The present effort is particularly focused on the study of the non-reciprocal phenomena involved in periodic structures loaded with magnetized ferrites.