Contribution to the characterization of stratified structures : electromagnetic analysis of a coaxial cell and a microstrip line

The objective of this dissertation is the development of electromagnetic modelling software specific to the cells of microwave material characterization. This development is based on numerical methods that are alternative to finite element method which is widely used in commercial software. For the need to extract the properties of materials by inverse modelling methods, research into the numerical efficiency of direct analysis is the focus in this thesis. The characterization targeted cells in this work concern a coaxial cell and a planar line. The presence of an unknown material is modelled by a stratified heterogeneous transmission structure. The application of the transverse operator method (TOM) on the multi-layered coaxial cell allowed the determination of the propagation constant of fundamental mode and its corresponding field distribution of the electromagnetic fields, and the characteristics of higher-order modes for the need of the characterization of discontinuities between empty line and loaded line. In the case of the microstrip line, the use of the modified transverse resonance method (MTRM) allowed the determination of characteristics of the fundamental and higher order modes. Since each cell consists of several different sections, the matrix S of the set will be determined by the use of the several modal methods, such as modal connection method (''mode matching'') and multimodal variational method (MVM). The direct analysis codes are coupled with several optimization programs to constitute the software for extracting the material parameters. These are applied to material samples in cylinder form holed by the coaxial cell, or thin rectangular wafer by the microstrip line. Broadband extraction results were obtained, values are comparable with those published. Both high-loss dielectrics and nanostructured materials have been studied by our method

Nonlinear optics

Nonlinear light-matter interactions have been drawing attention of physicists since the 1960's. Quantum mechanics played a significant role in their description and helped to derive important formulas showing the dependence on the intensity of the electromagnetic field. High intensity light is able to generate second and third harmonics which translates to generation of electromagnetic field with multiples of the original frequency. In comparison with the linear behaviour of light, the nonlinear interactions are smaller in scale. This makes perturbation methods well suited for obtaining solutions to equations in nonlinear optics. In particular, the method of multiple scales is deployed in paper 3, where it is used to solve nonlinear dispersive wave equations. The key difference in our multiple scale solution is the linearity of the amplitude equation and a complex valued frequency of the mode. Despite the potential ill-posedness of the amplitude equation, the multiple scale solution remained a valid approximation of the solution to the original model. The results showed great potential of this method and its promising wider applications. Other methods use pseudo-spectral methods which require an orthogonal set of eigenfunctions (modes) used to create a substitute for the usual Fourier transform. This mode transform is only useful if it succeeds to represent target functions well. Papers 1 and 2 deal with investigating such modes called resonant and leaky modes and their ability to construct a mode transform. The modes in the first paper are the eigenvalues for a quantum mechanical system where an external radiation field is used to excite an electron trapped in an electrical potential. The findings show that the resonant mode expansion converges inside the potential independently of its depth. Equivalently, leaky modes are obtained in paper 2 which are in close relation to resonant modes. Here, the modes emerge from a system where a channel is introduced with transparent boundaries for simulation of one-directional optical beam propagation. Artificial index material is introduced outside the channel which gives rise to leaky modes associated with such artificial structure. The study is showing that leaky modes are well suited for function representation and thus solving the nonlinear version of this problem. In addition, the transparent boundary method turns out to be useful for spectral propagators such as the unidirectional pulse propagation equation in contrast to a perfectly matched layer

Scattering by irregular particles in anomalous diffraction and discrete dipole approximations

November 30, 1992.Includes bibliographical references.Sponsored by National Science Foundation ATM-8812353.Sponsored by U.S. Air Force Office of Scientific Research AFOSR-91-0269

Review on solving the forward problem in EEG source analysis

Background. The aim of electroencephalogram (EEG) source localization is to find the brain areas responsible for EEG waves of interest. It consists of solving forward and inverse problems. The forward problem is solved by starting from a given electrical source and calculating the potentials at the electrodes. These evaluations are necessary to solve the inverse problem which is defined as finding brain sources which are responsible for the measured potentials at the EEG electrodes. Methods. While other reviews give an extensive summary of the both forward and inverse problem, this review article focuses on different aspects of solving the forward problem and it is intended for newcomers in this research field. Results. It starts with focusing on the generators of the EEG: the post-synaptic potentials in the apical dendrites of pyramidal neurons. These cells generate an extracellular current which can be modeled by Poisson's differential equation, and Neumann and Dirichlet boundary conditions. The compartments in which these currents flow can be anisotropic (e.g. skull and white matter). In a three-shell spherical head model an analytical expression exists to solve the forward problem. During the last two decades researchers have tried to solve Poisson's equation in a realistically shaped head model obtained from 3D medical images, which requires numerical methods. The following methods are compared with each other: the boundary element method (BEM), the finite element method (FEM) and the finite difference method (FDM). In the last two methods anisotropic conducting compartments can conveniently be introduced. Then the focus will be set on the use of reciprocity in EEG source localization. It is introduced to speed up the forward calculations which are here performed for each electrode position rather than for each dipole position. Solving Poisson's equation utilizing FEM and FDM corresponds to solving a large sparse linear system. Iterative methods are required to solve these sparse linear systems. The following iterative methods are discussed: successive over-relaxation, conjugate gradients method and algebraic multigrid method. Conclusion. Solving the forward problem has been well documented in the past decades. In the past simplified spherical head models are used, whereas nowadays a combination of imaging modalities are used to accurately describe the geometry of the head model. Efforts have been done on realistically describing the shape of the head model, as well as the heterogenity of the tissue types and realistically determining the conductivity. However, the determination and validation of the in vivo conductivity values is still an important topic in this field. In addition, more studies have to be done on the influence of all the parameters of the head model and of the numerical techniques on the solution of the forward problem.peer-reviewe

Adaptive model order reduction techniques for the broadband finite element simulation of electromagnetic structures

Model order reduction methods provide a powerful means for the broadband simulation of passive microwave devices. In particular projection-based moment matching methods are well-suited for the reduction of sparse finite element systems. However, for real-world problems, where high-dimensional systems of linear equations are assembled and a large number of excitations is considered in the right-hand side, the projection matrix may fill the main memory and render the process inefficient. In this thesis, techniques were developed which, as a result of reduced memory requirements, make model order reduction applicable to a large set of real-world problem simulations. A new adaptive multi-point reduction method is introduced whose core is an incremental error measure. For the proposed single-point method, which is based on the well-conditioned asymptotic waveform evaluation, memory requirements are reduced by means of a block algorithm, whose moment matching properties are proven in this thesis. Memory swapping mechanisms for both approaches keep the main memory requirements for the projection matrix at a constant low level during the computations. This thesis also includes an adaptive multi-point method for the broadband finite element simulation of waveguide problems and a broadband sensitivity analysis technique.Verfahren der Modellordnungsreduktion stellen einen leistungsfähigen Ansatz für die breitbandige Simulation passiver Mikrowellenkomponenten dar. Insbesondere projektionsbasierte, momentenabgleichende Methoden eignen sich für die Reduktion der schwach besetzten Finite-Elemente Systeme. In praxisrelevanten Problemstellungen hingegen, bei denen hochdimensionale Gleichungssysteme assembliert werden und eine große Anzahl Anregungen in der rechten Seite berücksichtigt werden, kann die Projektionsmatrix den Arbeitsspeicher füllen und der Prozess ineffizient werden. In dieser Dissertation werden Algorithmen entwickelt, die aufgrund des reduzierten Speicherbedarfs Reduktionsverfahren auf eine große Auswahl praxisrelevanter Simulationen anwendbar machen. Ein neues Mehrpunktverfahren wird eingeführt, dessen Kern ein inkrementelles Fehlermaß ist. Für das entwickelte Einpunktverfahren, welches auf der Well-Conditioned Asymptotic Waveform Evaluation basiert, wurde der Speicheraufwand mit Hilfe eines Blockalgorithmus reduziert, dessen momentenabgleichenden Eigenschaften in dieser Dissertation bewiesen werden. Datenauslagerungsmechanismen für beide Ansätze halten den Arbeitsspeicherbedarf für die Projektionsmatrix während der Berechnung konstant niedrig. Diese Arbeit beinhaltet des Weiteren ein adaptives Mehrpunktverfahren für die breitbandige Finite-Elemente-Simulation von Wellenleiterproblemen und ein Verfahren zur breitbandigen Sensitivitätsanalyse

Feasibility of superconductivity in semiconductor superlatices

The objective of this thesis is to explore superconductivity in semiconductor superlattices of alternating hole and electron layers. The feasibility of superconductivity in semiconductor superlattices is based on a model formulated by Harshrnan and Mills. In this model, a semiconductor superlattice forms the layered electron and hole reservoirs of high transition temperature (high-Tc) superconductors. A GaAs-A1xGa1-xAs semiconductor structure is proposed which is predicted to superconduct at Tc = 2.0 K and may be analogous to the layered electronic structure of high-Tc superconductors. Formation of an alternating sequence of electron- and hole-populated quantum wells (an electron-hole superlattice) in a modulation-doped GaAs- A1xGa1-xAs superlattice is considered. In this superlattice, the distribution of carriers forms a three-dimensional Wigner lattice where the mean spacing between carriers in the x-y plane is the same as the periodic distance between wells in the superlattice. This geometrical relationship mimics a prominent property of optimally doped high - Tc superconductors. A Schrodinger-Poisson solver, developed by Snider, is applied to the problem of determining the appropriate semiconductor layers for creating equilibrium electron-hole superlattices in the GaAs-A1xGa1-xAs system. Formation of equilibrium electron-hole superlattices in modulation-doped GaAs-A1xGa1-xAs is studied by numerical simulations. Electron and heavy-hole states are induced by built-in electric fields in the absence of optical pumping, gate electrodes, or electrical contacts. The GaAs-A1xGa1-xAs structure and the feasibility of meeting all the criteria of the Harshman model for superconductivity is studied by self-consistent numerical simulation. In order to test the existence of superconductivity, the physics of sensor arrays and their ability to create synthetic images of semiconductor structures, is explored. Approximations are considered and practical applications in detecting superconductivity in superlattices are evaluated

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

13th Annual Review of Progress in Applied Computational Electromagnetics at the Naval Postgraduate School, Monterey, CA, March 17-21, 1997, Conference Proceedings Volumes I & II

Includes Volumes 1 &