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 &

Development and application of hybrid finite methods for solution of time dependent maxwell's equations

Ph.DDOCTOR OF PHILOSOPH

The Partial Elements Equivalent Circuit Method: The State Of The Art

This year marks about half a century since the birth of the technique known as the partial element equivalent circuit modeling approach. This method was initially conceived to model the behavior of interconnect-type problems for computer-integrated circuits. An important industrial requirement was the computation of general inductances in integrated circuits and packages. Since then, the advances in methods and applications made it suitable for modeling a large class of electromagnetic problems, especially in the electromagnetic compatibility (EMC)/signal and power integrity (SI/PI) areas. The purpose of this article is to present an overview of all aspects of the method, from its beginning to the present day, with special attention to the developments that have made it suitable for EMC/SI/PI problems

Lattice QED photonic wavepackets on ladder geometries

openIn this thesis we explore numerical simulations, including Tensor Networks (TNs) methods, to study Hamiltonian Lattice Gauge Theories (LGTs), a numerical framework for investigating non-perturbative properties of Quantum Field Theories. We develop a model-independent approach for constructing Matrix Product Operators (MPOs) representations of 1-dimensional quasiparticles with definite momenta, and apply it to Hamiltonian Lattice Quantum Electrodynamics (QED) on a ladder geometry. By means of exact diagonalization at intermediate system sizes, we obtain the first excitation band states (the Bloch functions) representing the single-(quasi)particle states (the photons) expressed as entangled states of local lattice gauge fields. We then construct the corresponding maximally-localized Wannier functions through minimization of a spread functional. Once we identify, via a linear algebra problem, the operation that constructs the localized Wannier excitation from the ground state (dressed vacuum), we can express the creation operator, for any wavepacket of such quasiparticles, as a Matrix Product Operator. The aforementioned steps constitute a constructive strategy to prepare an arbitrary input state for a quasiparticle scattering simulation in real time, and the scattering process itself can be carried out with any standard algorithm for time-evolution with Matrix Product States.In this thesis we explore numerical simulations, including Tensor Networks (TNs) methods, to study Hamiltonian Lattice Gauge Theories (LGTs), a numerical framework for investigating non-perturbative properties of Quantum Field Theories. We develop a model-independent approach for constructing Matrix Product Operators (MPOs) representations of 1-dimensional quasiparticles with definite momenta, and apply it to Hamiltonian Lattice Quantum Electrodynamics (QED) on a ladder geometry. By means of exact diagonalization at intermediate system sizes, we obtain the first excitation band states (the Bloch functions) representing the single-(quasi)particle states (the photons) expressed as entangled states of local lattice gauge fields. We then construct the corresponding maximally-localized Wannier functions through minimization of a spread functional. Once we identify, via a linear algebra problem, the operation that constructs the localized Wannier excitation from the ground state (dressed vacuum), we can express the creation operator, for any wavepacket of such quasiparticles, as a Matrix Product Operator. The aforementioned steps constitute a constructive strategy to prepare an arbitrary input state for a quasiparticle scattering simulation in real time, and the scattering process itself can be carried out with any standard algorithm for time-evolution with Matrix Product States

Application of TLM for optical microresonators

Optical microresonators can form the basis of all-optical switching and control devices. The presented study is an exploration of the Transmission Line Modelling (TLM) method as a suitable candidate for designing optical microresonators. Chalcogenide glasses were identified as promising materials, with which to fabricate optical microresonators. The study presents the formulation of TLM in two dimensions to model nonmagnetic dielectric materials and a suitable computationally efficient yet flexible software design. Some methods for extracting spectral properties of resonators are compared and the modified difference Prony method was identified as a suitable tool to extract resonant frequencies and Q factors from a limited time signal. When applying TLM to microresonators of sub-wavelength dimensions it was understood that the method of discretisation plays an important role in accurately modelling microresonators. Two novel methods of discretisations -the same area method and the anti-aliasing method- were used to improve the accuracy significantly compared to existing mesh refinement techniques. Perfect matched layers (PMLs) were implemented to improve reflections from domain truncation using several methods. A Convolutional PML(CPML) was identified as the best, but it does not reach the efficiency of PMLs in the Finite Difference Time Domain (FDTD) method. Several frequency dependent refractive index models were proposed and implemented in TLM. A Tauc-Lorentz model was identified as the best fit to the experimental refractive index of three chalcogenide glasses, but a Sellmeier model with one term and a coefficient was efficient for TLM implementation. The main concern in the use of these models within TLM was shown to be the error arising due to mesh dispersion. Kerr nonlinear models were formulated and implemented in TLM and the models applied to the study of a waveguide junction. Compared to an equivalent implementation in a time domain beam propagation method, TLM models better represent the waveguide junction reflections

Amélioration du développement modal des champs électromagnétiques par une méthode d’interpolation

We consider optical structures where the dielectric permittivity is described as a rational function of the pulsation ω (Lorentz model). The electromagnetic fields can be computed on a large number of frequencies by computing the eigenmodes of the optical device and reconstructing the solution by expanding it on these eigenmodes. This modal expansion suffers from numerous limitations that are detailed in this report. In order to overcome these limitations, an interpolation procedure is proposed such that the direct computation of the electric field is needed only for a small number of interpolation points. Numerical experiments in 2-D and 3-D exhibit the efficiency of this approach.Nous considérons des structures optiques où la permittivité diélectrique est une fonction rationnelle de ω (modèle de Lorentz). Les champs électromagnétiques peuvent être calculés pour un grand nombre de fréquences en calculant les modes propres du dispositif optique et en reconstruisant la solution en la développant sur ces modes. Ce développement modal souffre de nombreuses limitations qui sont détaillées dans ce rapport. Afin de dépasser ces limitations,une procédure d’interpolation est proposée de telle sorte que le champ électrique est calculé directement pour un petit nombre de points d’interpolation. Des expériences numériques en 2-Det 3-D montrent l’efficacité de cette approche

Modeling EMI Resulting from a Signal Via Transition Through Power/Ground Layers

Signal transitioning through layers on vias are very common in multi-layer printed circuit board (PCB) design. For a signal via transitioning through the internal power and ground planes, the return current must switch from one reference plane to another reference plane. The discontinuity of the return current at the via excites the power and ground planes, and results in noise on the power bus that can lead to signal integrity, as well as EMI problems. Numerical methods, such as the finite-difference time-domain (FDTD), Moment of Methods (MoM), and partial element equivalent circuit (PEEC) method, were employed herein to study this problem. The modeled results are supported by measurements. In addition, a common EMI mitigation approach of adding a decoupling capacitor was investigated with the FDTD method

SCEE 2008 book of abstracts : the 7th International Conference on Scientific Computing in Electrical Engineering (SCEE 2008), September 28 – October 3, 2008, Helsinki University of Technology, Espoo, Finland

This report contains abstracts of presentations given at the SCEE 2008 conference.reviewe