Efficient eigenvalue based analysis of bounded and unbounded electromagnetic fields

Abstract

Eigenvalue problems find important applications in engineering electromagnetics. The most studied examples are cavity resonance problems and wave guidance problems, in which the electromagnetic fields are bounded or semi-bounded. Efficient eigenvalue based analysis is developed to investigate both bounded and unbounded fields in a unified manner. Incorporating a locally-conformal finite difference technique, a modal expansion based model order reduction is proposed to elucidate complicated physics of wave-matter interaction, and the fast field approximation provides quick guidance to design and optimization problems of a variety of devices. As the key to modal expansion, modal analysis for interior spectrum needs to be carried out efficiently in large scale applications. A null-space shift algorithm and a fast cosine- and sine- transform based preconditioning scheme are proposed to greatly enhance the performance of a conventional eigensolver. To model multi-junction parallel plate waveguides, both explicit and implicit mode matching schemes are introduced, where eigenanalysis are incorporated. Both schemes intelligently conform to the geometrical characteristics, which are suitable for demonstrating interesting phenomena of zero index materials. Finally, a differential forms inspired discretization scheme is proposed for the edge element based finite element analysis of waveguide problems where the variational expressions involve transverse fields only. Differential forms provide useful insight on the discretization of complicated variational expressions.