Fast multilevel algorithms for the electromagnetic analysis of quasi-planar structures.

摘要

The analysis of electromagnetic scattering and radiation from quasi-planar structures is a topic of great current interest, owing to the wide range of applications. A host of structures and surfaces are included in the quasi-planar class, including rough surfaces, quantum well infrared photodetector gratings, planar microwave circuits, microstrip arrays, diffractive optical elements, and solar cells. The prediction of electromagnetic radiation and scattering is essential in applications involving the structures listed above. Possibly the most widespread class of techniques for this purpose is based on integral-equation formulations and method of moments (MoM) solutions. In such an approach, analysis problems are reduced to solutions of matrix equations of dimension N, where N is dependent on the electrical dimensions of the scatterer. Direct inversion of a large matrix can become impractical for even moderately large N, owing to a computational cost of O(N{dollar}sp{lcub}3{rcub}{dollar}). Furthermore, even the O(N{dollar}sp{lcub}2{rcub}{dollar}) CPU time (per iteration) and memory requirements of iterative solvers can become prohibitive for frequently encountered, large-scale, realistic problems. In this dissertation, new multilevel, rigorous, integral-equation solution techniques, based on a steepest-descent fast multipole (SDFMM) formulation, are developed for solving scattering problems involving large quasi-planar structures. These techniques promise to open the door to the full-wave analysis of complex quasi-planar structures to an extent not possible to date, owing to their O(N) CPU time (per iteration) and memory requirements. The SDFMM relies on a combined steepest-descent path and an inhomogeneous plane-wave representation of Greens' functions, and exploits the quasi-planarity of scatterers to reduce the computational complexity. In this dissertation, the SDFMM is developed in its full generality to tackle a host of electromagnetic scattering problems that find application in remote sensing, microelectronic devices, and communication systems. Large and flexible computer codes are written for analyzing scattering from perfectly conducting and penetrable rough surfaces, for studying optical absorption by quasi-random gratings in quantum-well infrared photodetectors, and for predicting radiation and scattering from large and finite microstrip antenna arrays.