On the finite-difference modelling of electromagnetic problems in structured lattices

Abstract

The thesis concentrates on the numerical analysis of electromagnetic fields with the finite difference method. Simple and fast approximative techniques are studied and developed for the estimation of the electromagnetic properties of various structures. Especially, techniques which preserve the simplicity of a structured lattice are explored. The emphasis in the thesis is put more into the rapid estimations than into the absolute accuracy of the studied parameters. Another goal is to give information about the characteristics of the studied structures: filters, dielectric mixtures and frequency selective surfaces.

Filter structures are analysed with the finite-difference time-domain method. A simple trick is introduced to transform the curved shapes in a certain practical filter configuration into rectangular shapes to conform to the finite-difference computation lattice.

Procedures which use finite difference methods to analyse dielectric mixtures are introduced. They are applied to calculate effective permittivities of two-phase random mixtures. The results are compared with theoretical mixing models with a conclusion that none of them agrees with the numerical results in the whole range of volume fraction. Therefore, a new empirical mixing model is created based on the numerical results.

Polarisation transformation properties of frequency selective surfaces are also studied and some wide-band polariser structures are presented. It is shown how one-dimensional array models can give a good starting point for a two-dimensional array design.