Advanced mode solver using an integral equation technique and entire domain plane wave basis functions

This work deals with the analysis and modelling of optical and millimetre-wave integrated circuits. The mathematical formulation is based on the method of integral equations, which are subsequently solved numerically by employing Galerkin's technique. The novel concept in this work lies with the development of a set of entire domain basis functions used to expand the unknown electric field in the waveguides' cross-sections. These functions have the simple form of plane waves and satisfy Maxwell's equations, therefore representing a proper expansion mechanism. As a demonstration of the developed computer code, configurations of single and coupled rectangular dielectric waveguides in a wide variety of open and closed substrate geometries are examined. The results presented, concerning the dispersion curves and the field patterns, give excellent agreement with published results of other methods. Furthermore, attenuation constants of lossy waveguides are numerically investigated. The main conclusion of the research presented in this contribution is that the entire domain plane wave basis functions (PWBFs) introduced provide a powerful tool for the unified modelling of a wide class of optical and millimetre-wave transmission lines. This revised version was published online in November 2006 with corrections to the Cover Date.