A Source-Model Technique for Analysis of Waveguiding Across an Array of Arbitrary Smooth Cylinders Partially Buried in a Penetrable Substrate

A computational technique for modal analysis of an array of penetrable cylinders with smooth arbitrary cross section is described. The cylinders are partially buried between two penetrable half-space media, as may occur in fabricated device. Our suggested method is a rigorous full-wave frequency-domain source-model technique. The corner-like intersections of the cylinders with the substrate and superstrate are addressed with particular care, by intricately locating properly modulated fictitious sources, so that the rapid spatial variations of the fields can be effectively modeled. The spurious-free modal analysis scheme is sped up with an efficient serial mode-tracking scheme, which is based on the physical perturbation theory. The respective software tool is robust to the choice of materials, geometric parameters, and wavelength. Sample results are presented for circular and triangle-like cylinders. We demonstrate a red shift of the cut-off frequency of these potential waveguides as they are more deeply buried in a high refractive index medium, yet in general, the eigenmodes change rapidly but not necessarily monotonously as a function of the burial depth.