Analysis of nanostructures with complex shape using improved generalized method of moments

Summary form only given. The study of light-matter interactions is of great importance to many applications ranging from optical device characterization to material design to analysis of photonic band gap (PBG) structures etc. Many nanostructures of interest possess complex geometries and topologies that are difficult to model geometrically, and even more difficult to characterize in terms of electromagnetic response; for instance, modeling of biomimetic structures (including naturally occurring PBGs) such as butterfly wings. Furthermore, topology optimization for design requires a method that has the ability to adaptively manipulate and deform the geometry in an efficient manner. The use of canonical modeling methods to meet these challenges is difficult. Some of the authors recently introduced the Generalized Method of Moments (GMM) [N. Nair and B. Shanker, Proceedings of 2011 IEEE COMCAS, 1-4] that provides an effective framework both for geometry description and manipulation of locally smooth PEC surfaces, as well as great latitude in the choice and mixing of approximation function spaces. However, the method has not been advanced to the analysis of dielectric scatterers. The goal of this work is to extend GMM to a robust integral equation solver for complex dielectric nanostructures using locally smooth surface descriptions.