Analysis of scattering from complex dielectric objects using the generalized method of moments.

Integral equation-based analysis of scattering from dielectric objects has been a topic of research for many decades. Different integral equation formulations, discretization methods, and comparative data of their relative advantages have been well studied. Traditional discretization methods typically rely on a tight coupling between the underlying geometry discretization and the approximation function space that is defined on this discretization. As a result, it is difficult to stitch together different approximation spaces or nonconformal domains or match basis sets to local physics. Furthermore, the basis sets most commonly used in discretizing dielectric boundary integral operators impose limits on the variety of integral equation formulations that can be employed. We recently published a methodology [J. Opt. Soc. Am. A28, 328 (2011)10.1364/JOSAA.28.000328JOAOD61084-7529] that overcomes several of these bottlenecks. In the present paper, we introduce several extensions to these concepts for dielectric scattering problems. Specifically, we present a method that (i) uses mixed higher order local geometric descriptions and (ii) mixes multiple basis sets defined on this geometry, including higher order polynomials and classical Rao-Wilton-Glisson functions. Furthermore, we provide a unified description of different integral equation formulations that can be used for the analysis of scattering from dielectric objects, and show that the present approach admits a larger range of formulations than existing methods. A number of results demonstrating the efficiency of the method (in terms of accuracy and capability) together with applicability to different formulations are presented.