Efficient integral-equation-based method for accurate analysis of scattering from periodically arranged nanostructures

A plethora of applications are grounded on the physics of electromagnetic interaction with a periodic arrangement of nanostructures. These range from metamaterials and negative index materials to photonic band-gap structures to surface plasmon polariton optics to nanofrequency selective surfaces. There is therefore a need for rigorous physics based methods that are both accurate and fast to enable rapid design and analysis. Difficulties that need to be overcome to realize such a simulation tool are twofold: (i) at wavelengths in the range 200-1300 nm metals behave as dielectrics with negative real permittivity. Their frequency response must be explicitly accounted for in the simulation. (ii) The computational cost to compute response over a broad band of frequencies is high. This paper develops an integral-equation-based analysis technique that addresses these challenges. This integral equation relies on a periodic layered medium formulation. The Green's dyad for this formulation is derived, and separated into a superposition of two contributions: direct and reflected components. The means to accelerate the computation of the Green's dyad and the evaluation of inner products is prescribed. The proposed technique is validated extensively against available analytical data for hypothetical materials as well as silver. It is shown that this solver can accurately predict the enhanced transmission from perforated silver films for several configurations. While the application domain in this paper is the study of enhanced transmission in perforated silver films, the method presented herein is sufficiently general and can be applied to several other application domains with little or no change.