Numerically Efficient Analysis of Array of Plasmonic Nanorods Illuminated by an Obliquely Incident Plane Wave Using the Characteristic Basis Function Method

The goal of this paper is to present a computational scheme to accurately and efficiently characterize reflection and transmission coefficients for a periodic array of plasmonic nanorods illuminated by an obliquely incident plane wave. The problem is formulated by using integral equations and the Method of Moments (MoM) in conjunction with the Characteristic Basis Functions Method (CBFM) to significantly reduce the number of unknowns. The concept of progressively expanding rings is employed along with Parseval's theorem to evaluate the Galerkin's integrals for the periodic structure under consideration. The use of this novel approach offers significant computational advantages over conventional methods using slowly-convergent periodic Green's functions. Closed-form expressions for the reflection and transmission coefficients are derived for a plane wave illuminating the array at an arbitrary angle. The presented numerical method is general and can be applied to other periodic configurations, including metamaterials. The proposed method is validated by comparing it with the results obtained by using the Finite Difference Time Domain (FDTD) technique. Also, we show that the proposed computational scheme achieves a speed performance that is considerably superior to that of the conventional approaches for analyzing the problem at hand.