Accuracy study of low- and high-order numerical techniques for analysis of scattering on plasmonic nanosphere at THz frequencies

Abstract

Plasmonic resonances in the silver and gold particles of nano-scale size allow concatenations of such particles to support surface waves. Such waveguiding structures of nanometer dimensions have broad practical applications and are potential contenders to becoming transmission lines in future nano-electronics and photonics. Physical resonances in the plasmonic nano-particles are known to lead to negative values of permittivity at high-THz frequencies. This has been observed to cause high numerical errors associated with characterization of structures built of such particles when low-order numerical techniques are employed for their analysis. One such error mechanism appears to arise from low-order boundary-element discretization of the originally smooth surfaces of the nano particles with flat-panel elements of a triangular mesh such as featured in Rao-Wilton-Glisson (RWG) Method of Moments (MoM). Erroneously high concentration of the field has been observed to form at the junctions of flat triangular elements approximating the particle surface. In this study we consider the following three numerical techniques for analysis of radial electric dipole radiation near silver nano-sphere of 10nm radius in 700–800THz range: 1) Schaubert-Wilton-Glisson (SWG) MoM discretization of the D-formulated Volume Integral Equation (D-VIE); 2) RWG MoM discretization of PMCHWT surface integral equation; 3) High-Order (HO) Locally Corrected Nystrom (LCN) discretization of the surface Electric Field Integral Equation (EFIE). The LCN discretization of the EFIE is performed to higher order in both geometrical modeling and in the field representation within each element of the quadrilateral surface mesh. The latter is constructed using Non-Uniform-Bi-Splines (NURBS) representation of the spherical surface. Unlike conventional mesh generators (e.g. Gmsh) the NURBS representation of the geometry preserves continuity of the higher-order spatial derivatives of the position vector at the junctions between the elements. This property is shown to be critical for achieving the higher-order error behavior in modeling of scattering on both general 3D penetrable objects as well as in plasmonic nano-structures. We conduct comparative numerical study of the above numerical methodologies using the problem of radial dipole radiation near a plasmonic sphere. This solution is available with arbitrary precision in the analytical closed-form of Mie series. Hence it allows us to identify respective accuracies of both the low- and high-order boundary element methods, which are typically used for analysis of scattering phenomena on the plasmonic structures and compare those to analogous scattering scenarios on structures with convectional values of permittivity and permeability.