Coupled Solution of Volume Integral and Hydrodynamic Equations to Analyze Electromagnetic Scattering From Composite Nanostructures

A coupled system of volume integral and hydrodynamic equations is solved to analyze electromagnetic scattering from nanostructures consisting of metallic and dielectric parts. In the metallic part, the hydrodynamic equation relates the free electron polarization current to the electric flux and effectively “updates” the constitutive relationship to enable the modeling of nonlocality. In the metallic and dielectric parts, the volume integral equation relates the electric flux and the free electron polarization current to the scattered electric field. Unknown electric flux and free electron polarization current are expanded using Schaubert–Wilton–Glisson (SWG) basis functions. Inserting these expansions into the coupled system of the volume integral and hydrodynamic equations and using Galerkin testing yield a matrix system in unknown expansion coefficients. An efficient two-level iterative solver is proposed to solve this matrix system. This approach “inverts” the discretized hydrodynamic equation for the coefficients of the free electron polarization current and substitutes the result in the discretized volume integral equation. Outer iterations solve this reduced matrix system while the inner iterations invert the discretized hydrodynamic equation at every iteration of the outer iterations. Numerical experiments are carried out to demonstrate the accuracy, the efficiency, and the applicability of the proposed method.