Characteristic Mode Analysis of Composite Nanostructures using a Coupled System of Volume Integral and Hydrodynamic Equations

Abstract

Full-structure and sub-structure characteristic mode analysis (CMA) formulations are developed for composite metallic--dielectric nanostructures based on a coupled system of volume integral equations (VIE) and the hydrodynamic equation (HDE). In the full-structure CMA, the generalized eigenvalue equation (GEE) is constructed from the matrix of the complete coupled system, and the resulting characteristic currents describe the response of the entire composite nanostructure. In the sub-structure CMA, the GEE is constructed from a reduced system, derived from the coupled system by eliminating the dielectric-region unknowns, so that it is expressed only in terms of the metallic-region currents. This isolates the resonances of the metallic region while still incorporating the effect of the dielectric region through the reduced system. Because the reduced system has a smaller dimension, the sub-structure CMA is computationally more efficient than the full-structure CMA and, when the dielectric does not resonate in the frequency range of interest, identifies the same resonances. Both formulations are validated against extinction cross-section (ECS) results and are used to characterize how a dielectric environment reshapes the metallic resonances, including substrate-induced red-shifts and, for high-contrast substrates in direct contact, hybridized modal responses.