New surface integral equations for the light scattering of multi-metallic nanoscatterers

Based on the Stratton–Chu formulation, a set of new surface integral equations of Maxwell's equations was developed to investigate the interactions of an incident EM wave with multi-metallic nanoscatterers for a two-dimensional TM-mode problem. These equations in terms of the surface components of the tangential magnetic field Hz, the normal displacement field Dn and the tangential electric field Et can be solved systematically along the multi-connected interfaces of the scatterers and the host by using boundary-element method (BEM). Three interesting nanostructures (a dimer, a trimer and a hexagonal lattice) are studied to show the distinct optical responses of the coupling surface plasmon resonance. The numerical results show that even though the distance between the two nanoscatterers is very close (e.g. gap is less than 1 nm), these surface integral equations still can obtain a converged result of the surface components by increasing adaptively the number of the discretized nodes along the adjacent multi-connected boundary. In addition, an asymmetric dimer, which contains two scatterers of different diameters in different orders of magnitude, is studied to demonstrate the ability of BEM for solving multi-scale problems.