Green’s function surface integral equation method for theoretical analysis of scatterers close to a metal interface

Abstract

A method for theoretical analysis of light scattering by arbitrary shaped two-dimensional scatterers placed near a planar surface between two media is presented. We show that light scattering by an object near a planar interface can be analyzed (exactly) using Green's function surface integral equations that are form invariant with those for a scatterer in free space. All effects of the planar interface structure are built into the Green's function. An approach for calculating the Green's function is presented along with far-field approximations that enable efficient evaluation of scattering into waves propagating out of the surface plane and, in the case of a planar metal-dielectric interface, evaluation of scattering into surface plasmon-polariton (SPP) waves propagating along the interface. Finally, the method is exemplified by analysis of light scattering by a nm-thin and sub-$\ensuremath{\mu}\text{m}$-wide gold strip (resonator) placed between 5 and 200 nm above a planar gold surface. We compare the amount of scattering going into the out-of-plane propagating waves and SPPs, respectively, and, for our configuration, scattering into out-of-plane propagating waves dominates. Scattering into SPP waves has a maximum if the strip is placed approximately 20 nm from the surface. We also find that when placing the gold strip more than 50 nm from the interface, the scattering resonance wavelength is practically independent of the distance, whereas changing the distance from 50 to 5 nm results in a $\ensuremath{\sim}400\text{ }\text{nm}$ redshift of the resonance wavelength.