Integral Equation Formulation for Planar Plasmonic Structures With Finite Thickness in Layered Media

A detailed Volume Integral Equation (VIE) formulation for planar plasmonic nano structures with finite thickness in flat multi-layers medium is presented. The boundary condition along the localized metallic objects is expressed in terms of the unknown polarization current flowing through these objects in the form of an integral equation, which is solved using the Method of Moments (MoM). The Green's functions associated with a layered medium of practical importance are expressed in the spectral domain. The corresponding spatial domain Green's functions are obtained using the Discrete Complex Images Method (DCIM). Special treatment for the spectral function's asymptote at high spectral values is performed. The presented formulation is applied on different plasmonic structures immersed inside layered media. The structures include nano-rod and nano-patch excited by an incident plane wave. In addition, a simple band-stop filter based on quarter-wavelength stubs is considered. This filter is fed with a couple of plasmonic transmission lines. The obtained current distributions and S-parameters are compared with those obtained using a commercial full-wave electromagnetic simulator, namely CST Microwave Studio. A very good agreement is observed. The proposed integral equation formulation enjoys high degree of stability, numerical efficiency, and accuracy.