Abstract
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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> -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.
Highlights
R ECENT advances in fabrication technology allows the reduction of the device’s dimensions down to the nano-scale At this scale, the high power dissipation is a significant problem for classical electronic devices
The rod is excited by a plane wave propagating along the z-axis with its incident electric field polarized along the length of the rod, i.e. along x-axis, with EB of 1 V/m
The developed solver based on the presented formulation is applied on different plasmonic structures in layered media
Summary
R ECENT advances in fabrication technology allows the reduction of the device’s dimensions down to the nano-scale At this scale, the high power dissipation is a significant problem for classical electronic devices. A detailed volume integral equation formulation to analyze planar plasmonic devices with finite thickness in multilayered media, is developed. If higher accuracy and more flexibility in the shape of the plasmonic structure under investigation are needed, SIE has to be replaced with Volume Integral Equation (VIE) to be solved using the MoM. (4) The elements of the excitation vector are fully expressed for the conventional plane wave excitation of plasmonic structures, and for excitation with plasmonic transmission lines terminated with localized current sources, which makes the proposed formulation very suitable for analyzing plasmonic devices such as filters, couplers, splitters, and antennas.
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