Dispersion Relation for 2D Transverse Magnetic (TM) Plasmonic Wave: Analytic Versus FEM

A metal-dielectric interface has been studied in this paper in the light of wave propagation characteristics. A new analytical result, through a simpler approach for deriving the dispersion equation in plasmonic waveguides, has been reported and visualized. A two-dimensional Transverse Magnetic (TM) wave is theorized and analyzed with respect to its propagation along the boundary of metal and air. Mathematical analysis results in the relationship between the propagation parameter and wavelength of operation. The plots reveal good conformity with the previous studies. For comparison, the propagation characteristics in free space have also been included. To validate the proposed results of this study, Finite Element Analysis (FEA) has been used to visualize the distribution of fields near the metal-dielectric boundary