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Plasmonics is a phenomenon often considered in the visible light and near infrared, whereas typical metal waveguide modes are studied in the microwave regime. We demonstrate how plasmonic modes become conventional waveguide modes as the frequency varies from visible light to microwaves. In particular, given the metal permittivity at microwaves, the plasmonic dispersion becomes the conventional waveguide dispersion. Moreover, the surface plasmon dispersion at a single metal/insulator boundary can be extracted over a metal/insulator/metal (MIM) heterostructure if the metal-to-metal spacing is taken infinite. In doing so, the coupling effect of plasmonic modes is clearly revealed. As the symmetric coupled plasmon mode is known to correspond to the TEM (TM0) mode, we found that the antisymmetric coupled surface plasmon mode is essentially related to the TM1 mode.