Properties of the fundamental TM waveguide mode in the narrow metal/dielectric/metal waveguide

We derive analytic expressions of the propagation length and the effective index of the fundamental TM waveguide mode in the limit of the small waveguide width by using the exact mode equation in the one dimensional metal/dielectric/metal waveguide, and results from approximate analytic expressions are compared with the direct numerical solution of the exact mode equation. In addition, we compare the coupled waveguide mode with the linear superposition mode in the metal/dielectric/metal waveguide by using the FDTD method with the Lorentz-Drude model for silver. It provides a physical understanding of properties of the fundamental TM waveguide mode in the narrow metal/dielectric/metal waveguide.