Modal analysis of a periodic array of metallic pins embedded within a grounded dielectric substrate — An asymptotic solution for vanishing unit-cell size

In this paper, it is shown that the TM mode characteristic equation of the pin-lattice embedded in grounded dielectric substrate obtained by vector-potential method is identical to that presented in a classical book [1] derived by the transverse resonance technique (TRT). Here, we derive the characteristic equation of a grounded plain dielectric substrate by analyzing the electric and magnetic field instead of TRT. With the same threshold, we can extend it to the rectangular waveguide with pin-lattice loaded on the sidewalls in the future.