Modeling of Tunneling Effects in Epsilon-Near-Zero Waveguide

In this paper we present a simple method for efficient modeling of the tunneling effect in a non-homogeneous epsilon-near-zero (ENZ) waveguide, using an equivalent circuit approach. ENZ waveguide consists of rectangular waveguides filled with two-layered dielectric, E-step, and a narrow channel. It was shown that the E-step in a non-homogenous structure can be modeled rather simply using a shunt capacitor whose capacitance is determined analytically using the same expression which applies to homogeneous rectangular waveguide. In that case the error in determining the first resonance is less than 1%, while in the case of the second resonance the error is less than 2.5%, if the non-homogeneity is not very large, i.e. if the ratio between the relative permittivities of the dielectrics in the input waveguides and the channel is less than two.