The negative refraction between two-dimensional unloaded and loaded transmission line media

A two-dimensional scalar wave equation for a general two-dimensional distributed network is established. Voltage distribution, current distribution, impedance expressions in x-direction and z-direction, and propagation constant for the two-dimension loaded L, C transmission line media (negative-refractive-index media) and the unloaded transmission line media (positive-refractive-index media) are presented. These derived expressions are used in design of both the electrical parameters for these two media and proper excitation for plane wave. Plane voltage wave incident at an angle of 60deg on the interface between the positive-refractive-index media and negative-refractive-index media for a relative refractive index of -radic3 are simulated by microwave circuit. The simulation results show that the negative refraction happens at the interface, which verify the derived formulas in this paper.