We propose a complete set of periodic circuit networks which can realize electromagnetic wave propagation in different two-dimensional (2D) isotropic and anisotropic metamaterials (AMMs). We synthesize the periodic circuits with unit cells of series capacitor or inductor in orthogonal directions, together with either capacitor or inductor shunted to ground. The dispersion relations of the periodic circuits are derived by applying Bloch boundary conditions to the unit cell, which show either elliptic or hyperbolic dispersion surface in phase space. The effective constitutive parameters are obtained by choosing different types and values of the impedance elements in the unit cell. The validity of the circuit models is proved by showing examples that the anisotropic $L\text{−}C$ circuits could exhibit the wave propagation characteristics of two 2D AMMs with different cutoff properties, called never-cutoff or anti-cutoff medium. We construct interfaces between isotropic normal medium and AMMs with properly designed $L\text{−}C$ circuits and analyze the electromagnetic wave propagation using microwave circuit simulations. We demonstrate extraordinary electromagnetic wave reflection and refraction phenomena including negative refraction, total reflection with reversion of the critical angle and anomalous Brewster effect that have good agreements with the theoretical analysis. Furthermore, we show that the $L\text{−}C$ circuit models of AMMs could lead to different approach of actual implementation of 2D AMMs through capacitance loaded transmission line metamaterials. The simulation on actual microstrip line structure demonstrates similar wave propagation phenomena of AMMs, and the losses in the structure only affect the magnitude of the propagating energy.

• Received 8 July 2005

DOI:https://doi.org/10.1103/PhysRevB.72.245107