Numerical Calculation of Dispersion Diagrams and Field Distributions of Waves in 3-D Periodic Split-Ring Resonator Media

We present here a fully computational method for obtaining the dispersion diagrams and the field distributions of electromagnetic waves existing in periodic metamaterial structures. Using a finite-element E-B eigenmode formulation, we solve both for the complex propagation constants (eigenvalues) and the field distributions (eigenvectors) of the periodic structure at each given frequency of interest. As a result, we obtain information about the characteristics of the waves inside passbands and stopbands as well. By these means, the mechanisms of interaction of the electromagnetic waves with the eigenmodes of the metamaterials are revealed.