Modeling Split-Ring Resonator (SRR) and Complementary Split-Ring Resonator (CSRR) Loaded Transmission Lines Exhibiting Cross-Polarization Effects

The purpose of this letter is to understand and model the electromagnetic properties of transmission lines loaded with split-ring resonators (SRRs) and complementary split-ring resonators (CSRRs) arbitrarily oriented. It is shown that if the slits of these resonators are aligned in a nonorthogonal direction to the line axis, cross-polarization effects arise. Namely, the particles (SRRs or CSRRs) are excited through both magnetic and electric coupling. It is pointed out that the previously reported lumped element equivalent circuit models of SRR- and CSRR-loaded lines (where cross polarization is not considered) are valid as long as the slits are orthogonally oriented to the line axis, and new models that include cross polarization are presented and discussed. The validity and accuracy of the models is demonstrated through parameter extraction and comparison to full-wave electromagnetic simulations and measurements.