A Circuit Model for Analysis of Metal–Insulator–Metal Plasmonic Complementary Split-Ring Resonators

A circuit model based on the transmission line theory is proposed to analyze the recently introduced metal-insulator-metal (MIM) complementary split-ring resonators (CSRRs). It is shown that integer and noninteger modes of CSRRs can be characterized by transmission line models with short- and open-circuited terminals. The proposed circuit model is then extended to incorporate side-coupling effects between the CSRRs and straight MIM waveguides. Thereby, simple closed-form expressions are provided for the coupling quality factor. It is shown that waveguide resonator structures based on CSRRs at specific resonance frequency and bandwidth can be smaller than waveguide resonator structures based on conventional ring resonators. Thanks to the smaller size of CSRRs, the coupling in the former arrangement is stronger than it is in the latter. Therefore, CSRRs are not required to be in the extreme proximity of the waveguide as in the waveguide ring resonators.