Subcell models with application to split-ring resonators in the infrared

Simplified wire-type models for split-ring resonators (SRRs), both in free-space and above a dielectric half-space, are developed. The gap of the SRR in the wire model is accurately represented by including a lumped load which is the difference between the actual gap fringe capacitance and the capacitance inherent in the code wire kernel for a delta gap voltage source. The SRR arms are represented by generalized thin wires that have both an electric equivalent radius (for the rectangular conductor resting on a dielectric substrate) and a magnetic equivalent radius (for a rectangular conductor in free space, since the substrate is assumed to be nonmagnetic). In addition, an impedance per unit length (due to finite penetration of the fields into the metal) enters a local transmission line part of the generalized thin-wire algorithm. The results from the thin-wire subcell model are compared to full wave simulations of the arrays of SRR's. The full wave simulations require tens of thousands of unknowns to resolve the field penetration into the finite conductors for a single SRR, whereas the thin-wire model has good accuracy with only tens of unknowns.