Analysis of resonant responses of split ring resonators using conformal mapping techniques

摘要

We report a novel method for modeling the resonant frequency response of infra-red light, in the range of 2 to 10 microns, reflected from metallic spilt ring resonators (SRRs) fabricated on a silicon substrate. The calculated positions of the TM and TE peaks are determined from the plasma frequency associated with the filling fraction of the metal array and the equivalent LC circuit defined by the SRR elements. The capacitance of the equivalent circuit is calculated using conformal mapping techniques to determine the co-planar capacitance associated with both the individual and the neighbouring elements. The inductance of the equivalent circuit is based on the self-inductance of the individual elements and the mutual inductance of the neighboring elements. The results obtained from the method are in good agreement with experimental results and simulation results obtained from a commercial FDTD simulation software package. The method allows the frequency response of a SRR to be readily calculated without complex computational methods and enables new designs to be optimised for a particular frequency response by tuning the LC circuit.