Nanoscale Characterization of Individual Three-Dimensional Split Ring Resonator Systems

Abstract

In this work, we investigate the hybridization of three-dimensional plasmonic split ring resonator (SRR) pairs using focused electron beam nanospectroscopy and model their combined electric and magnetic responses using electromagnetic theory and numerical calculations. Specifically, we fabricate three-dimensional (3D) SRR dimers with varying in-plane rotations and out-of-plane tilts and perform electron energy loss spectroscopy (EELS) measurements to elucidate the impact of their 3D electric and magnetic interactions on the EEL spectrum of each individual SRR dimer. On the basis of the competition between the SRR’s electric and magnetic interactions within our model, we find that varying the 3D tilt angle diminishes the magnetic coupling but increases the level of overall mode mixing. Through further modeling of the experimental data, we determine the system’s electric and magnetic coupling constants, as well as the overall effective coupling constant, a useful metric for characterizing the strength of light–matter interaction. We additionally explore the potential for geometric frustration in the magnetic mode ordering of a coupled SRR trimer using both EELS experiment and companion theoretical modeling. Taken together, the insight gained into the behavior of coupled 3D SRRs serves as a stepping stone to the rational design of 3D photonic metamaterials endowed with even richer optical functionality.