From Dark to Bright: First-Order Perturbation Theory with Analytical Mode Normalization for Plasmonic Nanoantenna Arrays Applied to Refractive Index Sensing

We present a first-order perturbation theory to calculate the frequency shift and linewidth change of photonic resonances in one-and two-dimensional periodic structures under modifications of the surrounding refractive index. Our method is based on the resonant state expansion, for which we extend the analytical mode normalization to periodic structures. We apply this theory to calculate the sensitivity of bright dipolar and much darker quadrupolar plasmonic modes by determining the maximum shift and optimal sensing volume.