Simple analytical expression for the peak-frequency shifts of plasmonic resonances for sensing

We derive a closed-form expression that accurately predicts the peak frequency shift and broadening induced by tiny perturbations of plasmonic nanoresonators without critically relying on repeated electrodynamic simulations of the spectral response of nanoresonator for various locations, sizes, or shapes of the perturbing objects. In comparison with other approaches of the same kind, the force of the present approach is that the derivation is supported by a mathematical formalism based on a rigorous normalization of the resonance modes of nanoresonators consisting of lossy and dispersive materials. Accordingly, accurate predictions are obtained for a large range of nanoparticle shapes and sizes used in various plasmonic nanosensors even beyond the quasistatic limit. The expression gives quantitative insight and, combined with an open-source code, provides accurate and fast predictions that are ideally suited for preliminary designs or for interpretation of experimental data. It is also valid for photonic resonators with large mode volumes.