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We derive a closed-form expression that accurately predicts the peakfrequency-shift and broadening induced by tiny perturbations of plasmonicnanoresonators without critically relying on repeated electrodynamicsimulations of the spectral response of nanoresonator for various locations,sizes or shapes of the perturbing objects. The force of the present approach,in comparison with other approaches of the same kind, is that the derivation issupported by a mathematical formalism based on a rigorous normalization of theresonance modes of nanoresonators consisting of lossy and dispersive materials.Accordingly, accurate predictions are obtained for a large range ofnanoparticle shapes and sizes, used in various plasmonic nanosensors, evenbeyond the quasistatic limit. The expression gives quantitative insight, andcombined with an open-source code, provides accurate and fast predictions thatare ideally suited for preliminary designs or for interpretation ofexperimental data. It is also valid for photonic resonators with large modevolumes.

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