  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. The force of the present approach,
in comparison with other approaches of the same kind, 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.
