A Universal Law for Plasmon Resonance Shift in Biosensing

We derive an explicit expression for the resonance frequency shift for a subwavelength plasmonic nanocavity upon the adsorption or trapping of a single nanoparticle using rigorous perturbation theory. It reveals a simple linear dependence of the resonance frequency shift on the product of the local field intensity of a resonance mode, the material dispersion factor dω_i/dε of the nanocavity, and the polarizability of the nanoparticle. To verify this linear relation, we numerically simulate the nanoparticle-induced resonance shifts for subwavelength ellipsoids, rods, rod pairs, and split rings with different sizes and materials, and a very good agreement is found between the theory and the numerical results. Moreover, we discuss this approach from the energy perspective and find that the linear relation can be understood in the context of optical trapping. This work not only reveals the underlining physics of near-field couplings in plasmonic nanocavities but also provides theoretical guidelines for the design of ultrasensitive nanosensors.