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Detecting molecules with plasmonic resonators - Analytic expressions and bounds for the sensitivity and figure of merit

We derive analytic expressions for the sensitivity and figure of merit for refractive index sensing with plasmonic resonators in the quasistatic limit. Based on these expressions the limits of detection and their origins are investigated. The critical role of limited energy concentration within the resonators surrounding is shown. The classical figure of merit is found to be solely dependent on the ratio of real to imaginary part of the resonators permittivity . Based on these findings we discuss the optimum resonance wavelength and resonator size and shape for single molecule detection.