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Evaluation of surface roughness of metal films using plasmonic Fano resonance in attenuated total reflection

Attenuated total reflection (ATR) by surface plasmon polariton (SPP) is a method for evaluating the dispersion relation of SPP from the position of a dip in the reflection spectrum. However, recent studies have shown that the dips are displaced from SPP resonance because they are produced by a type of Fano resonance, i.e., the interference between the resonant reflection process accompanied by resonant excitation of SPP and the direct reflection process without resonant excitation. This result suggests that the system properties difficult to be achieved in the dispersion relation of SPP can be characterized using the ATR method. In this study, we investigate the effect of surface roughness due to nanosized dimples created in the initial stage of pitting corrosion on the ATR spectrum, from the viewpoint of Fano resonance. Using the temporal coupled-mode method, it is shown that the Fano resonance in ATR is caused by the phase change of direct reflection because of the absorption on the metal surface, and the spectral shape is determined by this phase, along with the ratio of the external (radiative) decay rate to the total decay rate of the resonant mode. Moreover, it is clarified that the internal and external decay rates extracted from the ATR spectrum provide information on corrosion, such as the effective thickness of the metal film and the randomness in dimple distribution.