  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.
