Counterintuitive dispersion effect near surface plasmon resonances in Otto structures

In this paper, we investigate the counterintuitive dispersion effect associated with the poles and zeros of reflection and transmission functions in an Otto configuration when a surface plasmon resonance is excited. We show that the zeros and/or poles in the reflection and transmission functions may move into the upper-half complex-frequency plane (CFP), and these locations of the zeros and poles determine the dispersion properties of the whole structures (i.e., the frequency-dependent change of both reflected and transmitted phases). Meanwhile, we demonstrate various dispersion effects (both normal and abnormal) related to the changes of the poles and zeros in both reflection and transmission functions when considering the properties of metal substrates. For a realistic metal substrate in an Otto structure, there are the optimal thickness and incident angle, which correspond to the transitions of the zeros in the reflection function from the upper-half to lower-half CFP. These properties may be helpful to manipulate light propagation in optical devices.