Photonic Localization of Interface Modes at the Boundary between Metal and Fibonacci Quasi-Periodic Structure

We investigated on the interface modes in a heterostructure consisting of a semi-infinite metallic layer and a semi-infinite Fibonacci quasi-periodic structure. Various properties of the interface modes, such as their spatial localizations, self-similarities, and multifractal properties are studied. The interface modes decay exponentially in different ways and the modes in the lower stable gap possess highest spatial localization. A localization index is introduced to understand the localization properties of the interface modes. We found that the localization index of the interface modes in the upper stable gap will converge to two slightly different constants according to the parity of the Fibonacci generation. In addition, the localization-delocalization transition is also found in the interface modes of the transient gap.