Structural and spectral properties of deterministic aperiodic optical structures

Abstract

In this comprehensive paper we have addressed structure-property relationships in a number of representative systems with periodic, random, quasi-periodic and deterministic aperiodic geometry using the interdisciplinary methods of spatial point pattern analysis and spectral graph theory as well as the rigorous Green’s matrix method, which provides access to the electromagnetic scattering behavior and spectral fluctuations (distributions of complex eigenvalues as well as of their level spacing) of deterministic aperiodic optical media for the first time.