Effects of classical and electromagnetic chaos phenomena in Sinai billiard-type rectangular systems and in photonic crystal waveguides

Abstract

The Sinai billiard describes the motion of a freeparticle bouncing within a bounded region; while in aphotonic crystal waveguide (PCW) consisting of parallel flat surfaces with a periodic arrangement of cylindrical inclusions of real conductor a monochromatic light beam propagates. In this study, two systems were considered: the first is a rectangular region with circular inclusions, where the dynamics of particle bounces within the space was studied, and in the second, the interaction of electromagnetic waves in a PCW. This periodic system presents a band structure characterized by its dispersion relation, which allows the description of the normal modes that were calculated using the Integral Equation Method (IEM). The results revealed disordered field intensity patterns in the PCW, which were analyzed using statistical properties such as the autocorrelation function and correlation length to characterize electromagnetic chaos phenomenon. Finally, Poincaré maps of the classical system were compared with the disordered patterns of the electromagnetic system.