Eigenfunction and eigenmode-spacing statistics in chaotic photonic crystal graphs

Abstract

The statistical properties of wave chaotic systems of varying dimensionalities and realizations have been studied extensively. These systems are commonly characterized by the statistics of the eigenmode-spacings and the statistics of the eigenfunctions. Here, we propose photonic crystal (PC) defect waveguide graphs as a new physical setting for chaotic graph studies. Photonic crystal waveguides possess a dispersion relation for the propagating modes which is engineerable. Graphs constructed by joining these waveguides possess junctions and bends with distinct scattering properties. We present numerically determined statistical properties of an ensemble of such PC-graphs including both eigenfunction amplitude and eigenmode-spacing studies. Our proposed system is compatible with silicon nanophotonic technology and opens chaotic graph studies to a new community of researchers.

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• Bound states in the continuum induced via local symmetries in complex structures
• Experimental Realization of Anti-Unitary Wave-Chaotic Photonic Topological Insulator Graphs Showing Kramers Degeneracy and Symplectic Ensemble Statistics
• Experimental study of the distributions of off-diagonal scattering-matrix elements of quantum graphs with symplectic symmetry