Eigenfunction and eigenmode-spacing statistics in chaotic photonic crystal graphs

TL;DR

This paper introduces photonic crystal defect waveguide graphs as a new platform for studying wave chaos, analyzing their eigenfunction and eigenmode-spacing statistics through numerical simulations, and highlighting their compatibility with silicon nanophotonics.

Contribution

It proposes a novel physical system using photonic crystal waveguides for chaotic graph analysis, enabling new experimental and theoretical research avenues.

Findings

Eigenfunction amplitude statistics characterized.

Eigenmode-spacing distributions analyzed.

System compatible with silicon nanophotonics.

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.