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Eigenfunction and eigenmode-spacing statistics in chaotic photonic crystal graphs.

Shukai Ma1,2, Thomas M Antonsen2,3, Steven M Anlage1,2,3

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Summary
This summary is machine-generated.

We introduce photonic crystal defect waveguide graphs as a novel physical system for studying wave chaotic graphs. This research explores eigenfunction amplitudes and eigenmode spacings in these engineered systems.

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Area of Science:

  • Physics
  • Condensed Matter Physics
  • Photonics

Background:

  • Wave chaotic systems are extensively studied using statistical properties like eigenmode spacing and eigenfunction statistics.
  • Existing research primarily focuses on abstract mathematical models rather than physical realizations.

Purpose of the Study:

  • To propose photonic crystal (PC) defect waveguide graphs as a novel physical platform for chaotic graph studies.
  • To investigate the statistical properties of these engineered PC graphs, including eigenfunction amplitudes and eigenmode spacings.

Main Methods:

  • Numerical determination of statistical properties for an ensemble of PC graphs.
  • Utilizing the engineerable dispersion relation of PC waveguides and their unique scattering properties at junctions and bends.

Main Results:

  • Statistically analyzed eigenfunction amplitudes and eigenmode spacings within the proposed PC graph system.
  • Demonstrated the feasibility of using PC waveguides to construct graphs with distinct scattering properties.

Conclusions:

  • Photonic crystal defect waveguide graphs offer a viable and physically realizable system for exploring wave chaos.
  • This approach is compatible with silicon nanophotonic technology, potentially engaging a new research community in chaotic graph studies.