Level spacing statistics for light in two-dimensional disordered photonic crystals.

Area of Science:

• Condensed matter physics
• Photonics and optical materials

Background:

• Photonic crystals offer control over light propagation.
• Disorder in photonic crystals can induce unique optical phenomena, such as Anderson localization.
• Understanding light behavior in disordered systems is crucial for developing novel optical devices.

Purpose of the Study:

• To investigate the distribution of eigenfrequency spacings (level spacing statistics) for light in a 2D disordered photonic crystal.
• To differentiate the statistical behavior of localized modes from non-localized modes.

Main Methods:

• Fabrication of a two-dimensional photonic crystal with circular silicon rods in air.
• Numerical simulations to analyze the eigenfrequency spectrum and mode localization.
• Statistical analysis of the distribution of mode spacings.

Main Results:

• Disorder introduces localized transverse-magnetic (TM) modes within the band gap.
• The level spacing statistics for these localized TM modes approaches the Poisson distribution.
• Transverse-electric (TE) modes and TM modes outside the band gap exhibit level spacing statistics following the Wigner-Dyson distribution.

Conclusions:

• The study reveals distinct statistical behaviors of light modes in disordered photonic crystals based on their localization and polarization.
• Localized modes in the band gap behave differently from extended modes, indicating a transition in quantum chaotic behavior.
• Findings contribute to the understanding of wave localization in disordered media and have implications for photonic device design.