Persistent random walk in a honeycomb structure: light transport in foams

Area of Science:

• Physics
• Materials Science
• Optics

Background:

• Light transport in disordered media is crucial for understanding wave phenomena.
• Honeycomb structures offer a simplified 2D model for studying complex light interactions.
• Geometrical optics provides a framework for analyzing photon pathways.

Purpose of the Study:

• To investigate light transport in a 2D honeycomb lattice.
• To analyze photon diffusion behavior and derive diffusion constants.
• To explore the dependence of diffusion on injection angle and compare with theoretical assumptions.

Main Methods:

• Application of geometrical optics to model photon movement.
• Setting up a persistent random walk model for photons.
• Analytical derivation of diffusion constants for specific injection angles (30, 60, 90 degrees).
• Numerical simulations to observe diffusion constant variations.

Main Results:

• Demonstrated diffusive behavior of photons in the honeycomb structure.
• Derived diffusion constants based on reflectance, edge length, and light velocity.
• Observed an unexpected dependence of the diffusion constant on the injection angle.
• Noted non-convergence of the diffusion constant near 30 degrees, explained by a two-state model.

Conclusions:

• Photon diffusion in honeycomb structures is angle-dependent, contrary to standard diffusive limit assumptions.
• A two-state model can explain anomalies in diffusion constants at specific injection angles.
• The study provides insights into light propagation in simplified 2D photonic materials.