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Updated: May 30, 2026
10:35
Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
Published on: September 26, 2014
Radiative energy transfer in disordered photonic crystals
M V Erementchouk1, L I Deych, H Noh
1Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA.
Summary
We present a new method for describing radiative transfer in disordered photonic crystals by considering both periodic and random scattering. This approach reveals that diffusion is typically anisotropic, becoming isotropic only in highly symmetric crystals.
Area of Science:
- Condensed matter physics
- Wave phenomena in periodic structures
Background:
- Describing radiative transfer in disordered photonic crystals is challenging due to the need to account for both periodic modulations and random inhomogeneities.
- Existing models often struggle to unify these scattering mechanisms.
Purpose of the Study:
- To develop a unified theoretical framework for radiative transfer in disordered photonic crystals.
- To analyze the diffusion limit and its dependence on structural symmetry and disorder.
Main Methods:
- Utilizing general multiple scattering theory for media with arbitrary dielectric function profiles.
- Applying the asymptotic solution of the Bethe-Salpeter equation.
- Deriving radiative transfer and diffusion equations from a limiting distribution.
Main Results:
- For weak disorder, the diffusion limit is an incoherent superposition of ideal structure modes, weighted by inverse group velocities.
- Radiative transfer and diffusion equations emerge as relaxations of this distribution.
- Diffusion is generally anisotropic, becoming isotropic only in highly symmetric lattices (e.g., 2D square, 3D cubic).
Conclusions:
- The developed theory provides a comprehensive description of radiative transfer in disordered photonic crystals.
- Anisotropy of diffusion is a key characteristic, directly linked to crystal symmetry.
- Isotropic diffusion, characterized by a single mean free path, occurs only in specific high-symmetry cases.
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