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Diffusion and anomalous diffusion of light in two-dimensional photonic crystals
A A Asatryan1, P A Robinson, R C McPhedran
1School of Mathematical Sciences, University of Technology, Sydney, New South Wales 2007, Australia.
Summary
This study examines electromagnetic wave transport in disordered photonic crystals. Results reveal reduced transport velocity and distinct wave propagation regimes, hinting at Anderson localization.
Area of Science:
- Physics
- Optics
- Condensed Matter Physics
Background:
- Photonic crystals offer unique wave manipulation properties.
- Disorder in photonic crystals significantly impacts wave transport.
Purpose of the Study:
- Investigate electromagnetic wave transport in disordered, finite, 2D photonic crystals.
- Characterize transport parameters like mean free paths and velocity.
- Explore the influence of disorder on wave propagation regimes.
Main Methods:
- Numerical calculations based on the Helmholtz equation.
- Analysis of transport parameters including transport and scattering mean free paths.
- Investigation of wave transport regimes: ordered propagation, diffusion, and anomalous diffusion.
Main Results:
- Calculated transport velocity can be significantly lower than free space values (up to 10^8 times less).
- Transport velocity outside the cluster can reach 0.3c.
- Identified distinct wave transport regimes, including diffusion and anomalous diffusion.
- Weak and strong disorder effects on transport velocity were analyzed.
Conclusions:
- The study specifies conditions for diffusion processes in disordered photonic crystals.
- Anderson localization is suggested to be incipient in the anomalous diffusion regime.
- Numerical results align well with the diffusion approximation, validating the model.