This document discusses engineering 2D photonic disorder and controlling light transport through correlated disorder. It summarizes that transport properties can be designed semi-analytically using the Baus-Colot model to calculate structure factors. Strong modifications of transport can be achieved by varying the topological correlation at fixed frequencies or observing pronounced frequency responses. Controlling the degree of correlation can tune the mode volume of localized states and induce a transition from quasi-extended to localized transport regimes.

1. Engineering 2D photonic disorder:
from incoherent transport to interference
effects.
Matteo Burresi
burresi@lens.unifi.it

2. The Color of Disorder
Cloud, snow, fog
Random systems are white

3. Randomness in nature?
Really?
Yin et al, PNAS (2012)
Noh et al, Adv. Mat. (2010)
Garcia, Adv. Mat. (2009)
Donev, Science (2004)
Treacy, Science (2012)
Amorphous Silicon
Non-iridescent coloring
Hard sphere

4. 2D engineered-disordered
nanophotonic structures
Sapienza L., Science (2010)
Vynck K., Nature Mater. (2012)
Noh H., Phys. Rev. Lett. (2011)
Redding B., Nature Photon. (2013)
Quantum
electrodynamics
Random lasers
Light harvesting
Integrated spectrometer

5. 2D correlated disorder
The point patterns
generated with the
Lubachevsky-Stillinger
algorithm.
M. Skoge, P.R. E (2006).
Wave transport in these disordered systems
Transport mean free path
Modified scattering cross-section (SCS)
Structure factor
S. Fraden, P.R.L. (1990).
How to calculate it?

6. Baus-Colot model and the modified SCS
A semi-analytical model to calculate the
structure factor valid in n-dimension.
We use n=2.
M. Baus and J. L. Colot, P.R. A (1987).
Backward scattering dominate transport
M. Conley et al, arXiv (2013).

7. Tuning transport: correlation and frequency
 Strong modifications at fixed frequency by varying the topology
 Pronounced frequency response
Not so white, is it?

8. Diffusion theory with the Baus-Colot model
and numerical calculations
Large deviation at the correlation frequency
Time-resolved 2D FDTD calculation of the
electromagnetic field in a unbound systems
Decay rate according
to diffusion theory
M. Conley et al, arXiv (2013).

9. Transition from quasi-extended
to localized regime
The mode volume of a localized state can be tuned by
controlling the degree of correlation
Breakdown of diffusion theory due to
localization effects
Expected a dramatic spectral evolution of the
localization length
L=15a
M. Conley et al, arXiv (2013).

10. Take-home message
 Transport properties can be designed semi-analytically by
employing the Baus-Colot model;
 Large photonic dispersion can be achieved. This leads to a
promising control of the extension of localized modes.

11. Acknowledgements
Kevin Vynck
Gora M. Conley
Filippo Pratesi
Diederik S. Wiersma