Recent experiments on three-dimensional icosahedral dielectric photonic quasicrystals have shown several unexpected features: transmitted femtosecond pulses developed a trailing “diffusive” exponential tail and the sum of (zeroth-order) transmittance and reflectance was well below unity. These experimental findings have previously been ascribed to sample imperfections. Here, we analyze these findings by using 3D periodic approximants of the ideal photonic quasicrystals. We show that the experimental observations can be explained in terms of multiple scattering of light within these structures, i.e., in terms of intrinsic rather than purely extrinsic quasicrystal properties.

© 2009 Optical Society of America

1. P. J. Lu and P. J. Steinhardt, "Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture," Science 315, 1106-1110 (2007). [CrossRef] [PubMed]
2. B. Grünbaum and G. C. Shephard, Tilings and Patterns (W. H. Freeman and Company, New York, 1986).
3. D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, "Metallic Phase with Long-Range Orientational Order and No Translational Symmetry," Phys. Rev. Lett. 53, 1951-1953 (1984). [CrossRef]
4. W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, "Experimental measurement of the photonic properties of icosahedral quasicrystals," Nature 436, 993-996 (2005). [CrossRef] [PubMed]
5. A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, "Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths," Nat. Mater. 5, 942-945 (2006). [CrossRef]
6. A. F. Koenderink, A. Lagendijk, and W. L. Vos, "Optical extinction due to intrinsic structural variations of photonic crystals," Phys. Rev. B 72, 153102:1-4 (2005).
7. A. W. Rodriguez, A. P. McCauley, Y. Avniel, and S. G. Johnson, "Computation and visualization of photonic quasicrystal spectra via Bloch’s theorem," Phys. Rev. B 77, 104201:1-10 (2008).
8. C. Janot, Quasicrystals - A Primer (Clarendon Press, Oxford, 1992).
9. D. M. Whittaker and I. S. Culshaw, "Scattering-matrix treatment of patterned multilayer photonic structures," Phys. Rev. B 60, 2610-2618 (1999). [CrossRef]
10. M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, "Direct laser writing of three-dimensional photonic crystal templates for telecommunications," Nat. Mater. 3, 444-447 (2004). [CrossRef]

Nat. Mater.

• A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, "Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths," Nat. Mater. 5, 942-945 (2006). [CrossRef]
• M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, "Direct laser writing of three-dimensional photonic crystal templates for telecommunications," Nat. Mater. 3, 444-447 (2004). [CrossRef]

Nature

• W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, "Experimental measurement of the photonic properties of icosahedral quasicrystals," Nature 436, 993-996 (2005). [CrossRef] [PubMed]

Phys. Rev. B

• A. F. Koenderink, A. Lagendijk, and W. L. Vos, "Optical extinction due to intrinsic structural variations of photonic crystals," Phys. Rev. B 72, 153102:1-4 (2005).
• A. W. Rodriguez, A. P. McCauley, Y. Avniel, and S. G. Johnson, "Computation and visualization of photonic quasicrystal spectra via Bloch’s theorem," Phys. Rev. B 77, 104201:1-10 (2008).
• D. M. Whittaker and I. S. Culshaw, "Scattering-matrix treatment of patterned multilayer photonic structures," Phys. Rev. B 60, 2610-2618 (1999). [CrossRef]

Phys. Rev. Lett.

• D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, "Metallic Phase with Long-Range Orientational Order and No Translational Symmetry," Phys. Rev. Lett. 53, 1951-1953 (1984). [CrossRef]

Science

• P. J. Lu and P. J. Steinhardt, "Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture," Science 315, 1106-1110 (2007). [CrossRef] [PubMed]

Other

• B. Grünbaum and G. C. Shephard, Tilings and Patterns (W. H. Freeman and Company, New York, 1986).
• C. Janot, Quasicrystals - A Primer (Clarendon Press, Oxford, 1992).

Click here to see a list of articles that cite this paper

Related Journal Articles

• Coherent reflectance in a system of random Mie scatterers and its relation to the effective-medium approach (JOSAA)
• Statistical theory of multiple scattering of waves applied to three-dimensional layered photonic crystals (JOSAB)
• Directional and angle-resolved optical scattering of high-performance translucent polymer sheets for energy-efficient lighting and skylights (AO)
• Coherent reflection of light from a turbid suspension of particles in an internal-reflection configuration: Theory versus experiment (OE)
• Visible and near-ultraviolet absorption spectrum of ice from transmission of solar radiation into snow (AO)

Related Conference Papers

• Multiple Scattering of Light in Three-Dimensional Photonic Quasicrystals
• Three-Dimensional Rhombicuboctahedral Photonic Quasicrystals
• Novel Optical Materials and Devices by Direct Laser Writing
• Photonic Band Structure of Circular Photonic Crystals in Silicon-on-Insulator Slab by Surface Coupling Reflectivity Technique
• Bio-Inspired Photonic Nanostructures and Lasers