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Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths


Quasicrystals1,2,3,4 are a class of lattices characterized by a lack of translational symmetry. Nevertheless, the points of the lattice are deterministically arranged, obeying rotational symmetry. Thus, we expect properties that are different from both crystals and glasses. Indeed, naturally occurring electronic quasicrystals (for example, AlPdMn metal alloys) show peculiar electronic, vibrational and physico-chemical properties. Regarding artificial quasicrystals for electromagnetic waves, three-dimensional (3D) structures have recently been realized at GHz frequencies5 and 2D structures have been reported for the near-infrared region6,7,8,9. Here, we report on the first fabrication and characterization of 3D quasicrystals for infrared frequencies. Using direct laser writing10,11 combined with a silicon inversion procedure12, we achieve high-quality silicon inverse icosahedral structures. Both polymeric and silicon quasicrystals are characterized by means of electron microscopy and visible-light Laue diffraction. The diffraction patterns of structures with a local five-fold real-space symmetry axis reveal a ten-fold symmetry as required by theory for 3D structures.

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Figure 1: Electron micrographs of fabricated 3D icosahedral quasicrystal structures.
Figure 2: Laue diffraction patterns of polymeric quasicrystals.
Figure 3: Silicon inverse quasicrystal.
Figure 4: Diffusive light scattering of polymeric quasicrystals.


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We acknowledge the support provided by the Deutsche Forschungsgemeinschaft (DFG) and the State of Baden-Württemberg through the DFG-Center for Functional Nanostructures (CFN) and by the European Union (EU) through contract number RII3-CT-2003-506350 (LENS) and NoE Phoremost (511616). The research of G.v.F. is further supported through a DFG Emmy-Noether fellowship. G.A.O. is Government of Canada Research Chair in Materials Chemistry. He is indebted to the Natural Sciences and Engineering Research Council of Canada for support of this research and the CFN for a Guest Professorship.

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Correspondence to Alexandra Ledermann.

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Ledermann, A., Cademartiri, L., Hermatschweiler, M. et al. Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths. Nature Mater 5, 942–945 (2006).

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