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Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups

Nature Materials volume 2, pages 664–667 (2003)Cite this article

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Abstract

The promise of photonic crystals and their potential applications1,2 has attracted considerable attention towards the establishment of periodic dielectric structures that in addition to possessing robust complete bandgaps, can be easily fabricated with current techniques. A number of theoretical structures have been proposed3,4,5,6,7,8,9,10,11,12,13,14,15. To date, the best complete photonic bandgap structure is that of diamond networks having Fd3m symmetry (2-3 gap). The only other known complete bandgap in a face-centred-cubic (f.c.c.) lattice structure is that of air spheres in a dielectric matrix (8-9 gap; the so called 'inverse-opal' structure). Importantly, there is no systematic approach to discovering champion photonic crystal structures. Here we propose a level-set approach based on crystallography to systematically examine for photonic bandgap structures and illustrate this approach by applying it to the 11 f.c.c. groups. This approach gives us an insight into the effects of symmetry and connectivity. We classify the F-space groups into four fundamental geometries on the basis of the connectivity of high-symmetry Wyckoff sites. Three of the fundamental geometries studied display complete bandgaps—including two: the F-RD structure with Fm3̄m symmetry and a group 216 structure with F4̄3m symmetry that have not been reported previously. By using this systematic approach we were able to open gaps between the 2-3, 5-6 and 8-9 bands in the f.c.c. systems.

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Figure 1: Bandgap maps for the f.c.c. structures as a function of volume fraction.
Figure 2: Three-dimensional representations of the sphere and level-set models for the basic geometries.

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  • 16 September 2003

    Changed authorname Craig W. Carter to W. Craig Carter

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Acknowledgements

The authors would like to thank their respective financial sources: M.M. and W.C.C., The Singapore-MIT alliance. C.U. and E.L.T., US Air Force DURINT in conjunction with the University of Buffalo. E.L.T., the US Army through the Institute for Soldier Nanotechnologies, under contract DAAD-19-2002 with the Army Research Office.

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  1. Martin Maldovan: There was an author name error in the AOP version of the paper published 14 September. W. Craig Carter appeared as Craig W. Carter. The error has since been corrected in the HTML and PDF versions; the paper will appear correctly in a forthcoming print issue.

Authors and Affiliations

  1. Department of Materials Science and Engineering, Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, 02139, Massachusetts, USA

    Martin Maldovan, Chaitanya K. Ullal, W. Craig Carter & Edwin L. Thomas

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  1. Martin Maldovan
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  2. Chaitanya K. Ullal
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  3. W. Craig Carter
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Correspondence to Edwin L. Thomas.

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Maldovan, M., Ullal, C., Carter, W. et al. Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups. Nature Mater 2, 664–667 (2003). https://doi.org/10.1038/nmat979

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