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Exploring Space Groups for Three Dimensional Photonic Band Gap Structures Via Level Set Equations: The Face Centered Cubic Lattice

Published online by Cambridge University Press:  01 February 2011

Martin Maldovan ,
Chaitanya K. Ullal ,
Craig W. Carter  and
Edwin L. Thomas
Martin Maldovan
Affiliation:
Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139, USA
Chaitanya K. Ullal
Affiliation:
Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139, USA
Craig W. Carter
Affiliation:
Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139, USA
Edwin L. Thomas
Affiliation:
Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139, USA
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Abstract

A level set approach was used to study photonic band gaps for dielectric composites with symmetries of the eleven face centered cubic lattices. Candidate structures were modeled for each group by a 3D surface given by f(x,y,z)-t=0 obtained by equating f to an appropriate sum of structure factor terms. This approach allows us to easily map different structures and gives us an insight into the effects of symmetry, connectivity and genus on photonic band gaps. It is seen that a basic set of symmetries defines the essential band gap and connectivity. The remaining symmetry elements modify the band gap. The eleven lattices are classified into four fundamental topologies on the basis of the occupancy of high symmetry Wyckoff sites. Of the fundamental topologies studied, three display band gaps--- including two: the (F-RD) and a group 216 structure that have not been reported previously.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 788: Symposium L – Continuous Nanophase and Nanostructured Materials , 2003 , L10.7
Copyright
Copyright © Materials Research Society 2004

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