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

ABSTRACTA 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.