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fc Δfa bc dExtended Data Fig. 5 | Inverse cubic diamond lattice of clusters. a, Structure
for a compression ratio of 0.76. The size ratio is chosen so that patches just
touch. The volume fraction of solid material is 0.32. b, Same as in a, but made
using a protective oxide layer with a thickness of 10% of the radius of the
spherical lobe of a cluster. The volume fraction of solid material is 0.20. c, Band
diagram for an inverse diamond lattice of clusters with a compression ratio of
0.76 (the structure shown in a), showing a complete photonic bandgap with a
relative width of 0.12 between the second and third bands (highlighted in blue).
The vertical axis is the dimensionless frequency fa/c, where f is frequency, a is
lattice constant and c is the speed of light in vacuum. Only the first five bands
are shown, but the first 50 were calculated and no other bandgaps were found.
d, Minimum index nmin at which a bandgap opens for a range of compression
ratios: direct lattice, blue; inverse lattice, red.