Extended 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 n_min at which a bandgap opens for a range of compression ratios: direct lattice, blue; inverse lattice, red.