Fig. 2.
Four designs of isotropic, dielectric heterostructures derived by using the protocol in Fig. 1 and their structure factors, S(k). (A) A disordered network design derived from a Poisson (nonhyperuniform) point pattern. (B) A network derived from a nearly hyperuniform equiluminous point pattern in which the structure factor S(k → 0) = S0>0 for k < kC. (C) A network derived from a RSA point pattern in which the structure factor S(k → 0) > 0, but there is more local geometric order than in B. D is derived from an isotropic, disordered, stealthy hyperuniform pattern, for which S(k) is precisely zero within the inner disk. Only D exhibits a complete PBG. Note the two concentric shells of sharply increased density just beyond the disk. These features sharpen as the ordering parameter χ increases; this trend coincides in real space with the exclusion zone around each particle increasing and the emergence of complete PBGs.