The optimal threshold conditions for forming photonic bandgaps in hyperuniform disordered structures and their applications

Hyperuniform disordered structures combine long-range hyperuniformity with short-range local self-similarity, enabling the formation of photonic band gaps in disordered structures. The inherited advantages of hyperuniform disordered structures include isotropy and tolerance to fabrication defects, making large-scale, cost-effective production of photonic band gap materials through bottom-up methods more feasible. In this study, we investigate the conditions for the formation of photonic bandgaps in disordered structures, identifying the optimal conditions for self-assembled hyperuniform disordered structures with the lowest refractive index threshold for forming photonic bandgaps and observing the evolution of hyperuniformity in the structures during the self-assembly process. We also explore applications of hyperuniform disordered photonic bandgap materials, including their use as waveguides and more efficient coupling receivers and emitters.