Gap Sensitivity Reveals Universal Behaviors in Optimized Photonic Crystal and Disordered Networks

Through an extensive series of high-precision numerical computations of the optimal complete photonic band gap (PBG) as a function of dielectric contrast for a variety of crystal and disordered heterostructures, we reveal striking universal behaviors of the gap sensitivity , the first derivative of the optimal gap-to-midgap ratio . In particular, for all our crystal networks, takes a universal form that is well approximated by the analytic formula for a 1D quarter-wave stack, . Even more surprisingly, the values of for our disordered networks converge to for sufficiently large . A deeper understanding of the simplicity of this universal behavior may provide fundamental insights about PBG formation and guidance in the design of novel photonic heterostructures.