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Through an extensive series of high-precision numerical computations of theoptimal complete photonic band gap (PBG) as a function of dielectric contrast$\alpha$ for a variety of crystal and disordered heterostructures, we revealstriking universal behaviors of the gap sensitivity $\mathcal{S}(\alpha)\equivd\Delta(\alpha)/d\alpha$, the first derivative of the optimal gap-to-midgapratio $\Delta(\alpha)$. In particular, for all our crystal networks,$\mathcal{S}(\alpha)$ takes a universal form that is well approximated by theanalytic formula for a one-dimensional quarter-wave stack,$\mathcal{S}_{\text{QWS}}(\alpha)$. Even more surprisingly, the values of$\mathcal{S}(\alpha)$ for our disordered networks converge to$\mathcal{S}_{\text{QWS}}(\alpha)$ for sufficiently large $\alpha$. A deeperunderstanding of the simplicity of this universal behavior may providefundamental insights about PBG formation and guidance in the design of novelphotonic heterostructures.

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