“Gap Sensitivity Reveals Universal Behaviors in Optimized Photonic Crystal and Disordered Networks” is Published in Physical Review Letters

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Link to the journal: here

Through an extensive series of high-precision numerical computations of the optimal complete photonic band gap (PBG) as a function of dielectric contrast \(\alpha\) for a variety of crystal and disordered heterostructures, we reveal striking universal behaviors of the gap sensitivity \(\mathcal{S}(\alpha)≡d\Delta(\alpha)/d\alpha\), the first derivative of the optimal gap-to-midgap ratio \(\Delta(\alpha)\). In particular, for all our crystal networks, \(\mathcal{S}(\alpha)\) takes a universal form that is well approximated by the analytic formula for a 1D quarter-wave stack, \(\mathcal{S}_{QWS}(\alpha)\). Even more surprisingly, the values of \(\mathcal{S}(\alpha)\) for our disordered networks converge to \(\mathcal{S}_{QWS}(\alpha)\) for sufficiently large \(\alpha\). 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.