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arXiv · 2107.07216

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

Michael A. Klatt·Paul J. Steinhardt·Salvatore Torquato
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Abstract

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

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Michael A. Klatt, Paul J. Steinhardt, Salvatore Torquato. 2021-07-15. Gap Sensitivity Reveals Universal Behaviors in Optimized Photonic Crystal and Disordered Networks. https://doi.org/10.1103/physrevlett.127.037401

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