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

TL;DR

This paper uncovers universal behaviors in the sensitivity of optimal photonic band gaps across various crystal and disordered networks, revealing that their responses align with a simple one-dimensional model, which could inform future photonic design.

Contribution

It demonstrates that the gap sensitivity in diverse photonic structures universally follows a simple analytic form, bridging complex networks with a fundamental 1D model.

Findings

Universal form of gap sensitivity $ ext{S}( ext{α})$ for crystal networks

Convergence of disordered networks' sensitivity to the universal form at high contrast

Insights into PBG formation and photonic heterostructure design

Abstract

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 $\mathcal{S}(\alpha)\equiv d\Delta(\alpha)/d\alpha$, 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 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 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.