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

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.

Main article: 6 pages, 3 figures; supplemental material: 8 pages, 4 figures

References in corpus (3)

• Designer disordered materials with large complete photonic band gaps
• Robust topology optimization of three-dimensional photonic-crystal band-gap structures
• Fabrication of mesoscale polymeric templates for three-dimensional disordered photonic materials

Cited by in corpus (4)

• Bandgap fluctuations and robustness in two-dimensional hyperuniform dielectric materials
• Characterization of Anisotropic Gaussian Random Fields by Minkowski Tensors
• Density of photonic states in aperiodic structures
• Deep-subwavelength engineering of stealthy hyperuniformity