Gyromorphs: a new class of functional disordered materials

TL;DR

This paper introduces Gyromorphs, a novel class of disordered materials with unique liquid-like translational disorder and rotational order, demonstrating superior optical bandgap properties and enabling multi-bandgap structures for advanced photonic applications.

Contribution

The paper presents the design, generation, and analysis of Gyromorphs, a new class of materials with combined disorder and order, and demonstrates their superior optical properties compared to existing structures.

Findings

Gyromorphs outperform quasicrystals and hyperuniform structures in forming isotropic bandgaps.

They exhibit strong rotational order with no long-range translational order.

Polygyromorphs enable multiple bandgaps through multi-scale rotational symmetries.

Abstract

We introduce a new class of functional correlated disordered materials, termed Gyromorphs, which uniquely combine liquid-like translational disorder with quasi-long-range rotational order, induced by a ring of $G$ delta peaks in their structure factor. We generate gyromorphs in $2d$ and $3d$ by spectral optimization methods, verifying that they display strong discrete rotational order but no long-range translational order, while maintaining rotational isotropy at short range for sufficiently large $G$. Using a coupled dipoles approximation, we numerically show that these structures outperform quasicrystals, stealthy hyperuniformity, and Vogel spirals in the formation of low-index-contrast isotropic bandgaps in $2d$, for both scalar and vector waves, and open complete isotropic bandgaps in $3d$. This claim is further supported by analytical effective-medium theory and by numerical estimates of scattering mean-free paths. Finally, we introduce ``polygyromorphs'' with several rotational symmetries at different length scales (i.e., multiple rings of delta peaks), enabling the formation of multiple bandgaps in a single structure, thereby paving the way for fine control over optical properties.