Stealthy-Hyperuniform Wave Dynamics in Two-Dimensional Photonic Crystals

Abstract

Hyperuniform structures are spatial patterns whose fluctuations disappear on long length scales, making them effectively homogeneous when observed from afar. Mathematically, this means that their spectral density, $\tilde{\rho}({\bf k})$, approaches zero for low wavenumber, $|\textbf{k}|$. Crystalline lattices are hyperuniform, as are certain quasicrystals, maximally random jammed packing of spheres, and electrons in the fractional quantum Hall state. Stealthy-hyperuniformity is an even stronger constraint on the spectral density: it requires that $\tilde{\rho}({\bf k})$ is strictly zero in a finite range of wavevectors around $\mathbf{k}=\mathbf{0}$, called the stealthy regime, or exclusion region. Since the degree of scattering by disorder is, to leading order, proportional to $\tilde{\rho}({\bf k})$, waves propagating through such structures may do so without scattering for sufficiently long wavelengths and short distances. Here, we measure scattering by disorder in photonic crystal slabs with stealthy-hyperuniform disorder by measuring the linewidths of the photonic bands. We observe the transition between the stealthy and non-stealthy regimes, marked by a sharp increase in linewidth. We also observe the effects of multiple scattering in the stealthy regime, which implies diminishing transparency. Moreover, we show that residual single scattering in the stealthy regime arises from an intrinsically non-Hermitian effect: propagating light has a complex effective mass due to radiative loss out of the slab.