Fast Generation of Spectrally-Shaped Disorder for Optical Metamaterials*

Correlated disorder in material structures gives rise to nontrivial transport properties. However, unlike their crystalline counterparts, disordered photonic structures remain difficult to design at scale. Utilizing non-uniform fast Fourier transforms, we devised an algorithm capable of generating continuous or discrete material structures with arbitrary spectral properties in quasilinear time (O(N log N)), creating point patterns containing as many as one billion (10⁹) points. We demonstrate the specificity of our algorithm by imposing complex features in Fourier space, e.g. high-resolution images. Additionally, for finite systems, we can impose Bragg-like peaks to create structures exhibiting crystalline or quasicrystalline order, thus providing a possible method for designing particle interactions that enable the self-assembly of long-range crystalline or quasicrystalline structures by direct optimization. We analyze the transmission properties of our structures at the single scattering level, finding evidence of a transmission gap in stealthy hyperuniform structures, but also of even stronger transmission gaps in non-hyperuniform structures. Finally, we aim to explore fabrication methods for such nanoarchitected materials to demonstrate how our structures translate into real materials.