Photonic network solids exhibit surprising universal behavior

Together with Paul Steinhardt and Salvatore Torquato, I performed an intensive simulation study of the photonic band gaps of crystal and disordered networks. Our surprising discovering has now been published in Physical Review Letters.

M. A. Klatt, P. J. Steinhardt, S. Torquato. Gap Sensitivity Reveals Universal Behaviors in Optimized Photonic Crystal and Disordered Networks. Phys. Rev. Lett. 127:037401-1–6 (2021).

Photonic solids possessing large complete band gaps that block light waves in all directions and polarizations for a range of frequencies are key characteristics in photonic devices because they act as semiconductors for light. One of the computational challenges is finding the largest band gap possible for a given symmetry and structure type, e.g., a three-dimensional heterostructure in the form of a network of high dielectric material. The problem is inherently nonlinear, time-consuming to compute numerically, and requires many repetitions in order to optimize over the numerous network parameters (such as the network rod radius and the dielectric constant of the material). Hence, it is both surprising and of great practical use to discover universal behaviors shared by a wide class of photonics solids, as is identified in this Letter for the case of network solids, since it greatly reduces the computations needed to find optimal structures. In particular, we have identified a quantity called the gap-sensitivity (a measure of how much the optimal band gap changes with dielectric constant) that is to good approximation the same for a wide range of crystal networks and, for high dielectric constants, the same for a wide range of disordered networks. Even more specifically, the universal behavior of the gap sensitivity for these three-dimensional networks is well described by the analytic formula for an optimal solid composed of a periodic stack of alternating planar slabs of different dielectrics. As a result, given a new network, one only has to compute the band gap at a single value of the dielectric constant to predict the optimal band gap for all values. 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.

Photonic crystal networks: the crystal diamond network (left) and a nearly-hyperuniform network (right).

The Supplemental Videos also show how the band structure plots change with the dielectric contrast.


Universal hidden order in amorphous cellular geometries

In this paper, we analyze the evolution of random point patterns and their Voronoi diagrams as “quantizer” of space. Applying an iterative local optimization of their so-called Quantizer energy, we show that the patterns converge to the apparently same effectively hyperuniform state regardless of their initial conditions.

M.A. Klatt, J. Lovrić, D. Chen, S. C. Kapfer, F. M. Schaller, P. W. A. Schönhöfer, B. S. Gardiner, A.-S. Smith, G. E. Schröder-Turk, S. Torquato. Universal hidden order in amorphous cellular geometries. Nature Communications 10, 811 (2019)

Partitioning space into cells with certain extreme geometrical properties is a central problem in many fields of science and technology. Here we investigate the Quantizer problem, defined as the optimisation of the moment of inertia of Voronoi cells, i.e., similarly-sized ‘sphere-like’ polyhedra that tile space are preferred. We employ Lloyd’s centroidal Voronoi diagram algorithm to solve this problem and find that it converges to disordered states associated with deep local minima. These states are universal in the sense that their structure factors are characterised by a complete independence of a wide class of initial conditions they evolved from. They moreover exhibit an anomalous suppression of long-wavelength density fluctuations and quickly become effectively hyperuniform. Our findings warrant the search for novel amorphous hyperuniform phases and cellular materials with unique physical properties.