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.


Phoamtonics: Photonic band gaps of 3D foams

In our paper, published in PNAS, we show how to construct a foam-based photonic crystal with a substantial band gap using the famous Weaire-Phelan foam.

M. A. Klatt, P. J. Steinhardt, S. Torquato. Phoamtonic designs yield sizeable 3D photonic band gaps. Proc. Natl. Acad. Sci. U.S.A. 116:23480–23486 (2019)

A report by Steven Schultz about our study has been featured on the main webpage of Princeton University:


See also, the original post of the engineering department:

The Weaire-Phelan foam has the smallest surface area among all known tessellations with equal-volume cells. While it has only a slightly smaller surface area than the Kelvin foam. Its corresponding photonic network provides a distinctly larger band gap and a much smaller critical refractive index. To determine the latter, we have created a detailed map of gap sizes.

Among the promising prospects that phoamtonics offers for applications are multifunctional characteristics, the self-organization of large photonic networks, and a high degree of isotropy.

We published all data generated or analyzed for our phoamtonics study, including configurations, parameter files, raw output, and postprocessed data, in a Zenodo
( DOI: 10.5281/zenodo.3401635