Phoamtonic designs yield sizeable 3D photonic band gaps

Michael A. Klatt; Paul J. Steinhardt; Salvatore Torquato

doi:10.1073/pnas.1912730116

New Research In

Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved October 7, 2019 (received for review July 23, 2019)

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Significance

Foams appear ubiquitously in many fields of science and technology. However, applications to photonics have not been possible because until now, foam-based 3D heterostructures with substantial complete photonic band gaps have not been identified. Here we provide explicit examples based on the edges of dry-crystalline foams, including the famous Weaire–Phelan foam. More generally, foam networks based on Frank–Kasper phases offer new, promising approaches to the rapid self-organization of large photonic networks. Moreover, foams are excellent candidates for designer materials with versatile multifunctional characteristics.

Abstract

We show that it is possible to construct foam-based heterostructures with complete photonic band gaps. Three-dimensional foams are promising candidates for the self-organization of large photonic networks with combinations of physical characteristics that may be useful for applications. The largest band gap found is based on 3D Weaire–Phelan foam, a structure that was originally introduced as a solution to the Kelvin problem of finding the 3D tessellation composed of equal-volume cells that has the least surface area. The photonic band gap has a maximal size of 16.9% (at a volume fraction of 21.6% for a dielectric contrast ε=13) and a high degree of isotropy, properties that are advantageous in designing photonic waveguides and circuits. We also present results for 2 other foam-based heterostructures based on Kelvin and C15 foams that have somewhat smaller but still significant band gaps.

Footnotes

↵¹To whom correspondence may be addressed. Email: mklatt{at}princeton.edu, steinh{at}princeton.edu, or torquato{at}princeton.edu.

Author contributions: M.A.K., P.J.S., and S.T. designed research; M.A.K., P.J.S., and S.T. performed research; M.A.K. analyzed data; and M.A.K., P.J.S., and S.T. wrote the paper.
The authors declare no competing interest.
This article is a PNAS Direct Submission.
Data deposition: All data generated or analyzed for this study, including configurations, parameter files, raw output, and postprocessed data, are available at the Zenodo repository, https://zenodo.org/, as Databases 1–3 (DOI: 10.5281/zenodo.3401635).
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1912730116/-/DCSupplemental.

Published under the PNAS license.

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