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Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved October 7, 2019 (received for review July 23, 2019)
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
- Plateau’s laws for dry foam
- Weaire–Phelan foam
- TCP structures and Frank–Kasper phases
- self-organization
- complete photonic band gap
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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Phoamtonic designs yield sizeable 3D photonic band gaps
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