Robust topology optimization of three-dimensional photonic-crystal band-gap structures
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Main article
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Author(s)
Lee, K. Y. K.
Men, Han
Freund, Robert Michael
Peraire, Jaime
Johnson, Steven G.
Date Issued
September 2014
Journal
Optics Express
Publisher
Optical Society of America
Citation
Men, H., K. Y. K. Lee, R. M. Freund, J. Peraire, and S. G. Johnson. “Robust Topology Optimization of Three-Dimensional Photonic-Crystal Band-Gap Structures.” Optics Express 22, no. 19 (2014): 22632.
Version
Author's final manuscript
Abstract
We perform full 3D topology optimization (in which “every voxel” of the unit cell is a degree of freedom) of photonic-crystal structures in order to find optimal omnidirectional band gaps for various symmetry groups, including fcc (including diamond), bcc, and simple-cubic lattices. Even without imposing the constraints of any fabrication process, the resulting optimal gaps are only slightly larger than previous hand designs, suggesting that current photonic crystals are nearly optimal in this respect. However, optimization can discover new structures, e.g. a new fcc structure with the same symmetry but slightly larger gap than the well known inverse opal, which may offer new degrees of freedom to future fabrication technologies. Furthermore, our band-gap optimization is an illustration of a computational approach to 3D dispersion engineering which is applicable to many other problems in optics, based on a novel semidefinite-program formulation for nonconvex eigenvalue optimization combined with other techniques such as a simple approach to impose symmetry constraints. We also demonstrate a technique for robust topology optimization, in which some uncertainty is included in each voxel and we optimize the worst-case gap, and we show that the resulting band gaps have increased robustness to systematic fabrication errors.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Massachusetts Institute of Technology. Department of Mathematics
Sloan School of Management
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DOI of Published Version
https://doi.org/10.1364/OE.22.022632
