Advanced Search
DSpace@MIT

Bandgap Optimization of Two-Dimensional Photonic Crystals Using Semidefinite Programming and Subspace Methods

Research and Teaching Output of the MIT Community

Show simple item record

dc.contributor.author Men, H.
dc.contributor.author Nguyen, Ngoc Cuong
dc.contributor.author Freund, Robert Michael
dc.contributor.author Parrilo, Pablo A.
dc.contributor.author Peraire, Jaime
dc.date.accessioned 2012-03-09T17:12:39Z
dc.date.available 2012-03-09T17:12:39Z
dc.date.issued 2010-01
dc.date.submitted 2010-01
dc.identifier.uri http://hdl.handle.net/1721.1/69624
dc.description.abstract In this paper, we consider the optimal design of photonic crystal structures for two-dimensional square lattices. The mathematical formulation of the bandgap optimization problem leads to an infinite-dimensional Hermitian eigenvalue optimization problem parametrized by the dielectric material and the wave vector. To make the problem tractable, the original eigenvalue problem is discretized using the finite element method into a series of finite-dimensional eigenvalue problems for multiple values of the wave vector parameter. The resulting optimization problem is large-scale and non-convex, with low regularity and non-differentiable objective. By restricting to appropriate eigenspaces, we reduce the large-scale non-convex optimization problem via reparametrization to a sequence of small-scale convex semidefinite programs (SDPs) for which modern SDP solvers can be efficiently applied. Numerical results are presented for both transverse magnetic (TM) and transverse electric (TE) polarizations at several frequency bands. The optimized structures exhibit patterns which go far beyond typical physical intuition on periodic media design. en_US
dc.language.iso en_US
dc.publisher Elsevier en_US
dc.relation.isversionof http://dx.doi.org/10.1016/j.jcp.2010.01.023 en_US
dc.rights Creative Commons Attribution-Noncommercial-Share Alike 3.0 en_US
dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/ en_US
dc.source Prof. Freund via Alex Caracuzzo en_US
dc.title Bandgap Optimization of Two-Dimensional Photonic Crystals Using Semidefinite Programming and Subspace Methods en_US
dc.type Article en_US
dc.identifier.citation Men, H. et al. “Bandgap optimization of two-dimensional photonic crystals using semidefinite programming and subspace methods.” Journal of Computational Physics 229.10 (2010): 3706-3725. en_US
dc.contributor.department Massachusetts Institute of Technology. Department of Aeronautics and Astronautics en_US
dc.contributor.department Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science en_US
dc.contributor.department Sloan School of Management en_US
dc.contributor.approver Freund, Robert Michael
dc.contributor.mitauthor Nguyen, Ngoc Cuong
dc.contributor.mitauthor Freund, Robert Michael
dc.contributor.mitauthor Parrilo, Pablo A.
dc.contributor.mitauthor Peraire, Jaime
dc.relation.journal Journal of Computational Physics en_US
dc.identifier.mitlicense OPEN_ACCESS_POLICY en_US
dc.eprint.version Author's final manuscript en_US
dc.type.uri http://purl.org/eprint/type/JournalArticle en_US
eprint.status http://purl.org/eprint/status/PeerReviewed en_US
dspace.orderedauthors Men, H.; Nguyen, N.C.; Freund, R.M.; Parrilo, P.A.; Peraire, J. en


Files in this item

Name Size Format
Downloadable Full Text - PDF

This item appears in the following Collection(s)

Show simple item record

Creative Commons Attribution-Noncommercial-Share Alike 3.0 Except where otherwise noted, this item's license is described as Creative Commons Attribution-Noncommercial-Share Alike 3.0
Open Access