Bandgap optimization of two-dimensional photonic crystals using semidefinite programming and subspace methods

@article{Men2010BandgapOO,
  title={Bandgap optimization of two-dimensional photonic crystals using semidefinite programming and subspace methods},
  author={Han Men and Ngoc Cuong Nguyen and Robert M. Freund and Pablo A. Parrilo and Jaime Peraire},
  journal={J. Comput. Physics},
  year={2010},
  volume={229},
  pages={3706-3725}
}
In this paper, we consider the optimal design of photonic crystal band structures for twodimensional square lattices. The mathematical formulation of the band gap 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… CONTINUE READING

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