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Han Men(mennus.edu.sg) Abstract: 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 infinitedimensional 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 finitedimensional eigenvalue problems for multiple values of the wave vector parameter. The resulting optimization problem is largescale and nonconvex, with low regularity and nondifferentiable objective. By restricting to appropriate eigenspaces, we reduce the largescale nonconvex optimization problem via reparametrization to a sequence of smallscale 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. Keywords: photonic crystal design, band gap optimization, semidefinite programming Category 1: Applications  Science and Engineering (Optimization of Systems modeled by PDEs ) Category 2: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Citation: Download: [PDF] Entry Submitted: 07/13/2009 Modify/Update this entry  
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