Bandwidth optimization of single-polarization single-mode photonic crystal fibers

We present an algorithm for computing single-polarization single-mode (SPSM) photonic crystal fibers with optimal bandwidth. Our approach is a topology optimization strategy based on convex conic optimization combined with a subspace method. The original problem of maximizing the bandwidth between the fundamental guided mode and the higher order unguided modes is reformulated as a problem of optimizing the band gap between two orthogonal subspaces of eigenvectors. By restricting the subspaces to a small number of judiciously chosen eigenmodes, we reduce the problem to a sequence of small-scale convex conic optimization programs for which modern interior-point method solvers can be efficiently applied. Our methodology is applied to optimize the cladding and core structures of SPSM photonic crystal fibers. 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