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Adaptive methods for photonic crystal fibers – 2006, FFFair 4, Zurich 

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In this talk we shall discuss the calculation of the spectrum of PDEs arising in models of photonic crystal fibers (PCFs) in both periodic and non-periodic cases.
For periodic PCF problems, under the assumptions of TE and TM polarizations, we derive error estimators for approximated eigenvalues and eigenvectors, arising from discretization of typical cell problem. We give numerical illustrations of how the adaptivity copes with internal interfaces in the device and with high contrast media.
We shall also give illustrations of the use of our error estimates in an adaptive procedure for finding spectral gaps and related trapped modes in devices with defects.