Defect modes in otherwise perfect photonic crystal and photonic crystal fibres

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De Sterke C et al. 2005, 'Defect modes in otherwise perfect photonic crystal and photonic crystal fibres', SPIE, Washington, USA, pp. 595002-1-595002-13.
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Many of the applications of photonic crystals and photonic crystal fibres require the periodic structure tohave some type of defect. In photonic crystal fibers a point defect defines the fiber core, whereas in photonic crystals a line defect acts as a waveguide, and point defects act as cavities. The modeling of these defects usually either makes use of periodic boundary conditions, by which the defect is replicated periodically, or models a photonic cyrstal of finite extent. HOwever, some applications, for example the cut-off behaviour of a defect mode where the field extends very widely, require methods that can model a defect in an otherwise infinite and perfectly periodic structure. Here we present such a method. It combines the method of fictitious sources with averaging over the Brillouin zone, and we apply it to study the long wavelength behavior of the fundamental mode of photonic crystal fibers.
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