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Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Nov;66(5 Pt 2):056604. Epub 2002 Nov 19.

Cylinder gratings in conical incidence with applications to modes of air-cored photonic crystal fibers.

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School of Mathematical Sciences, University of Technology, Sydney, New South Wales 2007, Australia.


We develop a formulation for cylinder gratings in conical incidence, using a multipole method. The theory, and its numerical implementation, is applied to two-dimensional photonic crystals consisting of a stack of one-dimensional gratings, each characterized by its plane wave scattering matrix. These matrices are used in combination with Bloch's theorem to determine the band structure of the photonic crystal from the solution of an eigenvalue problem. We show that the theory is well adapted to the difficult task of locating the complete band gaps needed to support air-guided modes in microstructured optical fibers, that is, optical fibers in which the confinement of light in a central air hole is achieved by photonic band-gap effects in a periodic cladding comprising a lattice of air holes in a glass matrix.

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