Photonic crystal fibres: mapping Maxwell's equations onto a Schrödinger equation eigenvalue problem

Niels Asger Mortensen

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    Abstract

    We consider photonic crystal fibres (PCFs) made from arbitrary base materials and introduce a short-wavelength approximation which allows for a mapping of the Maxwell's equations onto a dimensionless eigenvalue equations which has the form of the Schröding equation in quantum mechanics. The mapping allows for an entire analytical solution of the dispersion problem which is in qualitative agreement with plane-wave simulations of the Maxwell's equations for large-mode area PCFs. We offer a new angle on the foundation of the endlessly single-mode property and show that PCFs are endlessly single mode for a normalized air-hole diameter smaller than ~042, independently of the base aterial. Finally, we show how the group-velocity dispersion relates simply to the geometry of the photonic crystal cladding.
    Original languageEnglish
    JournalJournal of the European Optical Society - Rapid Publications
    Volume1
    Pages (from-to)06009
    ISSN1990-2573
    DOIs
    Publication statusPublished - 2006

    Keywords

    • Photonic crystal fibre
    • Dispersion
    • Large-mode area

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