Effective index approximations of photonic crystal slabs: a 2-to-1-D assessment

Manfred Hammer, Alyona Ivanova

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    Abstract

    The optical properties of slab-like photonic crystals are often discussed on the basis of effective index (EI) approximations, where a 2-D effective refractive index profile replaces the actual 3-D structure. Our aim is to assess this approximation by analogous steps that reduce finite 2-D waveguide Bragg-gratings (to be seen as sections through 3-D PC slabs and membranes) to 1-D problems, which are tractable by common transfer matrix methods. Application of the EI method is disputable in particular in cases where locally no guided modes are supported, as in the holes of a PC membrane. A variational procedure permits to derive suitable effective permittivities even in these cases. Depending on the structural properties, these values can well turn out to be lower than one, or even be negative. Both the “standard��? and the variational procedures are compared with reference data, generated by a rigorous 2-D Helmholtz solver, for a series of example structures.
    Original languageUndefined
    Pages (from-to)267-283
    Number of pages17
    JournalOptical and quantum electronics
    Volume41
    Issue number4
    DOIs
    Publication statusPublished - 2009

    Keywords

    • EWI-17845
    • Numerical modeling
    • Effective index approximation
    • Integrated Optics
    • METIS-266526
    • IR-71244
    • Photonic crystal slabs

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