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


Hammer, Manfred and Ivanova, Olena V. (2009) Effective index approximations of photonic crystal slabs: a 2-to-1-D assessment. Optical and quantum electronics, 41 (4). pp. 267-283. ISSN 0306-8919

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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.
Item Type:Article
Additional information:Open Access
Copyright:© 2009 Springer
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/71244
Official URL:https://doi.org/10.1007/s11082-009-9349-3
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