Optical and Quantum Electronics

, Volume 41, Issue 4, pp 267–283 | Cite as

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

  • Manfred Hammer
  • Olena V. Ivanova
Open Access


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.


Integrated optics Numerical modeling Photonic crystal slabs Effective index approximation 



This work has been supported by the Dutch Technology foundation (BSIK / NanoNed project TOE.7143). The authors thank Brenny van Groesen, Hugo Hoekstra, and Remco Stoffer for many fruitful discussions.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2009

Authors and Affiliations

  1. 1.MESA+ Institute for NanotechnologyUniversity of TwenteEnschedeThe Netherlands
  2. 2.Department of Applied MathematicsUniversity of TwenteEnschedeThe Netherlands

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