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Effective index approximations of photonic crystal slabs: a 2-to-1-D assessment Manfred Hammer, Olena V. Ivanova
 

Summary: Effective index approximations of photonic crystal slabs: a 2-to-1-D assessment
Manfred Hammer, Olena V. Ivanova
MESA+ Institute for Nanotechnology, University of Twente, Enschede, The Netherlands,
Abstract: The optical properties of slab-like photonic crystals (PCs) 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.
Keywords: integrated optics, numerical modeling, photonic crystal slabs, effective index ap-
proximation.
PACS codes: 42.82.m 42.82.Bq 42.82.Et
1 Introduction
The propagation of light through slab-like photonic crystals (PCs) [1] is frequently described in terms of effec-
tive indices (EIs). One replaces the actual 3-D structure by an effective 2-D refractive index profile, given by

  

Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente

 

Collections: Engineering