 
Summary: On effective index approximations
of photonic crystal slabs
Manfred Hammer and O. V. (Alyona) Ivanova
MESA+ Institute for Nanotechnology,
University of Twente, Enschede, The Netherlands
As a means to assess the quality of effective index approximations in simulations of pho
tonic crystal slabs, we consider a reduction of 2D Helmholtz problems for waveguide
Bragg gratings to 1D wave propagation, and compare with rigorous 2D reference solu
tions. Variational procedures permit to establish a reasonable effective index profile even
in cases where locally no guided modes exist.
Introduction
The propagation of light through slablike photonic crystals (PCs) is frequently described
in terms of effective indices (effective index method EIM, cf. e.g. Refs. [1, 2, 3]). One
replaces the actual 3D structure by an effective 2D permittivity, given by the propaga
tion constants of the slab modes of the local vertical refractive index profiles. Though the
approach is being described usually for the approximate calculation of waveguide modes,
it is just as well applicable to propagation problems. Our aim is to check the approxima
tion by analogous steps that reduce finite 2D waveguide Bragggratings, which in turn
can be seen as sections through 3D PC membranes, to 1D problems, which are tractable
by standard transfer matrix methods. A 2D Helmholtz solver ([4], reference) allows to
