Light propagation through coupled defects in photonic crystals
Rumen Iliew, Christoph Etrich, and Falk Lederer
Institut für Festkörpertheorie und Theoretische Optik,
Max-Wien-Platz 1, 07743 Jena, Germany
Efficient waveguiding around sharp bends is a key task in microoptics.
Using the reciprocity theorem we derive coupled-mode equations for light
propagation in coupled-defect waveguides. This can applied to
arrays of defects in two-dimensional photonic crystals and
three-dimensional photonic-crystal slabs.
Modes were calculated numerically and overlap integrals were calculated
from these results to obtain the coefficients for the equations of
motion for different configurations. The dispersion relations resulting
from these coupled-mode equations are compared to the dispersion relations
obtained from bandstructure calculations of the real structure.
We consider the case of multi-moded defects and the case where the
isolated defect is single-moded. In the two-dimensional case the validity
of the model is checked by means of finite-difference time-domain