Light propagation through coupled defects in photonic crystals

Rumen Iliew, Christoph Etrich, and Falk Lederer

Institut für Festkörpertheorie und Theoretische Optik,
Friedrich-Schiller-Universität Jena,
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 calculations.