Calculation of quasi dispersion curves and quality factors of coupled resonator optical waveguides in photonic-crystal slabs

Abstract

We propose a stabilization method to numerically calculate the dispersion relations and quality factors of optically confined finite structures. For the coupled resonator optical waveguide (CROW) made in a photonic-crystal slab (PCS) used as an example, the dispersion curve is normally not well defined due to the appearance of discontinuities, which do not occur in a two-dimensional CROW with infinite slab height. Therefore, there is less effort devoted to the calculation of quasi dispersion curves of the CROW in a slab. The dispersion relation of the PCS CROW can only be obtained by theoretical fitting to the experimental data under the tight-binding approximation. Here, we demonstrate the use of a stabilization method to calculate the quasi dispersion relation of a PCS CROW accurately. From the stabilization graph, we can calculate the quality factor for an eigenfrequency and properly choose the size of the simulation cell to avoid coupling the CROW modes with the unconfined modes and to accurately calculate the dispersion curve of the PCS CROW using the plane-wave expansion method. The proposed method and results not only provide important information for designing practical photonic devices such as slow-light optical waveguides and nonlinear photonic devices for the PCS CROWs but also can be applied to compute the quality factors and resonance frequencies of microcavities or nanocavities.