I. Introduction
Two-dimensional (2-D) photonic crystal defect waveguides have been the subject of active research [1]–[3] due to their potential to be a basic building block for densely integrated optics. They are most simply formed by inserting a linear defect in a 2-D triangular lattice of air holes in a dielectric slab. Photonic crystals provide a 2-D in-plane frequency bandgap for the guided modes of the slab. In the vertical direction, light is localized to the slab by means of total internal reflection. Although the in-plane photonic bandgap prohibits light to propagate anywhere but along the linear defect, a much weaker index confinement in the vertical direction raises the concern for the out-of-plane radiation loss.