Optical EngineeringSuggested procedure for the use of the effective-index method for high-index-contrast photonic crystal slabs
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A procedure for the use of the effective-index method (EIM) for high-index-contrast photonic crystal slabs (PCSs) is proposed and discussed. For such a structure, the unperturbed slab supports more than one guided mode in the vertical direction. If the EIM considering the fundamental mode only is used to deal with such a structure, large calculation errors will be introduced into the results. By comparing the gap map in the guided-mode spectrum of the hole-type PCS with those of hole-type two-dimensional photonic crystals (2-D PCs) with different refractive indices, we find that if the refractive index is selected appropriately, the agreement between these two gap maps is very good. The dispersion curves of the effective 2-D line-defect hole-type PC waveguide also agree very well with those of the line-defect hole-type PCS waveguide. However, for the pillar-type PCS, we cannot use the EIM to reduce the required calculation time and computer memory. We think that the main reason for this is the different guiding mechanisms of the optical field in these two types of PCSs.