Cutoff-inclusive generalized effective index method for waveguide design

The effective index method (EIM) is a simplified semi-analytical technique for analyzing 2D optical waveguides by decomposing them into two sequential 1D calculations. A main limitation of conventional EIM is its inability to account for regions with thickness below the cutoff, where guided modes cannot exist. Furthermore, the accuracy of the method degrades noticeably for modes near the cutoff. To address these shortcomings, we propose a generalized effective index method (gEIM) that handles cutoff problems. This cutoff-inclusive gEIM is particularly advantageous for designing 2D waveguides fabricated on 1D photonic crystals, where modes frequently operate near cutoff and exhibit significant penetration into external media. The proposed method is implemented as a free Windows program, which computes both the effective refractive indices and the spatial profiles of 2D waveguide modes.