Delay-Time-Enhanced Flat-Band Photonic Crystal Waveguides with Capsule-Shaped Holes on Silicon Nanomembrane

A slow-group-velocity- and low-group-velocity-dispersion photonic crystal slab waveguide is designed by using capsule-shaped air holes in hexagonal lattice. The theoretical study shows that adjusting the aspect ratio of holes in the innermost rows can fine-tune the dispersion tail. The presented design can achieve nearly flat-band photonic crystal waveguides with group index of 21–36 over the normalized bandwidth ( $\Delta \omega / \omega$) of 1.38%–0.4%. We also discuss the effects of the change in the holes’ aspect ratio combined with a slight size adjustment. The group index in the range of 21–43 for normalized bandwidth of about 1.5%–0.3% is obtained with the combination effect. The optimized designed exhibits a nearly constant group index of 21 over 22.7 nanometer bandwidth at $\lambda = \hbox{1.55}\ \mu$m.