Improved extinction ratios for both cross and bar states using two-sectionultra short vertical directional couplers

We show that both cross and bar states with high extinction ratios larger t han 30dB can be achieved in ultra short vertical directional couplers with two sections. Various combinations of the refractive indices in the two sec tions are studied using the improved coupled mode theory and the beam propa gation method. Design guidelines to achieve high extinction ratios with lar ge tolerances are presented.