Improved Extinction Ratios for Both Cross and Bar States Using Two-Section Ultra Short Vertical Directional Couplers

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