Characteristics of vertical bent coupling between straight and curved rectangular optical waveguides

In terms of the coupled mode theory (CMT) and the transfer matrix method, we present a technique and relative formulas including the bent coupling coefficient, amplitude coupling ratio, amplitude transmission ratio and propagation power for analyzing the vertical bent coupling between a curved rectangular waveguide and a straight one. Investigations show that the bent coupling appears in an effective coupling region by both sides of the central coupling point. Beyond this effective coupling region, however, the bent coupling is very weak, and the propagation power in the waveguide is closer to a constant. As the bent radius increases, or the thickness of the coupling layer between these two waveguides decreases, this effective coupling region becomes wider, in which the coupling behavior becomes stronger.