Computing Optimal Waveguide Bends With Constant Width

A numerical method is developed for computing waveguide bends that preserve as much power as possible in fundamental mode. The method solves an optimization problem for a small number of points used to define the bend axis by cubic-spline functions. A wide-angle beam-propagation method formulated in a curvilinear coordinate system is used to compute the wave field in the bend. Compared with a circular bend and an S-bend given by a cosine curve, optimal bends have a smaller curvature near the two ends for a better connection with the straight input and output waveguides. For multimode waveguides, the optimal bends can be used to remove the coupling between the fundamental mode and other propagating modes.