Universal Design of Waveguide Bends in Silicon-on-Insulator Photonics Platform

We propose a universal and analytic step-by-step method to calculate the optimal 90° and 180° waveguide bends (L-bends and U-bends) in silicon-on-insulator photonics platform. This approach consists of first building an analytic model of loss per unit length as a function of radius of curvature and then using a variational optimization of the bending loss. It is shown that the shape of the optimal bends is ultimately determined either by the radiation loss of tight bends if the curvature of the bend is set to eliminate mode-mismatch losses or by the sidewall roughness loss if the radius of curvature is large. Numerical results from full wave simulations and comparison of the optimal bend with the Bezier, Euler, and Hybrid Euler-Circular bend are also provided to show the validity of our approach.