Generalized polynomial curve construction with optimal curvature profile for low-loss SOI waveguide bends

Waveguide bends are indispensable building blocks in photonic integrated circuits (PICs). However, in large-scale and high-density scenarios, the sheer volume of waveguide bends poses significant challenges to both circuit layout and insertion loss. To address the loss issues in 90° silicon-on-insulator (SOI) waveguide bends, we propose a generalized construction method for septic polynomial curves. By analyzing loss mechanisms, we identify radiation loss and mode mismatch loss as the primary targets for optimization. Accordingly, the septic polynomial curve with optimal curvature profile is derived by introducing boundary constraints and utilizing curve length as the key control variable. Numerical simulations demonstrate that this curve effectively reduces the loss of 90° SOI waveguide bends with a cross-section of 500 × 220 nm for the fundamental transverse electric (TE) mode over the wavelength range of 1520 to 1580 nm, achieving a maximum loss improvement of 69.8% compared to the traditional quarter circle. Furthermore, in compact dimensions with an effective bending radius of less than 5 μm, it also exhibits excellent loss suppression characteristics in comparison with Bezier, Euler, and hybrid curves. This paper provides an efficient forward design solution for low-loss waveguide bends and holds potential engineering value for the advancement of photonic integration technology.