In this study, the trajectory of a 90° bend is divided into two symmetric halves that are mirror images of each other as referenced to the symmetry axis at 45°, and each half is segmented into small curved sections. The bending radius and waveguide width for every section are parameters to be determined using a particle swarm optimization algorithm. The optimization is performed to maximize the transmission of the waveguide bends, which is calculated by using the three-dimensional finite-difference time-domain technique. The results indicate that the total bending loss of the optimized 90° bends with radii of 2, 3, 4, and 5 μm are 0.0106, 0.0051, 0.0025, and 0.0023 dB, respectively, at the wavelength λ = 1550 nm. In addition, the optimal devices are fabrication tolerant, with fabrication errors in width and height within 10 nm, and less wavelength-dependent compared with circular bends.

中文翻译：

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使用粒子群优化算法设计的超紧凑硅波导弯曲

在这项研究中，90° 弯曲的轨迹被分成两个对称的一半，以 45° 的对称轴为参考，它们互为镜像，每一半被分割成小的弯曲部分。每个部分的弯曲半径和波导宽度是使用粒子群优化算法确定的参数。执行优化以最大化波导弯曲的传输，这是通过使用三维有限差分时域技术计算的。结果表明，半径为 2、3、4 和 5 μm 的优化 90° 弯曲的总弯曲损耗分别为 0.0106、0.0051、0.0025 和 0.0023 dB，波长 λ = 1550 nm。此外，最佳器件具有制造公差，宽度和高度的制造误差在 10 nm 以内，