用B样条函数对S形弯曲波导进行结构优化

S形弯曲波导是集成光器件中不可缺少的部分。在光开关阵列、星形耦合器以及阵列波导光栅等器件中。以及将多个元件集成到一个芯片上时，都需要很多的S形弯曲波导来实现波导的侧向位移和连接。其尺寸和损耗直接影响整个器件的损耗以及集成密度。弯曲波导插入损耗(不包括由于结构缺陷而产生的光的散射损耗)由两部分组成：纯弯曲损耗和过渡损耗。从弯曲损耗产生的机理人手，提出用B样条泛函逼近理论实现任意边界条件下S形的优化方法，得到纯弯曲损耗尽可能小，并消除与直波导相连处过渡损耗的S形波导。且与正弦、余弦和双圆弧曲线得到的S形进行对比，用光束传播法验证。结果表明优化曲线插入损耗明显小于双圆弧和余弦曲线。

Configuration Optimization of S-Shaped Bend Waveguide Using B-Spline

S shaped bend waveguide is indispensable to realize the lateral displacement and connections in the integrated optical devices, such as the optical switch matrix, star coupler and arrayed waveguide grating (AWG). Even when various optical devices are integrated onto one chip, S bend also plays important roles. Its size and optical loss directly influences the integration dense and loss of whole device. The insertion loss (except the dispersion loss produced by the configuration defection) of S bend includes two parts: pure bending loss and transition loss. A method using functional approximation theory of B spline to realize the optimization of S shaped bend under the arbitrary boundary condition is set forth in this paper. Eventually, S shaped bend waveguide with characteristic of pure bending loss as small as possible is got. Moreover, the transition loss at the ends connecting with other waveguides is eliminated completely. Contrast among sin, cosine, double arc generated S shaped bend and the curve got by B spline is performed and verified using the beam propagation method (BPM). The result shows that the loss of optimized curve got in this paper is obviously less than that of double arc and cosine generated S bend; a good agreement is reached.