Efficient Shape and Topology Optimization Based on Sensitivity Analysis for Optical Waveguide Devices Utilizing Full-Vectorial BPM

We present a new design approach of shape and topology optimization utilizing the full-vectorial beam propagation method (FV-BPM) so as to achieve efficient design for high-refractive-index contrast optical waveguides and devices based on gradual mode-evolution. In our design approach, material distribution is represented via normalized density parameters, and these design parameters are updated with sensitivity computed based on an adjoint variable method (AVM). The sensitivity analysis method and the design procedure are offered in the specific case where the density method, the AVM, and the FV-BPM based on an alternative direction implicit method (AIDM) are employed. The applicability of our design approach is numerically studied by designing high-refractive-index contrast photonic components which induce polarization rotation: a TM0-to-TE1 mode order converter and a polarization rotator. The results of the design examples indicate that our approach has potential to be suitable for efficient initial design of optical devices based on gradual mode-evolution.

我们提出一种利用全矢量光束传播法（FV - BPM）的形状和拓扑优化的新设计方法，以便实现基于渐变模式演化的高折射率对比度光波导和器件的高效设计。在我们的设计方法中，材料分布通过归一化密度参数表示，并且这些设计参数根据基于伴随变量法（AVM）计算出的灵敏度进行更新。在采用密度法、AVM以及基于交替方向隐式法（AIDM）的FV - BPM的特定情况下，给出了灵敏度分析方法和设计流程。通过设计引起偏振旋转的高折射率对比度光子元件：一个TM0到TE1模式阶数转换器和一个偏振旋转器，对我们设计方法的适用性进行了数值研究。设计实例的结果表明，我们的方法有可能适用于基于渐变模式演化的光学器件的高效初始设计。