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.

中文翻译：

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利用全矢量 BPM 的光波导器件基于灵敏度分析的有效形状和拓扑优化

我们提出了一种利用全矢量光束传播方法 (FV-BPM) 进行形状和拓扑优化的新设计方法，以实现基于渐变模式演化的高折射率对比光波导和器件的有效设计。在我们的设计方法中，材料分布通过归一化密度参数表示，这些设计参数根据基于伴随变量法 (AVM) 计算的灵敏度进行更新。在采用密度法、AVM 和基于替代方向隐式方法 (AIDM) 的 FV-BPM 的特定情况下，提供了灵敏度分析方法和设计程序。我们的设计方法的适用性是通过设计引起偏振旋转的高折射率对比光子组件进行数值研究的：TM0 到 TE1 模式阶数转换器和偏振旋转器。设计实例的结果表明，我们的方法有可能适用于基于渐进模式演化的光学器件的高效初始设计。