Valley photonic crystals (VPCs) offer topological kink states that ensure robust, unidirectional, and backscattering-immune light propagation. The design of VPCs is typically based on analogies with condensed-matter topological insulators that exhibit the quantum valley Hall effect; trial-and-error approaches are often used to tailor the photonic band structures and their topological properties, which are characterized by the local Berry curvatures. In this paper, we present an inverse design framework based on frequency-domain analysis for VPCs with arbitrary pseudospin states. Specifically, we utilize the transverse spin angular momentum (TSAM) at the band edge to formulate the objective function for engineering the desired topological properties. Numerical experiments demonstrate that our proposed design approach can successfully produce photonic crystal waveguides exhibiting dual-band operation, enabling frequency-dependent light routing. Our pseudospin-engineering method thus provides a cost-effective alternative for designing topological photonic waveguides, offering novel functionalities.

翻译：谷光子晶体（VPCs）提供了拓扑扭结态，确保了鲁棒、单向且对背向散射免疫的光传播。VPCs的设计通常基于与展现量子谷霍尔效应的凝聚态拓扑绝缘体的类比；常采用试错法来调整光子能带结构及其拓扑性质，这些性质由局域贝里曲率表征。本文提出了一种基于频域分析的逆向设计框架，用于设计具有任意赝自旋态的VPCs。具体而言，我们利用能带边缘的横向自旋角动量（TSAM）来构建目标函数，以工程化所需的拓扑性质。数值实验表明，我们提出的设计方法能够成功产生展现双频带操作的光子晶体波导，实现频率相关的光路由。因此，我们的赝自旋工程方法为设计拓扑光子波导提供了一种具有成本效益的替代方案，并提供了新颖的功能。