Inverse design of dual-band valley-Hall topological photonic crystals with arbitrary pseudospin states

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.