Creating anisotropic topological phases within inversely designed photonic crystals

Photonic topological insulators endow flexible manipulation of light with high efficiency and robustness. The majority of previous research concentrated on isotropic topological states, with anisotropic topological states receiving less attention. In this study, we investigate anisotropic topological edge states in two-dimensional photonic systems for both the transverse magnetic (TM) and transverse electric (TE) modes. First, using the topology optimization method, photonic crystals (PCs) with maximized odd-order band gaps, from the first-order to the seventh-order, are created. An anisotropic topological phase transition is then obtained by shifting the primitive unit cell (UC) of the optimized PC along the horizontal direction by half of the lattice constant. Tightly localized anisotropic topological edge states are thus formed at the interface between the primitive and translated UCs. Finally, the transmission properties of the anisotropic topological edge states are numerically demonstrated. Our findings could aid in the development of topological photonic devices that offer reliable directional transmissions and radiations.