Fig. 1. (a) Schematic diagram of surface waves at the metal/uniaxial crystal interface. As shown, the OA of the uniaxial crystal lies in the x-y plane and forms an angle Φ with the x axis. (b) Variation of the normalized propagation constant β/k0 of the surface waves with respect to the OA orientation angle Φ.

Fig. 2. Electric-field meron lattice with C4 symmetry for l=0. (a) Distribution of the normalized real part of the out-of-plane electric-field component Re(Ez) at Φ=0°. Black square markers indicate the boundaries of the unit cell located at the central region of the lattice. (b) 3D vector diagram of the electric-field meron lattice corresponding to (a). (c) Variation of the skyrmion number within the unit cell at the center of the lattice via Φ. The grid size in simulation is 0.633 μm and the number of sample points is 1001.

Fig. 3. Electric-field topological textures at Φ=0°, 45°, and 70°. (a)–(c) Distributions of Re(Ez) (background) with the orientations of the in-plane electric-field vectors (black arrows), and the insets show the corresponding Fourier space patterns. (d)–(f) Topological textures for Φ=0°, 45°, and 70°, respectively. A consistent mapping scheme is used throughout the paper to visualize the topological textures.

Fig. 4. Electric-field meron lattice with C4 symmetry for l=2. (a) 3D electric-field vector diagram of the meron electric-field lattice at Φ=0°. (b) Variation of the skyrmion number within the unit cell at the center of the lattice via Φ. (c) and (d) Distributions of Re(Ez) and the corresponding topological textures at Φ=0°, 45°, and 90°, respectively. The grid size in simulation is 0.8862 μm, and the number of sample points is 1001.

Fig. 5. Spin meron lattices in C4 rotational symmetry for l=1 and 3. At Φ=0°, (a) and (b) present the normalized out-of-plane SAM distributions Sz for l=1 and 3, respectively. (c) and (d) show the corresponding 3D vector diagrams of the spin meron lattices. (e) Variation of the skyrmion number within the unit cell at the center of the lattices via Φ, for l=1 (blue curve) and l=3 (orange curve). The grid size in simulation is 0.633 μm, and the number of sample points is 1001.

Fig. 6. Spin meron lattices textures at Φ=0°, 45°, and 70°. The first row shows Sz distributions, with black arrows representing the orientations of the normalized in-plane SAM vectors, and the insets show the corresponding Fourier space patterns. The second row presents the phase distributions (background) of Ez for hybrid surface waves, with black arrows representing the directions of the normalized Poynting vectors. The vortex center of the Poynting vector corresponds to a phase singularity. The third row shows the corresponding topological spin textures for Φ=0°, 45°, and 70°. The left panel (a) corresponds to the case of l=1, while the right panel (b) shows the results for l=3. The scale bar represents 0.3λ.