Fig. 1. Nontrivial space-time propagation diagram of a cosmic string simulated by a metasurface waveguide. (a) Space-time of different cosmic strings; (b) linear mass density is negative; (c) trivial flat space-time; (d) linear mass density is positive. The arrows at the bottom represent the coupled laser, the grating in the figure represents the laser coupling into the waveguide, and the points represent the position of the laser excitation

Fig. 2. Metasurface waveguide. (a) Schematic of a slab waveguides and the iso-frequency dispersion for TE and TM modes; (b) schematic of a metasurface waveguide and the iso-frequency dispersion for distributed TE and TM modes; (c) a micro-image of a rotational metasurface fabricated with a focused ion beam; (d) rotational metasurface with isotropic indices which are denoted by elliptical curves, and the local elliptical iso-frequency contour of the metasurface waveguide

Fig. 3. Directional scattering of electromagnetic waves by cosmic string space-time simulated with the metasurface waveguide. (a)-(d) Experimental results and (d)-(f) simulation results of negative mass density cosmic strings at different incident distances (from up to down: b=4.84 μm, b=0 μm, b=-7.14 μm). The negative topological defect with negative mass density η≈1.065 has the same deflection angle θ1=11.0° under three cases. (g)-(i) Experimental results and (j)-(l) simulation results of positive mas

Fig. 4. Symmetry breaking phase transition under the different material loss. (a) Dependence of the propagation length of the TE mode lTE, TM mode lTM, and coherence length lc on the structural parameter δ with the different loss parameter γ; (b) relationship between the iso-frequency curves of TE and TM modes and thickness parameter δ. (c) relationship between ellipticity and thickness parameter δ of TE and TM modes

Fig. 5. Topological defects with the different mass densities and structured beam in topological spaces. (a) Experimental result and (d) simulation result when mass density of cosmic string is η≈1.065; (b) experimental result and (e) simulation result when mass density of cosmic string is η≈1.05; (c) experimental result and (f) simulation result when mass density of cosmic string is η≈1.025; (g) experimental result and (k) simulation result of optical interference in the trivial flat space; (h) experime