Fig. 1: Structures of a PC-WS₂ sample and steady-state optical properties.

a schematic of polariton formation in a WS₂ ML that is supported on a self-assembled plasmonic crystal (PC), where excitons consisting of electrons (e⁻) and holes (h⁺) are coupled to plasmon waves. The Al₂O₃ spacer is not depicted for similicity. right insets: side and top-view scanning electron microscope images; b angle-resolved transmission spectra under p-polarised illumination and their projection (top x–y plane), in which the spectral positions of exciton A (X_A, red dashed line) and B (X_B, green dashed line), calculated dispersions of plasmon lattice modes (black dashed curves), and upper and lower branches of polaritons (orange curves) are indicated. The tuned angle (θ = 22°) is marked with a black dash-dotted line. c The p-polarised transmission spectra (black curves) of a PC-WS₂ sample measured at θ = 0, 22, 40°; thick orange curves indicate the fitted results using supplementary Eq. S1, and thin dotted curves represent the fitting components, whose amplitudes have been adjusted for visualation. d spectral positions of the fitted resonances (solid blue circles) in the PC-WS₂ sample at different illumination angles; the red (green) dashed line indicates the spectral position of exciton A (B); the black dashed curves indicate the simulated dispersions of plasmon resonances, while orange solid curves indicate the fitted dispersions using supplementary Eq. S2.