Fig. 4: Self-coupled polariton dispersions in 1D MoS₂ gratings.

a Measured and (b) simulated angle-resolved extinction spectra for 1D MoS₂ gratings (A1-A3) along \({{{{{{\bf{k}}}}}}}_{y}\)(\({{{{{{\bf{k}}}}}}}_{x}\)=0). The white dashed lines represent the dispersions of surface lattice resonances (SLRs) of the MoS₂ grating where the symbol \(\pm 1\) represents the \(\pm 1\) diffraction orders, i.e., the so-called Rayleigh anomalies (RAs) (see Supplementary Note 2 for more details). The white dotted curves indicate the A excitonic resonance. Red and yellow lines represent the dispersions of the upper polariton (UP) and lower polariton (LP) separately, where the \(+\)/\(-\) symbol represents the polariton formed from the SLR(+1)/SLR(−1) mode. c Zoomed-in regions of white box (1) and box (2) indicated in (a)_. d Permittivity calculated by the Lorentz model for oscillator strengths \(f\)=0 (I), \(f\)=0.2 (II), and \(f\)=0.4 (III) respectively. e Calculated angled-resolved extinction spectra of 1D dielectric grating for different dielectric functions shown in (c). f Coupling strengths \({g}_{{{{{{\rm{A}}}}}}}\) extracted from the polariton dispersions from (a, b). g Mode areas \({\sigma }_{{{{{{\rm{m}}}}}}}\) and cross-sectional areas \({\sigma }_{{{{{{\rm{c}}}}}}}\) calculated from the simulation results from (b). h Comparisons of coupling strengths (\({2g}_{{{{{{\rm{A}}}}}}}\) represents the Rabi splitting) and effective areas \({\sigma }_{{{{{{\rm{eff}}}}}}}\) for A1-A3.