Fig. 4: Nonlinear exciton–polaritons and saturation of the strong-coupling regime.

a, Comparison of the PL angular emission for a vdW-HM (δ = –94 meV) at low (10⁻¹³ J cm⁻²) and high (10⁻¹⁰ J cm⁻²) excitation fluences. The grey dashed line represents the exciton energy, whereas the black dashed lines mark the peak position of the LP emission peak. b, Transmittance for a vdW-HM (δ = 20 meV) excited using a supercontinuum laser with a repetition rate of 2.05 kHz. Similar to the emission, we observe—even in absorption—a transition to weak coupling at fluences above 10⁻⁹ J cm⁻². c, Normalized PL emission for a metasurface, δ = 20 meV, as a function of the excitation fluence. The exciton peak in the emission doublet is prominent at low power, but it gradually loses its weight, leaving the lower polariton branch to dominate the PL emission until fluences approaching 10⁹ J cm⁻², where we observe a collapse to a single optical transition. d, Normalized PL emission of a vdW metasurface on a second sample (δ = –55 meV) under increasing fluences. We observe the same saturation of the strong-coupling regime when approaching 10⁻⁹ J cm⁻² excitation fluences. e, Peak maxima positions for the exciton (X) and LP peaks for increasing the excitation fluence. Both peaks exhibit a redshift with increasing power, eventually leading to the collapse of both peaks into a single emission channel. f, Integrated PL intensity as a function of excitation fluence, exhibiting no saturation up to values approaching 10⁹ J cm⁻². g, Full-width at half-maximum (FWHM) values extracted for the exciton peak and LP peak as a function of excitation fluence. The exciton exhibits the expected broadening due to the increased non-radiative processes, whereas on the contrary, for the LP, we observe a reduction in the linewidth.