Fig. 2: Towards large polaritonic nonlinearity under photon-exciton strong coupling.

a Left, Experimentally measured energy-momentum photoluminescence (PL) spectrum (at 6 K) and simulated absorption (Abs) spectrum of a self-hybridized perovskite metasurface with \(\alpha\) = 0.30 and scaling factor = 0.76, showing the strong coupling between the photonic cavity mode and perovskite excitons. LP, lower polariton branch. Right, Simulated reflectance (Reflec) spectrum of a hypothetical perovskite metasurface of the same geometrical parameters but with the exciton resonance turned off (see Supplementary Note 1). b Fitted Hopfield coefficients as a function of momentum for the studied device in (a). A coupled oscillator model is applied to fit the energy-momentum PL spectrum (see “Methods” and Supplementary Note 3). The shaded green and pink backgrounds denote photon-like and exciton-like fractions, respectively. c, d The same as (a, b) respectively, but for another perovskite metasurface with \(\alpha\) = 0.30 and scaling factor = 0.88. e Fitted coupling strengths \(g\) of devices with a fixed asymmetry parameter \(\alpha\) = 0.30 and different scaling factors. f Fitted coupling strengths \(g\) of devices with a fixed scaling factor = 0.88 and different asymmetry parameters \(\alpha\), revealing a maximum at the cavity critical coupling condition. g Theoretical total polaritonic nonlinearity strength as a function of Hopfield coefficient |C| that represents the proportion of photon in the polariton state. |C| can be tuned in the momentum space as shown in (b, d).