Fig. 4: Nonlinear response of the IE polariton.
From: Highly nonlinear dipolar exciton-polaritons in bilayer MoS2
a The Hopfield coefficients of the lower IE polariton showing the contributions of cavity photon and the four excitons as a function of k∥. b Experimentally measured blueshift of the IE lower branch as a function of k∥ at a polariton density ~95 μm−2. Here k∥ is converted to cavity Hopfield coefficient using the previous plot. The blueshift of the lower branch of IE (\({{\Delta }}{E}_{{{{{{{{\rm{LP}}}}}}}}}^{{{{{{{{\rm{IE}}}}}}}}}\)) is highest close to the zero-detuning k∥, but the shape looks like a tilted parabola. This can be explained by taking both exciton-exciton interaction and saturation effect into account. Inset shows the theoretically expected dependence of exciton-exciton interaction and saturation effect on ∣C∣. It can be seen that superimposition of these two graphs can explain the tilted parabola shape of \({{\Delta }}{E}_{{{{{{{{\rm{LP}}}}}}}}}^{{{{{{{{\rm{IE}}}}}}}}}\) in our data. c Cartoon showing the IE polariton dispersion at two different excitation powers where the combined effect of exciton-exciton interaction and saturation effect is present. Here, X1 and X2 are the exciton energies at power P1 and P2, respectively. The zero-detuning k∥ increases with increasing power since the exciton blueshifts. Due to the combined effect of exciton blueshift and saturation, the lower IE polariton branch moves more than upper IE polariton branch. d Ratio of estimated saturation nonlinearity and exciton-exciton interaction nonlinearity as a function the IE lower branch polariton density. The error bars in energy represent the uncertainty in determining the peak of the Lorentzian fit (polariton energy) to the reflection data.
