Fig. 3

Excitation dispersion relations. Measured DR \(\hslash \omega (\theta )\) as obtained from the numerical analysis of the EPL (solid colored lines) for WPA (a) and WPB (f). Four states of the fluids are shown according to their position along \({I}_{0}(P)\) (plotted in Fig. 2a for WPA): “0” is the free-particle DR (green line), “1” is a lower branch state of \({I}_{0}(P)\) (blue), “2” and “3” are two upper branch states (red and magenta). The calculated free polariton DR is the thick light green line underneath the measured one. b, d and g, i are zoomed in plots of DR “2” (narrow red line) and “3” (narrow magenta line) of WPA and WPB, respectively, in units of condensate excitation energy \(\hslash {\omega }_{{\rm{e}}}=\hslash \omega -\hslash {\omega }_{{\rm{l}}}\). The \(95 \% \) confidence interval amplitude (CI) of the measured DRs is shown for each DRs in panels c, h and e, j for WPA and WPB, respectively, with the same color codes. The theoretical DRs in the rigid blueshift limit (dashed black line) and in the GGPE limit (blue dashed line) are shown in b, d, g, and i. The full vectorial theory is also shown as a thick red and magenta lines visible underneath the measured DR; the line thickness represents the 95% confidence interval of the fitting procedure with the data. In each panels, the laser energy and angular spread are shown as a red segment, and the vertical blue line shows the angle of excitation. The hatched rectangle is the spectral range rejected by the notch filter in a and f