Figure 1

PL spectra (top panels) and spatial profiles of pump and filtered signals $|{\psi }_C^s(x,0,t)|$ (bottom panels) for three regimes: (i) OPO (left panels) for a smoothened top-hat pump above threshold ($f_p=1.12f_p^{(\mathrm{th})}$)—polaritons, continuously injected at $(k_p,0)$ and ${\omega }_p$, undergo stimulated scattering into signal and idler stationary steady states (${\kappa }_{X,C}=0.2\mathrm{meV}$). (ii) TOPO (middle panels): A short, ${\sigma }_t=1\mathrm{ps}$, Laguerre-Gauss $m=2$ (top panel) and Gaussian $m=0$ (bottom panel) probe [Eq. (2)] resonant with $(k_{\mathrm{pb}},0)$ and ${\omega }_{\mathrm{pb}}$ triggers propagating signal and conjugate states, which lock to the same group velocity (${\kappa }_X=0$, ${\kappa }_C=0.02\mathrm{meV}$). (iii) Conditions similar to (ii) but ${\kappa }_{X,C}=0.09\mathrm{meV}$ (right panels); now there is no amplification of the probe, and both the signal and conjugate decay exponentially. LP and upper polariton (UP) (blue dashed lines), and bare cavity photon ($C$) and exciton ($X$) dispersions (gray dashed lines) are shown for reference.Reuse & Permissions

Figure 2

Left panel: Group velocity $v_g^s$ of the propagating signal wave packet versus the probe momentum $k_{\mathrm{pb}}$. The black dots are determined from simulations, whereas the solid line (red) is the derivative of the LP dispersion evaluated at $k_{\mathrm{pb}}$, $v_{k_{\mathrm{pb}}}^{\mathrm{LP}}$. The green dashed line indicates where the LP dispersion deviates from the quadratic. Right panel: Signal (solid lines) and conjugate (dashed lines) states for $k_{\mathrm{pb}}=1.4\mu {\mathrm{m}}^{-1}$ at different times after the arrival of the probe.Reuse & Permissions

Figure 3

Profiles of the TOPO signal intensity $|{\psi }_C^s(\mathbf{r},t)|$ and phase ${\varphi }_C^s(\mathbf{r},t)$ (inset) after the arrival (at $t=0$) of an $m=2$ vortex pulsed probe [Eq. (2)] with ${\sigma }_{\mathrm{pb}}\simeq 87\mu \mathrm{m}$. The conditions are the same as the middle panels of Fig. 1, but with $k_{\mathrm{pb}}=0.2\mu {\mathrm{m}}^{-1}$ (a, c) and $k_{\mathrm{pb}}=1.4\mu {\mathrm{m}}^{-1}$ (b, d). While in (a, c) the $m=2$ vortex does not split within its lifetime, in (b, d) the vortex splits soon after the probe arrives. The intensity scale in (c) is 200 times smaller than in (a).Reuse & Permissions

Figure 4

Filtered signal profile and currents above OPO threshold $f_p=1.12f_p^{(\mathrm{th})}$ for a top-hat pump with FWHM ${\sigma }_p=35\mu \mathrm{m}$ at $t=-3\mathrm{ps}$ (left panel) before the arrival of an $m=2$ probe at $t=0\mathrm{ps}$ (right panel). The double quantized vortex splits into two $m=1$ vortices even before the probe reaches its maximum intensity.Reuse & Permissions