Figure 1

(Color online) Numerical results of generalized GPE simulations in the absence of disorder for [(a)–(d)] a large ${\sigma }_p=20\mu \mathrm{m}$ and [(e)–(h)] a small ${\sigma }_p=2\mu \mathrm{m}$ circular excitation pump spot, respectively. (a) and (e) give the $(k,E)$ emission pattern, (b) and (f) the polariton distribution in momentum space, (c) and (g) the polariton distribution in real space, and (d) and (h) the local wave vector $k_c\left(r\right)$. The wave vector $k_{c0}$ of a free polariton at ${\omega }_c$ is indicated by the dotted lines in (a), (b), (e), and (f); the dashed line in (g) is the analytical approximations to the density tail, and the dashed lines in (d) and (h) are the LDA predictions to the local wave vector. All quantities in real (momentum) space depend only on the radial coordinate $r=\mid \mathbf{r}\mid$ $(k=\mid \mathbf{k}\mid )$. The values of the parameters used in the simulations are as follows: $\hslash g=0.015\mathrm{meV}\mu {\mathrm{m}}^2$, $\hslash {\gamma }_c=0.5\mathrm{meV}$, $\hslash {\gamma }_R=2\mathrm{meV}$, $\hslash R\left[n_R\right]=\left(0.05\mathrm{meV}\mu {\mathrm{m}}^2\right)\times n_R\hslash g_R=0$, $\mathcal{G}=0.0175\mu {\mathrm{m}}^2$, and $P∕P_{\mathit{th}}=2$ (left panels) and $P∕P_{\mathit{th}}=8$ (right panels).Reuse & Permissions

Figure 2

(Color online) Numerical GPE simulations for a large pump spot in the presence of disorder. (a) Disorder potential (gray scale with $1\mathrm{meV}$ range), polariton distribution in two-dimensional (b) real and (c) momentum space. The arrows in (b) indicate the polariton current. The radius of the dotted circle in (c) is the free polariton wave vector $k_{c0}$. Same parameters as in Figs. 1a, 1b, 1c, 1d.Reuse & Permissions

Figure 3

(Color online) Wigner–Monte Carlo results (full line with error bars) for [(a) and (e)] the momentum space polariton distribution and [(b) and (f)] the $(k,E)$ emission patterns including the noncondensed polaritons for [(a) and (b)] large and [(e) and (f)] small spot sizes, respectively. For comparison, the dashed line shows the mean-field momentum distribution. Same parameters as in the corresponding panels of Fig. 1.Reuse & Permissions