Optically Controlled Orbital Angular Momentum Generation in a Polaritonic Quantum Fluid

Applications of the orbital angular momentum (OAM) of light range from the next generation of optical communication systems to optical imaging and optical manipulation of particles. Here we propose a micron-sized semiconductor source that emits light with predefined OAM pairs. This source is based on a polaritonic quantum fluid. We show how in this system modulational instabilities can be controlled and harnessed for the spontaneous formation of OAM pairs not present in the pump laser source. Once created, the OAM states exhibit exotic flow patterns in the quantum fluid, characterized by generation-annihilation pairs. These can only occur in open systems, not in equilibrium condensates, in contrast to well-established vortex-antivortex pairs.

Figure 1

(a) Sketch of cylindrical semiconductor microcavity with distributed Bragg reflector (DBR) mirrors and one (or several) semiconductor quantum wells. (b) Schematic of a four-wave mixing (FWM) scattering process involving two incoming polaritons with orbital angular momentum $m_p$ and two outgoing polaritons (spontaneously created if FWM exhibits instability) with $m_1$ and $m_2$.

Figure 2

The maximum growth rate $\mathrm{\Lambda }$ vs $|{\overline{\psi }}_p^{+}|$. The brackets $(|m|,n)$ indicate the OAM and $n$th 0, respectively. Here, $m=\pm 1,\pm 2,\pm 3,\pm 4$ OAM modes have a positive growth rate. The growth rates of instabilities against radial fluctuation modes (with number of nodes indicated) are shown as grey areas ($n>2$ are stable). We see a range of $|{\overline{\psi }}_p^{+}|$ values (just below $5\mu {\mathrm{m}}^{-1}$) where (4,1) exhibits instability while ${\overline{\psi }}_p^{+}$ is radially stable [cf., Fig. 3].

Figure 3

Left: The polariton density OAM fractions $N_m$ under self-sustained optical parametric oscillation conditions (rounded values indicated in the figure). Spontaneously created modes have OAM (a) $m_1=+2$ and $m_2=-2$, (b) $m_1=+4$ and $m_2=-4$, and (c) $m_1=6$ and $m_2=-4$. Parameters: (a) $m_p=0$, ${\mathrm{\Delta }}_p=0.7\mathrm{meV}$, $\gamma =0.05\mathrm{meV}$, $|{\overline{\psi }}_p^{+}|=4.0\mu {\mathrm{m}}^{-1}$; (b) $m_p=0$, ${\mathrm{\Delta }}_p=1.5\mathrm{meV}$, $\gamma =0.15\mathrm{meV}$, $|{\overline{\psi }}_p^{+}|=5.5\mu {\mathrm{m}}^{-1}$; (c) $m_p=1$, ${\mathrm{\Delta }}_p=2.0\mathrm{meV}$, $\gamma =0.15\mathrm{meV}$, $|{\overline{\psi }}_p^{+}|=5.7\mu {\mathrm{m}}^{-1}$. Right: [(d)–(f)] Corresponding real-space distribution of polariton density $|{\mathrm{\Psi }}^{+}(\mathbf{r}){|}^2$ (units of $\mu {\mathrm{m}}^{-2}$).

Figure 4

The real-space flow pattern given by the normalized current density $\mathbf{j}(\mathbf{r})/|\mathbf{j}(\mathbf{r})|$ (arrows) and the divergence of the current, $\overrightarrow{\nabla }·\mathbf{j}(\mathbf{r})$, shown as a color plot, with units of $\mu {\mathrm{m}}^{-2}{\mathrm{ps}}^{-1}$, for the case of Figs. 3 and 3. The circulation at the origin, here trivially generated by the $m_p=1$ pump, is surrounded by five generation-annihilation pairs that emerge as part of the self-sustained optical parametric oscillation. For additional flow patterns see Supplemental Material [40].