Spin Rings in Semiconductor Microcavities

New effects of self-organization and polarization pattern formation in semiconductor microcavities, operating in the nonlinear regime, are predicted and theoretically analyzed. We show that a spatially inhomogeneous elliptically polarized optical cw pump leads to the formation of a strongly circularly polarized ring in real space. This effect is due to the polarization multistability of cavity polaritons which was recently predicted. The possible switching between different stable configurations allows the realization of a localized spin memory element, suitable for an optical data storage device.

Figure 1

(a) The spinor polariton population $n_{\sigma }$ as a function of pumping intensity $P_{\sigma }$ for a single polariton state. With increasing intensity, the population $n_{\sigma }$ jumps when $P_{\sigma }=P_1$ to the upper branch of the bistability curve. (b) Gaussian pump profile showing the ${\sigma }_{+}$ polarized intensity (black) and ${\sigma }_{-}$ intensity (gray). When $P_{\sigma }$ is greater than $P_1$ (solid part of curves), $n_{\sigma }$ lies on the upper branch of its bistability curve, otherwise (dashed part) it lies on the lower branch.

Figure 2

Polariton field caused by excitation with a Gaussian pump with ${\rho }_c^{\mathrm{pump}}=0.1$. (a) The total intensity of the polariton field in a $0.25\times 0.25\mathrm{mm}$ area in real space at $t=500\mathrm{ps}$ (when quasiequilibrium is established). (b) The corresponding circular polarization degree. (c) The time dependence of the total intensity of a radial slice in real space. (d) Time dependence of the circular polarization degree. Parameters used for (a)–(d): $\tau =3\mathrm{ps}$, ${\alpha }_2/{\alpha }_1=-0.1$, $E_p-E_{\mathrm{LP}}(0)=0.4\mathrm{meV}$, $R=0.17\mathrm{mm}$, $m={10}^{-4}\times m_e$ ($m_e$ is the free electron mass). The pump is switched on at $t=50\mathrm{ps}$. (e) Cross section of the fields (at $t=500\mathrm{ps}$) showing $n_{+}$ (solid line) and $n_{-}$ (dashed line) for the case of finite (black) and infinite effective mass (gray). Vertical lines show the radii at which turning points in the S-shaped curves [shown by spots in Fig. 1b] occur. These can be calculated from Eq. (2) or by using a diagram like Fig. 3 of Ref. 17. (f) The same as (e) but for the case ${\alpha }_2=0$.

Figure 3

Temporal dynamics of the total polariton intensity (a) and circular polarization degree (b) in real space for a polarization switching experiment. A linearly polarized Gaussian pump is turned on at $t=50\mathrm{ps}$. Pulses arrive at 550, 1050, 1550, and 2050 ps, with ${\sigma }_{+}$, ${\sigma }_{-}$, ${\sigma }_{+}$, and ${\sigma }_{-}$ polarizations, respectively. The first two pulses are in phase with the cw pump; the second two are out of phase. The other parameters were identical to those used in Fig. 2.

Figure 4

Intensity of overlapping identically (a) and oppositely polarized spin rings (b) in a $0.4\times 0.2\mathrm{mm}$ region in space. (c),(d) show the corresponding circular polarization degrees. The parameters used were the same as in Fig. 2 but including a disorder potential with a Gaussian correlation length of $2\mu \mathrm{m}$ and a root mean squared value of 0.2 meV.