Ultrafast spin-polarized lasing in a highly photoexcited semiconductor microcavity at room temperature

We demonstrate room-temperature spin-polarized ultrafast $(\sim 10\mathrm{ps})$ lasing in a highly optically excited GaAs microcavity. This microcavity is embedded with InGaAs multiple quantum wells in which the spin relaxation time is less than 10 ps. The laser radiation remains highly circularly polarized even when excited by nonresonant elliptically polarized light. The lasing energy is not locked to the bare cavity resonance, and shifts $\sim 10\mathrm{meV}$ as a function of the photoexcited density. Such spin-polarized lasing is attributed to a spin-dependent stimulated process of correlated electron-hole pairs. These pairs are formed near the Fermi edge in a high-density electron-hole plasma coupled to the cavity light field.

Figure 1

(a) Laser energy diagram. (b) Schematic of the microcavity structure. The sinusoidal red curves represent the amplitude of the cavity light field. The $z$ axis is the growth direction and is parallel to the wave vector of the pump laser. (c) Pictorial representation of the high-density e-h plasma in the quantum wells embedded in the microcavity. Correlated e-h pairs are formed near the Fermi edge of the e-h plasma as a result of effective coupling to the cavity light field.

Figure 2

Spin-polarized lasing at room temperature. (a) Angle-resolved [$k$-space $(k_X,k_Y)$] luminescence images at the lasing threshold ($P$ = $P_{th}$) for cocircular (${\sigma }^{+}/{\sigma }^{+}$, left panel) and cross-circular (${\sigma }^{+}/{\sigma }^{-}$, right panel) components. Here, ${\sigma }^{\pm }/{\sigma }^{\pm }$ represent the polarization of pump/luminescence, respectively. $P_{th}\approx 2.5\times {10}^8$ photons per pulse (over an area of 80 $\mu {\text{m}}^2$), resulting in a photoexcited density $n_{th}\approx 3\times {10}^{12}{\text{cm}}^{-2}$ per QW per pulse for an estimated absorption of 10% for nine QWs. Insets are the corresponding real space (r space) luminescence images. (b) Energy ($E$) vs in-plane momentum ($k_{\parallel }$) dispersions along the $k_Y$ axis ($k_X=0,k_Y=k_{\parallel }$).

Figure 3

Photoexcited density dependence. (a) Emission flux integrated over $|k_{\parallel }|<3\mu {\text{m}}^{-1}$ under a circularly polarized ${\sigma }^{+}$ pump. (b) The degree of circular polarization (${\overline{\rho }}_c$), determined from the luminescence integrated near $k_{\parallel }\approx 0$ ($|k_{\parallel }|<0.3\mu {\text{m}}^{-1}$) under a ${\sigma }^{+}$ or ${\sigma }^{-}$ circularly polarized pump. The dashed lines are the calculated emission flux and the ${\overline{\rho }}_c$, with a spin-dependent stimulated process assumed (see the Appendix pp2: Rate-equation model).

Figure 4

Time-integrated polarized spectra. (a) 2D false-color images of microcavity luminescence/lasing spectra vs the pump flux for cocircular (${\sigma }^{+}/{\sigma }^{+}$, left panel) and cross-circular (${\sigma }^{+}/{\sigma }^{-}$, right panel) components. Spectra are normalized with respect to the cocircular component (${\sigma }^{+}/{\sigma }^{+}$) for each pump flux. Note that the intensities of the ${\sigma }^{+}/{\sigma }^{-}$ spectra for $0.8P_{th}<P<1.3P_{th}$ (shaded area) are scaled up by a factor of 10. (b) Spectral linewidths $\Delta E$ (FWHM) and peak energies determined from the emission spectra in (a). (c) Selected cocircular time-integrated polarized spectra for $P=0.8P_{th}$ (black), $1.0P_{th}$ (red), and $3.3P_{th}$ (blue). Spectral blueshifts and linewidth broadening with the increasing pump flux can be readily identified in these selected spectra. (d) Polarized time-integrated spectra (blue solid line, cocircular; blue dashed line, cross circular) and spectral $D_{CP}$ [$\overline{\rho }\left(E\right)$, black line] for $P=3.5P_{th}$. The time-integrated spectra reveal an apparent spin-dependent energy splitting of 1–2 meV.

Figure 5

Spin amplification under an elliptically polarized pump. (a) Representation of polarization states (Stokes vectors) in a Poincaré sphere. The pump polarization is varied along the meridian in the $s_1-s_3$ ($x-z$) plane. (b) The time-integrated $D_{CP}$ (${\overline{\rho }}_c$) of the spin-polarized laser radiation as a function of pump $D_{CP}$ (${\rho }_c^p$) (blue line) at $0.8P_{th}$ (black dots), $1.0P_{th}$ (magenta dots), and $1.2P_{th}$ (red dots). (c) External quantum efficiency (${\eta }_{ex}$) vs pump $D_{CP}$ (${\rho }_c^p$, represented by the altitude $\varphi$) at $1.2P_{th}, 1.0P_{th}$, and $0.8P_{th}$. The pump flux is maintained at a constant when ${\rho }_c^p$ is varied. For a specific $\varphi$, only the ${\eta }_{ex}$ of the majority polarized emission component is shown (${\sigma }^{+}$ for $0^{\circ }\le \varphi <{180}^{\circ }$ and ${\sigma }^{-}$ for ${180}^{\circ }\le \varphi <{360}^{\circ }$). ${\eta }_{ex}$ of the minority component is not shown because of a low signal-to-noise ratio for ${\rho }_c^p\sim \pm 1$. Error bars represent the standard deviation of ${\eta }_{ex}$ over five measurements.

Figure 6

Dynamics and energy relaxation. (a) Polarized time-dependent luminescence at $k_{\parallel }=0$ for $P=1.0P_{th}$ under a circularly polarized (${\sigma }^{+}$) pump. Blue (red) curves represent the cocircular $I^{+}\left(t\right)$ [cross-circular $I^{-}\left(t\right)$] components. Note that the cross-circular component shown at $P=P_{th}$ is multiplied by a factor of 100. The time zero is determined from the instrument response (black dashed curve), which is measured via pump laser pulses reflected off the sample surface. The time traces are spectrally integrated (temporal resolution $\approx 5$ ps). (b) Same as (a) but for $P=0.8P_{th}$. (c) Temporally and spectrally resolved streak spectral images of the cocircular component $I^{+}(\delta E,t)$ at $P=1.0P_{th}, 2.0P_{th}$, and $4.0P_{th}$. The $y$ axis ($\delta E$) is offset with respect to 1.408 eV, the lasing energy at $P_{th}$. The temporal resolution is $\approx 30$ ps because of the grating-induced dispersion.

Figure 7

Microcavity sample characterization. (a) $E$ vs $k_{\parallel }$ dispersions for the TE (left) and TM (right) modes under a circularly polarized pump at 1.579 eV and $P=0.6P_{th}$. The photoexcited density at $P_{th}$ is $\sim 2–3\times {10}^{12}{\text{cm}}^{-2}$ per quantum well per pulse. The simulated TE and TM dispersions are shown as magenta and black curves, respectively. The TE-TM energy splitting is less than 50 $\mu \text{eV}$ at $k_{\parallel }=0$, allowing the effective control of lasing polarization by optical pumping. (b) To determine the density-dependent spectral characteristics of PL in the InGaAs/GaAs MQWs, we measure the time-integrated and time-resolved PL in the sample, with the top DBR mirror layers removed, by selective wet etching [70]. PL spectra at $P=0.2$ (blue), 0.6 (magenta), and 1 $P_{th}$ (green) in the absence of the top DBR mirrors. Here, PL is attributed to the spontaneous radiative recombination of photoexcited carriers in the InGaAs/GaAs MQWs. The dual PL spectral peaks are attributed to the first- and second-quantized energy levels in the MQWs, respectively. The QW band gap ($E_g^{\prime }$) corresponds to the ground state, the transition between the first-quantized energy levels of the electron and the heavy-hole ($e1-hh1$). $E_g^{\prime }$ can decrease with the increasing photoexcited density (band gap renormalization). $\mu$ can be deduced from the PL from the excited state (second-quantized levels, $e2-hh2$ transition). With an increasing density, $E_g^{\prime }$ redshifts slightly because of band gap renormalization, whereas $\mu$ blueshifts considerably ($\sim 10$ meV) as a result of phase space filling (Pauli blocking) at a high photoexcited density ($\gtrsim {10}^{12}{\text{cm}}^{-2}$ per QW). (c) Normalized PL spectra near 1.40 eV, displaying a significant spectral blueshift of 15–20 meV with the increasing photoexcited density ($0.1P_{th}$ to $2P_{th}$).

Figure 8

Reflectance and laser spectral characteristics. (a) Reflectance spectrum at $k_{\parallel }=0$ from the front surface of a microcavity sample with 1.405 eV lasing energy at the threshold: measured (black solid line) and simulated (orange solid line). This sample is an as-grown sample not subject to a rapid thermal annealing process. The simulation is performed via a transfer matrix method, including the optical absorption in the GaAs layers, but excluding the complex dielectric constant of excitons (e-h pairs) in MQWs. The cavity resonance ($E_c$) is about 1.41 eV. (b) Emission spectra at $k_{\parallel }=0$ at pump $P=0.3P_{th}$ and $1.0P_{th}$. Above the threshold, luminescence is dominated by the lasing mode (red curve). (c) Spectral peak energy as a function of pump flux (photoexcited density) for emission peaks I, II, and III as indicated in (b). The vertical black and red dashed lines indicate $P=0.3P_{th}$ and $1.0P_{th}$, respectively. Emission peaks I and III correspond to a reflection minimum with energy below and above the reflection stop band, whereas peak II is near the cavity resonance. Peaks I and III experience less than 2 meV spectral shifts with an increasing pump flux. By contrast, peak II blueshifts by more than 10 meV for the same density range, a result indicating a strong optical nonlinearity induced by the coupling between the high-density e-h plasma and the cavity light field.

Figure 9

Transient lasing spectra at $P=4P_{th}$. Cross-sectional transient spectra at specified time delays extracted from the temporally and spectrally resolved streak images of the sample. Transient spectra are averaged over 5 ps and normalized to the maximal peak intensity of the cocircular component. The spectra are equally scaled but offset vertically by 1. Red lines represent the cocircular (${\sigma }^{+}/{\sigma }^{+}$) component, whereas blue lines represent the cross-circular (${\sigma }^{+}/{\sigma }^{-}$) one. The energy scale is measured with respect to 1.408 eV, which is the peak lasing energy at the threshold $P_{th}$. In the initial time delay of a few picoseconds after pulse excitation, the emission is spectrally broad and blueshifts by about 5 meV. For delays less than 20 ps, the co- and cross-circular components have the same spectral peak energy (vertical dashed lines), and this suggests that carrier interactions with the same spins and opposite spins are in a comparable magnitude. The spectral peak energy is determined by the total carrier density instead of individual spin-up or spin-down populations. On the other hand, the intensity of the cocircular component is higher than that of the cross-circular component within 20 ps after pulse excitation because the ineffective spin flipping in the reservoir results in an imbalanced spin population. The emission spectrum reaches a maximum at about 10 ps, and then gradually decreases in overall magnitude and redshifts with time. The temporal energy redshift in spectra is attributed to a descending chemical potential $\mu$ with a decreasing carrier density.

Figure 10

Spin-dependent stimulation. (a) Calculated stationary $D_{CP}$ ($\overline{{\rho }_c}$) with varying pump polarization ${\rho }_c^p$ (represented by the altitude) for $P=0.8P_{th}, 1.0P_{th}$, and $1.2P_{th}$. (b),(c) Calculated polarized time-dependent radiation intensity for cocircular ${\sigma }^{+}/{\sigma }^{+}\left[I^{+}\left(t\right)\right]$ and cross-circular ${\sigma }^{+}/{\sigma }^{-}\left[I^{-}\left(t\right)\right]$ components under a ${\sigma }^{+}$ pump for $P=1.0P_{th}$ and 2.0 $P_{th}$. The theoretical $P_{th}$ is set to the pump flux when the stationary ${\overline{\rho }}_c=0.5$ under a fully circularly polarized pump (${\rho }_c^p=1$).