High-frequency dynamics of spin-polarized carriers and photons in a laser

The high-frequency dynamics of spin-polarized carriers and photons in a spin laser have been studied. The transient response of the device obtained from the rate equations is characterized by two sets of relaxation oscillations in the carrier and photon distributions corresponding to the two polarization modes. Consequently two distinct resonant peaks are observed in the small-signal modulation response. The calculated transient characteristics indicate that the best results are obtained from a spin laser when only the favored polarization mode, with lower threshold, is operational. Under this condition the small-signal modulation bandwidth is higher than that in a conventional laser, the threshold current is lower and the output polarization can be 100% with appropriate bias conditions, independent of the spin polarization of carriers in the active region. Measurements were made at 230 K on a InAs/GaAs quantum dot spin vertical cavity surface emitting laser. A time-averaged output polarization of 55% is measured with an active region spin polarization of $5–6\mathrm{\%}$. The experimental results are in good agreement with calculated data.

Figure 1

(Color online) Calculated large-signal modulation characteristics of spin laser in presence of a bias step pulse applied at $t=0\text{ns}$, showing temporal variation and relaxation oscillations of (a) photon density, (b) electron density, and (c) output polarization. The output polarization of the spin laser reaches a value of 100% when only the favored mode is lasing and the relaxation oscillations are initiated after the less favored mode attains threshold.

Figure 2

(Color online) Calculated upper limit of relaxation oscillation frequency as a function of current density for the conventional and spin lasers. The oscillation frequency increases with increasing bias for both the polarization modes. The oscillation frequency of the conventional laser always lies in between the two modes of the spin laser.

Figure 3

(Color online) Calculated small-signal frequency response of the spin laser when: (a) the favored polarization mode and (b) both polarization modes are lasing. The response from a conventional laser is also shown for comparison. The spin laser bandwidth increases when only one mode is lasing and decreases when both the modes are lasing; (c) effect of gain compression $\left(\epsilon \right)$ on modulation bandwidth calculated for the spin and conventional lasers and (d) phasor diagram of the polarization modes.

Figure 4

(Color online) (a) Time-averaged output circular polarization $\left({\Pi }_{\text{c}}\right)$ as a function of time for various $t_{\text{on}}$ and $t_{\text{off}}$ of an ideal square pulse bias with zero rise and fall times. ${\Pi }_{\text{c}}$ can be tuned in a wide range by varying the ON and OFF periods. The output circular polarization can be made very high independent of the spin relaxation time in the active region by suitably tuning the pulse width and duty cycle of the bias current; (b) ${\Pi }_{\text{c}}$ calculated and measured for a spin laser with a pulse current bias having finite identical rise and fall times (1.5 ns). The simulations correspond to a quantum dot spin polarization of 6% estimated for a $10\mu \text{m}$ diameter VCSEL measured at 230 K. The filled circles correspond to the time averaged output polarizations measured in these devices.

Figure 5

(Color online) Spin VCSEL heterostructure grown by molecular-beam epitaxy. The $\text{MnAs}/{\text{Al}}_{0.1}{\text{Ga}}_{0.9}\text{As}$ spin injector is formed by epitaxial regrowth.

Figure 6

(Color online) (a) The measured dc light-current characteristics for a $10\mu \text{m}$ mesa diameter spin-VCSEL measured at 230 K in the Faraday geometry. Inset shows threshold current reduction vs applied magnetic field; (b) measured degree of time-average output circular polarization vs $t_{\text{on}}$ of the square pulse bias with rise and fall times of 1.5 ns. The inset shows the value of peak output polarization measured for different values of current bias and the corresponding voltage applied across the device.