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IEEE Journal of Quantum Electronics

Effect of Inhomogeneous Broadening on Gain and Phase Recovery of Quantum-Dot Semiconductor Optical Amplifiers

Jungho Kim, Christian Meuer, D. Bimberg, G. Eisenstein

Published Sep 8, 2010• 55 citations
Publisher

Abstract

We numerically investigate the effect of inhomogeneous broadening caused by quantum-dot (QD) size fluctuations on the gain and phase recovery of QD semiconductor optical amplifiers (SOAs). We establish 1088 coupled rate equations to simulate the carrier dynamics of the inhomogeneously broadened QD ensembles as inhomogeneous broadening increases. When all the QD ensembles are identical and inhomogeneous broadening becomes zero, eight coupled rate equations are solved for the homogeneous QDs. The gain and phase recovery responses are calculated when an ultrashort pump pulse is injected into a QD SOA. As the inhomogeneous broadening increases, the slow component of the phase recovery at the QD ground state increases due to the enlarged contribution from the slow phase recovery of carrier reservoirs such as the QD excited states. By separately calculating the gain and phase recovery responses of the homogeneous QDs with different sizes, we identify how increasing inhomogeneous broadening affects the enlarged slow phase recovery components from carrier reservoirs. We also demonstrate that the effect of inhomogeneous broadening on the temporal variation of the α-factor is more significant compared to the injection pump power.

DOI
10.1109/jqe.2010.2058793

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We numerically investigate the effect of inhomogeneous broadening caused by quantum-dot (QD) size fluctuations on the gain and phase recovery of QD semiconductor optical amplifiers (SOAs). We establish 1088 coupled rate equations to simulate the carrier dynamics of the inhomogeneously broadened QD ensembles as inhomogeneous broadening increases. When all the QD ensembles are identical and inhomogeneous broadening becomes zero, eight coupled rate equations are solved for the homogeneous QDs. The gain and phase recovery responses are calculated when an ultrashort pump pulse is injected into a QD SOA. As the inhomogeneous broadening increases, the slow component of the phase recovery at the QD ground state increases due to the enlarged contribution from the slow phase recovery of carrier reservoirs such as the QD excited states. By separately calculating the gain and phase recovery responses of the homogeneous QDs with different sizes, we identify how increasing inhomogeneous broadening affects the enlarged slow phase recovery components from carrier reservoirs. We also demonstrate that the effect of inhomogeneous broadening on the temporal variation of the α-factor is more significant compared to the injection pump power.
The gain and phase recovery dynamics of quantum-dot (QD) semiconductor optical amplifiers are calculated, including all the optical transitions involved in successive carrier recovery processes. The carrier recovery dynamics of inhomogeneously broadened QDs is simulated by solving 1088 coupled rate equations. The respective contributions of QD states and quantum-well carrier reservoirs to the gain and phase changes are identified both temporally and spectrally. We show that the slow phase recovery component of the QD ground state is induced by the slow carrier dynamics of the carrier reservoir due to a slowly varying line shape function of the refractive index change.
We numerically investigate the influence of the pump-probe wavelength on the gain and phase recovery dynamics of quantum-dot (QD) semiconductor optical amplifiers (SOAs). The temporal variations of the gain and phase recovery response are calculated at various pump-probe wavelengths, covering the emission wavelength of both the QD ground and excited states. The gain recovery becomes faster at the longer pump-probe wavelength due to the enlarged carrier escape time. The initial phase change turns from a negative to a positive value as the pump-probe wavelength becomes smaller, which is determined by the spectral position of the pump-probe wavelength in reference to the Gaussian-shaped inhomogeneous broadening. The calculated results agree with the previous experimental results measured by other experimental groups.
We numerically investigate the influence of the optical pumping wavelength on the ultrafast gain and phase recovery acceleration of quantum-dot (QD) semiconductor optical amplifiers (SOAs) by solving 1088 coupled rate equations. The temporal variations of the gain and phase recovery response at the ground state (GS) of QDs are calculated at various signal wavelengths when the optical pumping wavelengths at the excited state (ES) of QDs are varied. The phase recovery response is fastest when the wavelength of the signal and pumping beams corresponds to the respective emission wavelength of the GS and the ES in the same size of QDs. The absorption efficiency of the optical pumping beam at the ES is determined by the Lorentzian line shape function of the homogeneous broadening.
In this work, the ultrafast gain dynamics of a quantum dot (QD)-based semiconductor optical amplifier (SOA) is modeled on the basis of semiconductor Bloch equations that include microscopically calculated nonlinear scattering rates between QD carriers and the surrounding carrier reservoir. This enables us to separately study the dynamics of electrons and holes inside the device as well as the coherent effects related to the fast polarization dynamics. We show that the optical pulse power and the dephasing time of the polarization mainly affect the gain depletion inside the active region, while the electric injection current density and thus the internal carrier dynamics influence the gain recovery. We observe that carrier–carrier scattering is the source of desynchronized behavior of electrons and holes in the recovery dynamics of QD-based SOAs. The amplification of pulse trains in the SOA predicted by our model agrees well with experimental data.
The effect of additional optical pumping injection into the ground-state ensemble on the ultrafast gain and the phase recovery dynamics of electrically-driven quantum-dot semiconductor optical amplifiers is numerically investigated by solving 1088 coupled rate equations. The ultrafast gain and the phase recovery responses are calculated with respect to the additional optical pumping power. Increasing the additional optical pumping power can significantly accelerate the ultrafast phase recovery, which cannot be done by increasing the injection current density.
We numerically investigate the effect of the wetting-layer (WL) density of states on the gain and phase recovery dynamics of quantum-dot semiconductor optical amplifiers in both electrical and optical pumping schemes by solving 1088 coupled rate equations. The temporal variations of the ultrafast gain and phase recovery responses at the ground state (GS) are calculated as a function of the WL density of states. The ultrafast gain recovery responses do not significantly depend on the WL density of states in the electrical pumping scheme and the three optical pumping schemes such as the optical pumping to the WL, the optical pumping to the excited state ensemble, and the optical pumping to the GS ensemble. The ultrafast phase recovery responses are also not significantly affected by the WL density of states except the optical pumping to the WL, where the phase recovery component caused by the WL becomes slowed down as the WL density of states increases.