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Semiconductor Science and Technology

Nonlinear gain dynamics of quantum dot optical amplifiers

Miriam Wegert, Niels Majer, Kathy Lüdge, S. Dommers, Jordi Gomis‐Brescó, Andreas Knorr, U. Woggon, Eckehard Schöll

Published Nov 24, 2010• 29 citations
Publisher

Abstract

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.

DOI
10.1088/0268-1242/26/1/014008

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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 gain recoveries in quantum dot semiconductor optical amplifiers are numerically studied by rate equation models. Similar to the optical pump-probe experiment, the injection of double optical pulses is used to simulate the gain recovery of a weak continuous signal for the QD SOAs. The gain recoveries are fitted by a response function with multiple exponential terms. For the pulses duration of 10 ps, the gain recovery can be described by three exponential terms with the time constants, and for the pulse with the width of 150 fs, the gain recovery can be described by two exponential terms, the reason is that the short pulse does not consume lot of carriers.
Quantum dot (QD)-based semiconductor optical amplifiers offer unique properties compared with conventional devices based on bulk or quantum well material. Due to the bandfilling properties of QDs and the existence of a nearby reservoir of carriers in the form of a wetting layer, QD semiconductor optical amplifiers may be operated in regimes of high linearity, i.e. with a high saturation power, but can also show strong and fast nonlinearities by breaking the equilibrium between discrete dot states and the continuum of wetting layer states. In this paper, we analyse the interplay of these two carrier populations in terms of a simple rate equation model. Based on the steady-state and small-signal properties of the model, we analyse and discuss the optical modulation response and the four-wave mixing properties of QD semiconductor optical amplifiers, in particular emphasizing the role of ultrafast gain dynamics.
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.
We present an analytical description of ultrashort femtosecond pump–probe experiments and investigate the gain response of quantum dot (QD) semiconductor optical amplifiers. The calculation provides a full analytical solution of numerical studies to recent experiments in such structures (Gomis-Bresco et al 2008 Phys. Rev. Lett. 101 256803). Our approach is based on QD Bloch equations, which are analytically evaluated within the third-order temporal perturbation theory (χ (3) level). In particular, we study the influence of the coherence and the population dynamics of two confined QD levels on the gain as a function of the delay time between the pump and the probe pulse. We discuss how to engineer optimal conditions for high-performance QD amplifiers, which are characterized by an ultrafast gain recovery and a pronounced gain depletion.
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.
Gain recovery dynamics are studied in electrically pumped quantum dot (QD) based semiconductor optical amplifiers (SOAs) after amplification of double femtosecond laser pulses using ultrafast pump-probe spectroscopy with heterodyne detection. The authors observe a distinct change in gain recovery in the ground state when a significant excited state population is achieved. A complete gain recovery is found when two 150fs pulses with 5ps time delay pass through the SOA in resonance to the ground state under high injection currents of 80–100mA. The obtained results open the way for ultrafast (>200GHz) operation in p-doped QD based SOAs at 1.3μm telecommunications wavelengths.