Abstract
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.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. Self-assembled quantum dots (QDs) are considered to be excellent candidates for applications such as optical amplifiers in ultrafast ethernet networks. They show a picosecond gain recovery time, which is much faster than in conventional amplifiers. This can be ascribed to the presence of the two-dimensional wetting layer, which acts as a charge carrier reservoir, enabling fast refilling of QD states. The aim of this work is to investigate optimal conditions for high-performance QD optical amplifiers, i.e. in particular to achieve ultrafast gain recovery even for high repetition frequencies.
Main results. Within the formalism of the density matrix theory and a third-order temporal perturbation theory, we provide a microscopical, analytical description of the gain response in such devices. We include microscopically calculated Coulomb scattering rates, which describe Auger processes between the wetting layer and QD states. We find that on the picosecond timescale, the gain follows the population dynamics. As a result, the gain recovery is determined by the Coulomb-induced population decay time, T1, see right figure. The shorter T1, the more complete is the gain recovery. Optimizing scattering channels, e.g. by increasing current, using smaller QDs with stronger confinement, or increasing the temperature, leads to an acceleration of gain recovery.
Wider implications. The analytical results obtained can be used to identify optimal conditions for QD amplifiers to achieve an ultrafast gain recovery and a pronounced gain depletion.
Figure. The left figure shows the gain as a function of the pump–probe delay time. The right figure illustrates the gain recovery as a function of the decay time, T1, dephasing time, T2, and the pump pulse width, α.