Analytical description of gain depletion and recovery in quantum dot optical amplifiers

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.