Maxwell–Bloch Equation Approach for Describing the Microscopic Dynamics of Quantum-Dot Surface-Emitting Structures

We present a theoretical investigation of the optical properties of an electrically pumped surface-emitting structure composed of quantum dot (QD) layers as active medium and Bragg reflectors. The electric field propagation and the carrier dynamics of QDs embedded into a 2-D wetting layer (WL) are calculated using QD-WL Maxwell-Bloch equations. The equations are evaluated using the finite-difference time-domain (FDTD) method. To provide a detailed understanding of the carrier dynamics, microscopically calculated Coulomb scattering rates as well as the dephasing time are incorporated into the equations. The approach is applied to investigate the normal mode coupling as a function of the WL carrier densities. The mode splitting only appears at small WL carrier densities within strong coupling regime where Coulomb scattering is of minor importance. The transmission is studied as a function of the pump pulse intensity. At high intensities, saturation or inversion of the optically active QD levels is reached resulting in an enhanced transmission. Furthermore, the switch-on dynamics of the vertical cavity surface-emitting laser (VCSEL) with a time-dependent injection current is calculated. It is shown to be characterized by strongly damped electric field. We find a characteristic lasing delay time accounting for the time charge carriers need to scatter from bulk WL states into QD states and to relax radiatively.