A full-time-domain approach to spatio-temporal dynamics of semiconductor lasers. I. Theoretical formulation

In this first part of a two-part article we derive and discuss a novel theory for the (coupled) spatio-temporal light-field and carrier dynamics of novel semiconductor lasers. Our microscopic, spatially resolved model combines a density matrix description of the optoelectronic properties of quantum well gain media with the full-time-domain Maxwell equations for the electromagnetic (i.e. the coupled electric and magnetic) field dynamics. The full-time-domain Maxwell semiconductor Bloch equations take into account many-particle interactions, a diversity of time scales and gain saturation mechanisms, and grasp, in particular, the fast-oscillating carrier wave dynamics as well as the field dynamics with a subwavelength spatial resolution. This provides a new basis for the modelling of the dynamics of ultrafast carrier effects and optical nonlinearities in quantum well lasers, the engineering of the mode structure in microcavities, and the study of their impact on the laser emission characteristics. Optical dephasing and carrier and energy redistribution due to the screened Coulomb interaction and scattering with phonons are explored in detail.