FDTD simulation of the nonlinear gain dynamics in active optical waveguides and semiconductor microcavities

We use the finite-difference time-domain (FDTD) solution of the full-wave vectorial Maxwell-Bloch equations for a two-level quantum system developed earlier , to investigate the nonlinear gain spatio-temporal dynamics of active optical waveguides and semiconductor microcavities. The numerical model has been successfully validated against density matrix theory of gain saturation in homogeneously broadened two-level quantum systems for optical waveguides containing resonant gain nonlinearities. The semiclassical equations have been extended employing the Langevin formalism to account for the quantum noise and the spontaneous emission. We have numerically demonstrated the time evolution of the coherent oscillations build up at the output laser facet identifying the lasing threshold and the fast relaxation oscillations until the settlement of a steady-state emission. Our simulation predictions of the lasing wavelength in a number of vertical-cavity surface-emitting laser geometries, when the spontaneous emission is the only source of radiation, agree very well with standard results and, thus, allow us to infer and subsequently optimize important emission characteristics, such as the spontaneous emission rate, the laser line shape, and the relaxation oscillation frequencies and decay rates.