Partial differential rate equations for semiconductor lasers

Summary form only given. The numerical integration of a field, polarization, and carrier density with transverse and longitudinal dependence for realistic semiconductor laser parameters is extremely difficult. To get around this problem, we use an approach similar to that outlined in D'Alessandro et al. (1996) to systematically remove the fast time scale from the problem and reduce the system to a new set of rate equations. We have applied this technique of adiabatic elimination to a semiconductor laser model to obtain a new set of rate equations. We have shown that the new equations are a order of magnitude faster to integrate numerically and, at the same time, the evolution of the field and carrier density is extremely close to that of the original model. The price to be paid is that the resultant equations are rather complicated. Close to threshold, however, they resemble the standard rate equations with an added set of spatial derivatives that take into account diffraction, propagation, and the different response of the medium to the different frequency components of the electric field.