A reassessment of standard rate equations for low facet reflectivity semiconductor lasers using traveling wave rate equations

A set of traveling wave equations, which are a simple extension of the common rate equations, is used to study the effect of longitudinal gain saturation in Fabry-Perot semiconductor lasers. Analytical solutions are derived which are valid for both low and high Q cavities. A comparison is made to a theory with no spatial dependence. The maximum longitudinal carrier density deviation from the threshold value under lasing conditions is calculated for arbitrary facet reflectivities. It is shown that this deviation leads to linear equations for the emitted output power when compared to a standard rate equation theory. Improved designs for semiconductor lasers are suggested from this analysis.>