A complex‐coupled distributed feedback laser using a novel mechanism for creating a periodic gain is investigated. A one‐dimensional longitudinal analysis is developed to predict the change in the coupling strength when the carrier density is perturbed. Earlier reports have shown that this differential coupling affects the linewidth, with negative differential coupling offering the possibility for the most significant reductions in the linewidth enhancement factor. The analysis predicts that the linewidth enhancement factor can be reduced by about a factor of 2 because of the negative differential coupling for the particular design studied. ©1996 American Institute of Physics.