Relaxation oscillation frequency of DFB lasers with gain coupling

Using the spatially-dependent rate equations based on the Green´s function analysis, we investigate the dependency of the relaxation oscillation frequency on the complex coupling coefficient and other parameters of gain-coupled DFB lasers by simultaneously considering spatial-hole-burning, gain saturation and gain compression. An explicit expression for the relaxation oscillation frequency for DFB lasers including the longitudinal spatial effects has been obtained. It is found that antiphase gain-coupling significantly enhances the local effective differential gain in the gain-coupled DFB laser and hence increases the relaxation oscillation frequency. We have also shown for the first time that the modal linewidth enhancement factor α_M plays an important role in determining the relaxation oscillation frequency of gain-coupled DFB lasers, especially when the built-in index coupling is weak