Spatio-temporal characteristics of filamentation in broad-area semiconductor lasers

Using the time dependent rate equations appropriate for semiconductor lasers, we perform a linear stability analysis to derive an analytic expression for the filament gain as a function of the filament spacing, oscillation frequency, linewidth-enhancement factor, pumping level, and nonlinear refractive index. The spatio-temporal characteristics of filamentation are obtained for a given set of operating parameters by maximizing the filament gain. Our theory predicts that there is a critical value of the linewidth-enhancement factor below which broad-area lasers remain stable even at high pumping levels. Moreover, under certain conditions, the self-defocusing Kerr-type nonlinearity can be used to suppress filamentation even when the linewidth-enhancement factor exceeds this critical value.