So far, dissipative temporal solitons in a laser with a saturable absorber have been studied mainly in the context either of Haus's master equation or of the cubic-quintic complex Ginzburg-Landau equation.
We present here a study based on an equation which includes saturation of the amplifier via a cubic approximation and saturation of the absorber at all orders. The equation describes well a system where both gain and absorption are fast, the laser is close to threshold, the unsaturated absorption is small, and the saturation intensity of the amplifier is much larger than that of the absorber. The model is appropriate for fast semiconductor lasers, such as quantum cascade lasers, since it encompasses the relevant phase-amplitude coupling via the linewidth enhancement factors of the gain and absorption media. Our study shows the crucial role played by these factors in the transition from cw emission to various types of pulsed emission, including dissipative temporal solitons.
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