Dark solitons of the power-energy saturation model: application to mode-locked lasers

The generation and dynamics of dark solitons in mode-locked lasers is studied within the framework of a nonlinear Schrodinger equation which incorporates power-saturated loss, as well as energy-saturated gain and filtering. Mode-locking into single dark solitons and multiple dark pulses are found by employing different descriptions for the energy and power of the system defined over unbounded and periodic (ring laser) systems. Treating the loss, gain and filtering terms as perturbations, it is shown that these terms induce an expanding shelf around the soliton. The dark soliton dynamics are studied analytically by means of a perturbation method that takes into regard the emergence of the shelves and reveals their importance.