Plethora of soliton-like pulses in passively mode-locked fiber lasers

There is a great interest in soliton generation in actively and passively mode-locked fiber lasers [1, 2, 3, 4]. The mode-locked soliton fiber lasers can generate pulses with a wide range of durations, pulse powers, and repetition rates. Theoretical studies of the soliton fiber lasers are based on the complex Ginzburg-Landau (CGLE). Different forms of this have been used, including the cubic GLE [5], cubic CGLE with saturation [6, 7], quintic CGLE [8, 9, 10, 11, 12], and more complicated models. All these models (except the cubic CGLE without saturation) have solutions in the form of stable pulses. In this study we have found two new forms of pulse-like solutions which have been missed in previous works. In particular, we discover that besides the well-known solution in the form of bell-shaped pulse (plain pulse), and two other forms found in [13], the quintic CGLE has two additional branches of stable stationary solutions in the form of wide composite pulses with a dual-frequency spectrum. These two solutions can co-exist with known pulses but exist for a narrower range of value of the parameters.