Multisoliton regime of pulse generation by lasers passively mode locked with a slow saturable absorber

The passively mode-locked laser1–5 has been a muchstudied device in recent years. Ultrashort-pulse generation in laser systems makes use of a variety of schemes, including figure-of-eight fiber laser design,1 fast saturable absorbers,4 additive-pulse mode locking,5 and nonlinear polarization rotation.6,7 The use of a semiconductor saturable absorber mirror8 with a relatively slow response time and an even slower recovery time has been suggested for a passively mode-locked soliton laser.9 Experimental verification of this possibility has been reported in Ref. 10. Pulse-train generation in passively mode-locked lasers has been observed both in regular11 and chaotic12 regimes. Pulsing behavior with two or three pulses inside the cavity has also been observed.13 Usually multiplepulse generation is suppressed so that there is more energy in a single pulse.14 However, multipulse laser operation could be useful in a number of applications. In this work we make a theoretical study of the multipulse regime of a solid-state laser with a slow saturable absorber. It is common practice3 to model the laser as a distributed system if the pulse shape changes only slightly during each round trip. The pulse evolution is then governed by a modified complex Ginzburg–Landau equation with nonlinear nonconservative terms9,15: