Since the first ruby laser was invented in 1960, lasers have been developing for over forty years. Lasers have been utilized to everywhere in our life because of their good monochromaticity, coherence, directivity and high brightness, and they have been influencing and changing our life continuously. With the rapid development of ultrashort and ultrafast laser technique, more and more attentions have been paid on ultrashort pulse width and ultrahigh energy of pulse peak in many research fields. Lots of research has been done on additive pulse mode locking lasers and Kerr lens mode locking lasers, regeneratively mode locking laser is the same as other lasers, it is one of the best ultrashort pulse sources. Although many papers have been published to report laser systems'steady state pulse output and their stability, the paper on the steady-state output and its stability of regeneratively mode locking system is very little. Besides, laser output tends to be more ultrashort and higher energy, this will lead the nonlinear effects inside of laser system to be stronger. How are these nonlinear effects going to affect the laser output parameters? What kind of condition that the pulse parameters and nonlinear effects have to be satisfied in order to keep the stability of the lasers, and how to suppress the noise in laser systems? In order to answer these questions, it is very meaningful to study the stability and noise suppression of regeneratively mode locking lasers.Three autonomous equations for pulse parameters and their analytical expressions were deduced by substituting quasi-solition solution to Nonliear Schr?dinger Equation (NLSE) of regeneratively mode locking lasers for the first time. The effects of nonlinearity and modulation on pulse parameters and the stability of the pulse are discussed by numerical simulations. The condition for noise suppression was deduced too. All these results provide theoretical basis for future experiments.The main and new results of this thesis are as following:1. Three autonomous equations for pulse parameters were deduced by introducing quasi-solition solution to NLSE of regeneratively mode locking lasers. The steady-state solutions without chirp and with chirp were derived and their stability was analyzed by the method of linear stability analysis. The results demonstrate that the steady-state output parameters of the system evolve with different values of modulation parameters, group velocity dispersion (GVD) and self phase modulation (SPM). Steady-state output can be controlled by modulating the parameters in the systems.2. The analytical expressions of pulse parameters were derived for the first time, to the best of our knowledge. Chirp, pulse duration, bandwidth, and stability are set up as functions of self phase modulation and group velocity dispersion in addition to modulation parameter. The numerical simulations predict an interesting phenomenon which is new, namely, when chirp is a function of dispersion with SPM as a parameter, there are two crucial points in the figure, between these two crucial points, chirp changes with SPM totally reverse from the regularity that chirp obeys outside of these two crucial points. This is because SPM produces a chirp unless compensated by sufficient GVD. Between these two crucial points, GVD is approaching to zero, this means the effect of GVD is very small. Meanwhile, with the increasing of SPM, the effect of SPM is more dominant than that of GVD. That's why chirp increases with the SPM increasing in the regime where it is between these two crucial points. The new phenomenon found by numerical simulations provides theoretical basis to help with controlling chirp in laser systems.3. The criterion for the stability of solitons was deduced. The effects of modulation and SPM on pulse shortening and stability are investigated and compared. The numerical simulations demonstrated that pulse duration decreases with the modulation parameter increasing in both negative and positive GVD regime. In positive GVD regime, pulse width increases with the increasing of SPM. In negative GVD regime, pulse width decreases with the increasing of SPM, but closed to zero GVD, the pulse duration increases with the increase of SPM. The effect of modulation on pulse shortening is much stronger than that of SPM on pulse shortening, and in comparison with SPM, the effect of modulation on laser stability is much weaker. So appreciable pulse shortening seems feasible with the introduction of additional SPM in negative GVD and the adjustment of the modulation parameters.4. The theoretical results showed short pulse durations can be optimized not only with a proper balance of SPM and GVD, but also with proper choice of modulation parameters. Whereas, the improperly balanced SPM and GVD and unsuitable modulation parameters result in pulse broadening or instability. Although our theory has been formulated to describe systems that achieve short duration pulse by using regeneratively mode locking, it can be applied to describe the operation of any laser that uses an actively mode locking. Our numerical studies provide a theoretical basis for using them to optimize system design. It should be possible to develop a versatile ultrashort-pulse generation technology with solid-state medium to achieve short pulse durations that utilize an appreciable fraction of their gain bandwidths. In general, the results are applicable to a wide range of solid-state actively mode locking laser systems. 5. The condition for noise suppression and the stability of soliton were investigated by solving the modified NLSE with a noise term and using soliton perturbation method. The results show that the noise can be suppressed if the parameters are chosen properly, in other words, parameters have to lie within a certain range. Stable solitons can exist in the presence of the modulator and of gain dispersion if the gain dispersion and modulation meet a certain condition. The solitons are stable if the effect of gain dispersion is larger than the effect of modulation; The solitons are unstable if the effect of gain dispersion is smaller than the effect of modulation; the solitons are marginally stable if the effect of gain dispersion is equal to the effect of modulation. In conclusion, in real laser system, as long as the parameters of system are properly chosen, the noise can be contained, then the stability of laser will be improved. |