再生锁模激光系统的稳定性及噪声抑制的理论研究
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摘要
本文将准孤子解代入描述再生锁模激光系统的非线性薛定谔方程(Nonlinear Schr?dinger Equation, NLSE),首次推导出了脉冲参量的三个自治微分方程以及无啁啾和有啁啾两种情况下再生锁模激光系统的定态解。然后通过线性稳定性分析和数值模拟,深入探讨了该系统的稳定性,获得了如下一些创新性的理论研究成果。
研究显示,随调制深度、调制频率、群速色散和自相位调制等参量的变化,系统的定态输出随之出现一些很有意义的变化。
数值模拟显示出一个有趣的现象,即当啁啾作为色散的函数并随自相位调制参量变化时,数值模拟曲线中出现两个临界点,在两个临界点之间,啁啾随自相位调制变化的规律与其在两个临界点之外的变化规律相反。这是因为,只有足够大的群速色散补偿,才能抑制自相位调制产生的啁啾;而在两个临界点之间,啁啾在零群速色散附近,此时自相位调制的效应已经远远大于群速色散的效应,所以啁啾就会随着自相位调制的增大而增大。
通过比较调制效应和自相位调制对脉冲压缩和脉冲稳定性的影响发现,调制效应对脉宽的影响要比自相位调制效应对脉宽的影响大得多;调制效应对激光稳定性的影响要比自相位调制效应对激光稳定性的影响小的多。
本文在将噪声参量引入描述再生锁模激光系统的非线性薛定谔方程的基础上,运用孤子微扰理论,推导出了噪声抑制的条件,讨论了孤子的稳定性,首次研究了增益色散效应对噪声抑制以及孤子稳定性的影响。研究结果表明,如果系统参量处于确定的范围内,或者说,如果系统的参量满足推导出的噪声抑制条件,噪声就会被抑制;如果增益色散效应大于调制效应,孤子就是稳定的;如果增益色散效应小于调制效应,孤子就是不稳定的;如果增益色散效应等于调制效应,孤子就是临界稳定的。
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.
研究显示,随调制深度、调制频率、群速色散和自相位调制等参量的变化,系统的定态输出随之出现一些很有意义的变化。
数值模拟显示出一个有趣的现象,即当啁啾作为色散的函数并随自相位调制参量变化时,数值模拟曲线中出现两个临界点,在两个临界点之间,啁啾随自相位调制变化的规律与其在两个临界点之外的变化规律相反。这是因为,只有足够大的群速色散补偿,才能抑制自相位调制产生的啁啾;而在两个临界点之间,啁啾在零群速色散附近,此时自相位调制的效应已经远远大于群速色散的效应,所以啁啾就会随着自相位调制的增大而增大。
通过比较调制效应和自相位调制对脉冲压缩和脉冲稳定性的影响发现,调制效应对脉宽的影响要比自相位调制效应对脉宽的影响大得多;调制效应对激光稳定性的影响要比自相位调制效应对激光稳定性的影响小的多。
本文在将噪声参量引入描述再生锁模激光系统的非线性薛定谔方程的基础上,运用孤子微扰理论,推导出了噪声抑制的条件,讨论了孤子的稳定性,首次研究了增益色散效应对噪声抑制以及孤子稳定性的影响。研究结果表明,如果系统参量处于确定的范围内,或者说,如果系统的参量满足推导出的噪声抑制条件,噪声就会被抑制;如果增益色散效应大于调制效应,孤子就是稳定的;如果增益色散效应小于调制效应,孤子就是不稳定的;如果增益色散效应等于调制效应,孤子就是临界稳定的。
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.
引文
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