机械调Q二氧化碳激光器的动力学分析
摘要
本论文的工作主要分为三部分，首先是用机械调Q的方法对一台选支纵向激励二氧化碳激光器进行Q调制，得到激光器的脉冲输出；其次对这台脉冲二氧化碳激光器在谐振腔的稳定性方面进行实验和理论研究；最后用二能级速率方程和四能级振转模型对这台脉冲二氧化碳激光器的动力学过程进行了理论分析，并着重研究了参与激光过程的转动能级对理论分析的影响，通过理论与实验相模拟的方法我们确定了本台二氧化碳激光器的动力学参数。
第一部分用机械调Q的方法对一台选支纵向激励二氧化碳激光器进行Q调制,实现机械Q调制的装置是一部转速可达12000转/分的微型高速电机和一片超薄铝箔，具体的实验装置图如图一。我们可以得到峰值功率超过一千瓦，脉冲宽度为200纳秒左右的脉冲序列，在降低电机转速的情况下，峰值功率将降低，脉冲将加宽。
Grating
Chopper Focusing mirrors:M1,M2 ZnSe window Laser tube Output mirror
图一 机械调Q选支CO2激光原理图
第二部分对这台脉冲二氧化碳激光器在谐振腔的稳定性方面进
行实验和理论研究。实验方面，对脉冲二氧化碳激光器谐振腔的稳定性以及相应的输出功率随距焦镜等间距变化情况进行了研究。图二和图三分别给出了连续状态下二氧化碳激光器和脉冲状态下二氧化碳激光器随距焦镜等间距变化情况。
图二 连续功率随L变化图
理论方面，在对这台脉冲二氧化碳激光器设计原理研究的基础上，运用了二氧化碳激光器基本原理和光学谐振腔传播矩阵理论，对以上的实验现象进行了计算和分析。图四给出了二氧化碳激光器腔的稳定及功率分布图，图中的双曲线为腔稳定的分界线。在两条双曲线间的部分为
图三 脉冲功率随L变化图
稳定区域，处在这些区域的谐振腔都是稳定的,而处于其它区域，这种腔则是不稳定的。上图中的这条竖线实质是一条曲线，它是以g1，g2随L变化的关系曲线，由于g1变化很小并且扩大了g1的横坐标，所以在上图中看不出曲线分布。图中的曲线为本台二氧化碳激光器在连续工作状态下的功率随L变化的曲线，实质是连续功率随L变化图在此稳定图上的表示。图中的M点所对应的是本台二氧化碳激光器在连续工作状态下，所产生的最大功率8.8W，此时L改变了0.02㎜。从上图可以看出在稳定区域内功率是最大的，在非稳定区域内达到最小功率，在非稳区域内的最小到稳定区域内的最大，功率逐渐在递增，当功率达到最大（M所对应的点）之后，功率在逐渐递减，通过上述的实验数据分析得到了与理论分析相符合的结果。
图四 二氧化碳激光器腔的稳定及功率分布图
本文最后用二能级速率方程和四能级振转模型对这台脉冲二氧化碳激光器的动力学过程进行了理论分析，并着重研究了参与激光过程的转动能级对理论分析的影响，通过理论与实验相模拟的方法我们确定了本台二氧化碳激光器的动力学参数，并证明了对于描述脉冲二氧化碳激光器的动力学过程，振转模型要比速率方程准确的多。最终，我们得到了与实验结果符合得很好的理论曲线。
图五为二氧化碳分子中与激光相关的能级结构。能级1和2 是激光能级，J表示转动能级中参与激光动力学过程的能级个数，和分别代表向振动能级的正向和反向的弛豫速率。如果不考虑转动能级的作用,四能级振-转模型将转化为二能级速率方程。
我们通过龙格—库塔法来解这个动力学模型的数值解，以此来研究脉冲二氧化碳激光器的输入参数对输出脉冲的影响。因为参与激光过程的转动能级的个数J对激光脉冲有很大的影响，因此我们分别取了几
图五 二氧化碳分子中与激光相关的能级结构
个J的值来进行比较，如图六所示。当J=0时，四能级的振转模型转变为二能级模型，通过理论计算的曲线我们可以清楚地看到二能级速率模型与四能级振转模型的两个主要的区别：一个FWHM(激光脉冲的全波半高宽)，从二能级模型解出来的理论曲线的全波半高宽与实验结果相比明显要窄的多；另外一个区别是激光脉冲的拖尾，非常明显由振转模型解出来的理论曲线要与实验相符的多。由此可得出证明：在描述机械调Q脉冲二氧化碳激光器方面，引入转动能级与振动能级耦和的四能级振转模型要比二能级速率方程准确的多。
由于上下能级粒子数差的衰减速率和转动能级向激光能级的衰减数率(J+1)是由经验公式获得的，所以在描述二氧化碳激光的调Q动力学过程不一定是非常准确的，因此我们可以适当改变这两个动力学参数已得到与实验结果相符的理论曲线，相反也是通过理论与实验模拟的方法来确定本台脉冲二氧化碳激光器的动力学参数。通过大量的拟合，最终取=2.0×105 s-1,(J+1)=2.0×108 s-1最适合，取J=25,得到理论与实验符合最好的曲线，如图七。
到此为止，我们对二氧化碳激光器的Q调制；腔的稳定性分析及动力学分析进行了深入的研究，我们把研究的重点放在了实验同理论的拟合对比上面，毕竟实验数据同理论的统一才是对物理现象的最好掌握。本研究有两个重要的意义，一个是为下一步利用这台脉冲二氧化碳激光器作其它实验奠定了理论与实验基础；另一个是关于激光器动力学研究方面，我们这
This thesis is composed of three parts, the first part is setting up a mechanical Q-switched CO2 laser. The second part is the theoretical and experimental study of the stability of this laser. The last part is that We made a theoretical analysis for kinetic processes of the Q-switched CO2 laser. We put special emphasis on the effect of the non-laser vibro-rotational levels on describing the dynamic processes of this laser. The calculated pulse waveforms based on the vibro-rotational model are in good agreement with the experiment.
The first part is that we get the short laser pusle by using the mechanical Q-switched methed. A fast chopper with the rotation rate of 12000r/m is used to set up a mechanical Q-switched CO2 laser. The structure of mechanical Q-switched CO2 laser is shown in Fig.1. The repetition rate of the laser pulse we get is from 100 to 800Hz, the maximum peak power is 1152 W, with a pulse duration of about 200ns. The tailing phenomenon is obvious.
The second part is the theoretical and experimental study of the stability of this laser. In the experiment, we study the changes of the output power when we shift the situation the focus mirrors with the same distance. Fig2 and Fig3
Grating
Chopper Focusing mirrors:M1,M2 ZnSe window Laser tube Output mirror
Fig.1 the structure of mechanical Q-switched CO2 laser
are the output power of the CW CO2 laser and the Q-switched laser respectively when we changed the situation of the focus mirrors.
Fig2. the output power variation of CW laser vs the situation of the focus mirrors
Fig3. the output power variation of pulse laser vs the situation of the focus mirrors
In the theoretical analysis, the basic theory of the CO2 laser and the theory of optical transmission matrix. Fig4 is the power distribution and the stability of the CO2 laser.
In Fig4, the hyperbolic curve is the dividing line of the stability of the laser cavity. The part between the two hyperbolic curves is the stable area, the resonant cavity in the area is stable, or is unstable. The vertical line in Fig4 is a curve actually, it is the variations g1 and g2 byL. The point M is the maximum output power of the CW laser, it is 8.8W, L is changed 0.02㎜. We can find that the output power in the stable area is larger than the unstable
Fig4 the power distribution and the stability of the CO2 laser.
area.From the unstable area to the stable area , and then to the unstable area again, the output power is from the minimum to the maximum point M, and then became small and small. It gives a good agreement with the theoretical analysis.
In the last part , we made a theoretical analysis for kinetic processes of the Q-switched CO2 laser. We put special emphasis on the effect of the non-laser vibro-rotational levels on describing the dynamic processes of this laser. We determined the dynamic parameters of this Q-switched CO2 laser by the fitting of the experimental and the theoretical analysis results. It is clear that the simple two-level atom model is too constrained to describe the behavior of such laser, and the four-level model using center-manifold techniques seems to be a particularly attractive candidate model for describing
it. The effect of the rotational levels involved in the population dynamics of the two relevant vibrational levels with the same relaxation rate on the output pulse is obvious and the calculated pulse waveform of the Q-switched CO2 laser is consistent with the experiment.
Fig5 is the structure of the CO2 laser energy level, the level one and two are the laser level, J is the number of rotational levels involved in the population dynamics of the two relevant vibrational levels and denotes the cross relaxation rate of each rotational sublevel into the lasing sublevel of the corresponding vibrational manifold
Fig.5 Energy level structure related with laser dynamics for a CO2 molecule.
The numerical calculation of this model can be achieved by using Runge-Kutta method, which allows o
第一部分用机械调Q的方法对一台选支纵向激励二氧化碳激光器进行Q调制,实现机械Q调制的装置是一部转速可达12000转/分的微型高速电机和一片超薄铝箔，具体的实验装置图如图一。我们可以得到峰值功率超过一千瓦，脉冲宽度为200纳秒左右的脉冲序列，在降低电机转速的情况下，峰值功率将降低，脉冲将加宽。
Grating
Chopper Focusing mirrors:M1,M2 ZnSe window Laser tube Output mirror
图一 机械调Q选支CO2激光原理图
第二部分对这台脉冲二氧化碳激光器在谐振腔的稳定性方面进
行实验和理论研究。实验方面，对脉冲二氧化碳激光器谐振腔的稳定性以及相应的输出功率随距焦镜等间距变化情况进行了研究。图二和图三分别给出了连续状态下二氧化碳激光器和脉冲状态下二氧化碳激光器随距焦镜等间距变化情况。
图二 连续功率随L变化图
理论方面，在对这台脉冲二氧化碳激光器设计原理研究的基础上，运用了二氧化碳激光器基本原理和光学谐振腔传播矩阵理论，对以上的实验现象进行了计算和分析。图四给出了二氧化碳激光器腔的稳定及功率分布图，图中的双曲线为腔稳定的分界线。在两条双曲线间的部分为
图三 脉冲功率随L变化图
稳定区域，处在这些区域的谐振腔都是稳定的,而处于其它区域，这种腔则是不稳定的。上图中的这条竖线实质是一条曲线，它是以g1，g2随L变化的关系曲线，由于g1变化很小并且扩大了g1的横坐标，所以在上图中看不出曲线分布。图中的曲线为本台二氧化碳激光器在连续工作状态下的功率随L变化的曲线，实质是连续功率随L变化图在此稳定图上的表示。图中的M点所对应的是本台二氧化碳激光器在连续工作状态下，所产生的最大功率8.8W，此时L改变了0.02㎜。从上图可以看出在稳定区域内功率是最大的，在非稳定区域内达到最小功率，在非稳区域内的最小到稳定区域内的最大，功率逐渐在递增，当功率达到最大（M所对应的点）之后，功率在逐渐递减，通过上述的实验数据分析得到了与理论分析相符合的结果。
图四 二氧化碳激光器腔的稳定及功率分布图
本文最后用二能级速率方程和四能级振转模型对这台脉冲二氧化碳激光器的动力学过程进行了理论分析，并着重研究了参与激光过程的转动能级对理论分析的影响，通过理论与实验相模拟的方法我们确定了本台二氧化碳激光器的动力学参数，并证明了对于描述脉冲二氧化碳激光器的动力学过程，振转模型要比速率方程准确的多。最终，我们得到了与实验结果符合得很好的理论曲线。
图五为二氧化碳分子中与激光相关的能级结构。能级1和2 是激光能级，J表示转动能级中参与激光动力学过程的能级个数，和分别代表向振动能级的正向和反向的弛豫速率。如果不考虑转动能级的作用,四能级振-转模型将转化为二能级速率方程。
我们通过龙格—库塔法来解这个动力学模型的数值解，以此来研究脉冲二氧化碳激光器的输入参数对输出脉冲的影响。因为参与激光过程的转动能级的个数J对激光脉冲有很大的影响，因此我们分别取了几
图五 二氧化碳分子中与激光相关的能级结构
个J的值来进行比较，如图六所示。当J=0时，四能级的振转模型转变为二能级模型，通过理论计算的曲线我们可以清楚地看到二能级速率模型与四能级振转模型的两个主要的区别：一个FWHM(激光脉冲的全波半高宽)，从二能级模型解出来的理论曲线的全波半高宽与实验结果相比明显要窄的多；另外一个区别是激光脉冲的拖尾，非常明显由振转模型解出来的理论曲线要与实验相符的多。由此可得出证明：在描述机械调Q脉冲二氧化碳激光器方面，引入转动能级与振动能级耦和的四能级振转模型要比二能级速率方程准确的多。
由于上下能级粒子数差的衰减速率和转动能级向激光能级的衰减数率(J+1)是由经验公式获得的，所以在描述二氧化碳激光的调Q动力学过程不一定是非常准确的，因此我们可以适当改变这两个动力学参数已得到与实验结果相符的理论曲线，相反也是通过理论与实验模拟的方法来确定本台脉冲二氧化碳激光器的动力学参数。通过大量的拟合，最终取=2.0×105 s-1,(J+1)=2.0×108 s-1最适合，取J=25,得到理论与实验符合最好的曲线，如图七。
到此为止，我们对二氧化碳激光器的Q调制；腔的稳定性分析及动力学分析进行了深入的研究，我们把研究的重点放在了实验同理论的拟合对比上面，毕竟实验数据同理论的统一才是对物理现象的最好掌握。本研究有两个重要的意义，一个是为下一步利用这台脉冲二氧化碳激光器作其它实验奠定了理论与实验基础；另一个是关于激光器动力学研究方面，我们这
This thesis is composed of three parts, the first part is setting up a mechanical Q-switched CO2 laser. The second part is the theoretical and experimental study of the stability of this laser. The last part is that We made a theoretical analysis for kinetic processes of the Q-switched CO2 laser. We put special emphasis on the effect of the non-laser vibro-rotational levels on describing the dynamic processes of this laser. The calculated pulse waveforms based on the vibro-rotational model are in good agreement with the experiment.
The first part is that we get the short laser pusle by using the mechanical Q-switched methed. A fast chopper with the rotation rate of 12000r/m is used to set up a mechanical Q-switched CO2 laser. The structure of mechanical Q-switched CO2 laser is shown in Fig.1. The repetition rate of the laser pulse we get is from 100 to 800Hz, the maximum peak power is 1152 W, with a pulse duration of about 200ns. The tailing phenomenon is obvious.
The second part is the theoretical and experimental study of the stability of this laser. In the experiment, we study the changes of the output power when we shift the situation the focus mirrors with the same distance. Fig2 and Fig3
Grating
Chopper Focusing mirrors:M1,M2 ZnSe window Laser tube Output mirror
Fig.1 the structure of mechanical Q-switched CO2 laser
are the output power of the CW CO2 laser and the Q-switched laser respectively when we changed the situation of the focus mirrors.
Fig2. the output power variation of CW laser vs the situation of the focus mirrors
Fig3. the output power variation of pulse laser vs the situation of the focus mirrors
In the theoretical analysis, the basic theory of the CO2 laser and the theory of optical transmission matrix. Fig4 is the power distribution and the stability of the CO2 laser.
In Fig4, the hyperbolic curve is the dividing line of the stability of the laser cavity. The part between the two hyperbolic curves is the stable area, the resonant cavity in the area is stable, or is unstable. The vertical line in Fig4 is a curve actually, it is the variations g1 and g2 byL. The point M is the maximum output power of the CW laser, it is 8.8W, L is changed 0.02㎜. We can find that the output power in the stable area is larger than the unstable
Fig4 the power distribution and the stability of the CO2 laser.
area.From the unstable area to the stable area , and then to the unstable area again, the output power is from the minimum to the maximum point M, and then became small and small. It gives a good agreement with the theoretical analysis.
In the last part , we made a theoretical analysis for kinetic processes of the Q-switched CO2 laser. We put special emphasis on the effect of the non-laser vibro-rotational levels on describing the dynamic processes of this laser. We determined the dynamic parameters of this Q-switched CO2 laser by the fitting of the experimental and the theoretical analysis results. It is clear that the simple two-level atom model is too constrained to describe the behavior of such laser, and the four-level model using center-manifold techniques seems to be a particularly attractive candidate model for describing
it. The effect of the rotational levels involved in the population dynamics of the two relevant vibrational levels with the same relaxation rate on the output pulse is obvious and the calculated pulse waveform of the Q-switched CO2 laser is consistent with the experiment.
Fig5 is the structure of the CO2 laser energy level, the level one and two are the laser level, J is the number of rotational levels involved in the population dynamics of the two relevant vibrational levels and denotes the cross relaxation rate of each rotational sublevel into the lasing sublevel of the corresponding vibrational manifold
Fig.5 Energy level structure related with laser dynamics for a CO2 molecule.
The numerical calculation of this model can be achieved by using Runge-Kutta method, which allows o
引文
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M. A. Kovacs, G. W. Flynn, and A. Javan, Appl. Phys Letters,8, 62(1966).
Dietrich Meyerhofer, IEEE J. Quant. Electron, 4, 7621(1968).
T. J. Bridges, Appl. Phys. Letters, 9,174(1966).
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A. Szoke, V. Daneu and J. Goldhar, Appl. Phys. Letters, 15, 376(1969).
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