射频板条CO_2激光器的光束特性及其热稳定性研究
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摘要
光束特性及其热稳定性是高功率射频板条CO_2激光器中的重要理论问题和关键工程问题。本文研究了射频板条CO_2激光器的输出光束特性和腔内模式与损耗特性，射频板条电极的温度场与热变形问题、窗口镜的热畸变问题，热稳定性对光束特性的影响，并对射频板条选支CO_2激光器这一新的应用分支进行了探讨。主要研究内容如下：
（1）在一维非稳腔与一维波导腔的理论基础上，针对百瓦级射频板条CO_2激光器设计了正支非稳-波导混合腔，采用分离变量法分析了光束在波导与非稳两个方向的输出模式及传输特性。实验测量了输出光束近场远场分布及激光谐振腔的功率失调特性。研究表明输出光束在非稳方向呈近似的准直输出，硬边衍射效应对光场分布有着明显影响；波导方向为近似的基模输出，发散角为12mrad。
（2）从非稳腔的模式交叉特性入手，结合Collins公式与光学ABCD矩阵方法，将特征向量法的应用推广到非稳腔，计算过程中没有对腔镜的横向尺寸进行任何近似。采用该扩展的特征向量法分别对非对称和非共焦这两种不规则结构的非稳腔进行了数值模拟，可以准确的获得腔内各阶本征模和损耗。通过改变非稳腔的各种几何参数获得各阶模式损耗的变化曲线，为非稳腔的结构设计和深入理解提供了便捷的方法。
（3）针对2kW射频板条CO_2激光器，进行了板条电极热稳定性的研究。探讨了影响对流换热问题的关键参数——对流换热系数的取值。在不同的对流换热系数取值条件下进行了稳态热分析，结果表明当水流量超过一定值后，电极冷却效果增加不明显。然后在激光器满功率运行的条件下，分析了从开机到达到稳定状态的动态过程，结果表明更高的对流换热系数下板条电极达到稳态的时间更短，h=2000W/(m2·℃)时达到稳态过程约为五分钟。
（4）对板条电极和窗口镜的热应力和变形进行了有限元分析。设计了三种不同的电极安装结构并分别进行了热应力与变形的分析，证明采用绝缘陶瓷定位方案和自由无约束方案均适用，各有优劣。针对非稳-波导腔特殊的输出光束特性，研究了其对窗口镜的热影响。采用多项式拟合的方法构造了一个用于有限元分析的激光功率分布函数，精确模拟了窗口镜在条形光斑作用下的温度场分布和热应变情况，并讨论了高功率激光器窗口镜的热透镜效应。
（5）从选支调谐CO_2激光器的技术路线、研究进展和基本原理出发，对工作介质、能级结构、光栅选支方法等技术理论进行了分析，并讨论了选支调谐射频板条CO_2激光器的发展情况和关键技术问题。针对大功率射频板条选支CO_2激光器，设计了一种特殊的光栅-波导-折叠腔，该谐振腔在横向上表现为一个等效的稳定腔，而在垂直电极方向为波导腔。对这种大功率光栅腔的模式特征进行了分析，计算了在不同Littrow入射角、以及偏离Littrow波长时的腔内本征横模的光场分布和损耗特性。
Beam characteristic and its thermal stability of the radio frequency-exited waveguideCO_2laser are important both in theoretical researches and engineering design. Theintra-cavity and output beam characteristics of the RF-excited slab CO_2laser whichdetermined by the slab structure have been studied in this thesis. The temperaturedistribution and the hot distortion of the slab electrodes and the output window areanalysed by the finite element method, to find out the impact of the thermal stability onthe laser. The wavelength selected RF-excited waveguide CO_2lasers is summarized andintroduced as a branch application, and a large power grating-waveguide-folded resonatoris designed for this laser. The main contents are classified as follows.
(1) A positive-branch unstable-waveguide hybrid resonator is designed for thehundred watts level RF-excited slab CO_2lasers based on the theory of one-dimensionalunstable resonator and waveguide resonator. The output beam modes in these twodirections are analyzed with the method of separating variables. The optical fielddistributions in the near field and the far field and the characteristics of powermisalignment are measured experimentally. It is demonstrated that the beam isapproximately collimated in the unstable dimension, yet strongly affected by thehard-edge diffraction. Simultaneously, the beam mode is a similar fundamental mode inthe waveguide dimension with a big divergence angle.
(2) The eigenvector method is extended for unstable resonators combined with theCollins formula and the ABCD ray matrix. In the process of this method there is not anyapproximation on the aperture sizes of both mirrors. The mode behavior in a resonatorwith arbitrary irregular structures can be studied exactly and conveniently. Anasymmetrical practical unstable resonator and a non-confocal practical unstable resonatorare numerically simulated under varying structure parameters, and some newcharacteristics are found. The loss curves of some lower order modes versus differentgeometric parameters are obtained.
(3) Experiments for the stabilities are taken on a2kW RF-excited slab CO_2laser, toinvestigate how the thermal stability affects the beam characteristics. The steady state temperature distribution on the slab electrodes are simulated with thermodynamics FEMmethod. The value of the convective heat transfer coefficient, which is a key parameter inthe heat convection, is discussed, and several values are tried in the simulations. Atransient heat analysis of the slab electrode is taken. The dynamic thermodynamicsprocess from start to stability of some points on the electrode is simulated. It is shown thatwhen the convective heat transfer coefficient is given a higher value, this process will befast, and when h=2000W/(m2·℃) the time is about5min.
(4) The heat stress and heat distortion of the slab electrodes and the output windoware analyzed with FEM. Three different fixing structures of the electrodes are designedand analyzed. It is proven that the insulating ceramics fixing method and the free fixingmethod without restriction are both suitable, and the later method is more advanced for theelectrodes with large area. The impact of the output beam of the unstable-waveguidehybrid resonator on the output window is researched. A distribution function of the laserpower is composed with polynomial fitting in the FEM simulation. And then, the thermallens effect of the output window under a high laser beam is studied.
(5) Some technologies of the wavelength selected CO_2laser are summarized, such asthe actuating medium, the level structures, the tuning method with grating and so on. Thedevelopment and the key technologies of the tunable RF-excited slab CO_2laser arediscussed. A special grating-waveguide-folded resonator is designed for the high powertunable slab CO_2laser, and mode behaviors are researched. For a grating resonator, themode and misaligned characteristics under different Liitrow angle are studiedsystematically.
（1）在一维非稳腔与一维波导腔的理论基础上，针对百瓦级射频板条CO_2激光器设计了正支非稳-波导混合腔，采用分离变量法分析了光束在波导与非稳两个方向的输出模式及传输特性。实验测量了输出光束近场远场分布及激光谐振腔的功率失调特性。研究表明输出光束在非稳方向呈近似的准直输出，硬边衍射效应对光场分布有着明显影响；波导方向为近似的基模输出，发散角为12mrad。
（2）从非稳腔的模式交叉特性入手，结合Collins公式与光学ABCD矩阵方法，将特征向量法的应用推广到非稳腔，计算过程中没有对腔镜的横向尺寸进行任何近似。采用该扩展的特征向量法分别对非对称和非共焦这两种不规则结构的非稳腔进行了数值模拟，可以准确的获得腔内各阶本征模和损耗。通过改变非稳腔的各种几何参数获得各阶模式损耗的变化曲线，为非稳腔的结构设计和深入理解提供了便捷的方法。
（3）针对2kW射频板条CO_2激光器，进行了板条电极热稳定性的研究。探讨了影响对流换热问题的关键参数——对流换热系数的取值。在不同的对流换热系数取值条件下进行了稳态热分析，结果表明当水流量超过一定值后，电极冷却效果增加不明显。然后在激光器满功率运行的条件下，分析了从开机到达到稳定状态的动态过程，结果表明更高的对流换热系数下板条电极达到稳态的时间更短，h=2000W/(m2·℃)时达到稳态过程约为五分钟。
（4）对板条电极和窗口镜的热应力和变形进行了有限元分析。设计了三种不同的电极安装结构并分别进行了热应力与变形的分析，证明采用绝缘陶瓷定位方案和自由无约束方案均适用，各有优劣。针对非稳-波导腔特殊的输出光束特性，研究了其对窗口镜的热影响。采用多项式拟合的方法构造了一个用于有限元分析的激光功率分布函数，精确模拟了窗口镜在条形光斑作用下的温度场分布和热应变情况，并讨论了高功率激光器窗口镜的热透镜效应。
（5）从选支调谐CO_2激光器的技术路线、研究进展和基本原理出发，对工作介质、能级结构、光栅选支方法等技术理论进行了分析，并讨论了选支调谐射频板条CO_2激光器的发展情况和关键技术问题。针对大功率射频板条选支CO_2激光器，设计了一种特殊的光栅-波导-折叠腔，该谐振腔在横向上表现为一个等效的稳定腔，而在垂直电极方向为波导腔。对这种大功率光栅腔的模式特征进行了分析，计算了在不同Littrow入射角、以及偏离Littrow波长时的腔内本征横模的光场分布和损耗特性。
Beam characteristic and its thermal stability of the radio frequency-exited waveguideCO_2laser are important both in theoretical researches and engineering design. Theintra-cavity and output beam characteristics of the RF-excited slab CO_2laser whichdetermined by the slab structure have been studied in this thesis. The temperaturedistribution and the hot distortion of the slab electrodes and the output window areanalysed by the finite element method, to find out the impact of the thermal stability onthe laser. The wavelength selected RF-excited waveguide CO_2lasers is summarized andintroduced as a branch application, and a large power grating-waveguide-folded resonatoris designed for this laser. The main contents are classified as follows.
(1) A positive-branch unstable-waveguide hybrid resonator is designed for thehundred watts level RF-excited slab CO_2lasers based on the theory of one-dimensionalunstable resonator and waveguide resonator. The output beam modes in these twodirections are analyzed with the method of separating variables. The optical fielddistributions in the near field and the far field and the characteristics of powermisalignment are measured experimentally. It is demonstrated that the beam isapproximately collimated in the unstable dimension, yet strongly affected by thehard-edge diffraction. Simultaneously, the beam mode is a similar fundamental mode inthe waveguide dimension with a big divergence angle.
(2) The eigenvector method is extended for unstable resonators combined with theCollins formula and the ABCD ray matrix. In the process of this method there is not anyapproximation on the aperture sizes of both mirrors. The mode behavior in a resonatorwith arbitrary irregular structures can be studied exactly and conveniently. Anasymmetrical practical unstable resonator and a non-confocal practical unstable resonatorare numerically simulated under varying structure parameters, and some newcharacteristics are found. The loss curves of some lower order modes versus differentgeometric parameters are obtained.
(3) Experiments for the stabilities are taken on a2kW RF-excited slab CO_2laser, toinvestigate how the thermal stability affects the beam characteristics. The steady state temperature distribution on the slab electrodes are simulated with thermodynamics FEMmethod. The value of the convective heat transfer coefficient, which is a key parameter inthe heat convection, is discussed, and several values are tried in the simulations. Atransient heat analysis of the slab electrode is taken. The dynamic thermodynamicsprocess from start to stability of some points on the electrode is simulated. It is shown thatwhen the convective heat transfer coefficient is given a higher value, this process will befast, and when h=2000W/(m2·℃) the time is about5min.
(4) The heat stress and heat distortion of the slab electrodes and the output windoware analyzed with FEM. Three different fixing structures of the electrodes are designedand analyzed. It is proven that the insulating ceramics fixing method and the free fixingmethod without restriction are both suitable, and the later method is more advanced for theelectrodes with large area. The impact of the output beam of the unstable-waveguidehybrid resonator on the output window is researched. A distribution function of the laserpower is composed with polynomial fitting in the FEM simulation. And then, the thermallens effect of the output window under a high laser beam is studied.
(5) Some technologies of the wavelength selected CO_2laser are summarized, such asthe actuating medium, the level structures, the tuning method with grating and so on. Thedevelopment and the key technologies of the tunable RF-excited slab CO_2laser arediscussed. A special grating-waveguide-folded resonator is designed for the high powertunable slab CO_2laser, and mode behaviors are researched. For a grating resonator, themode and misaligned characteristics under different Liitrow angle are studiedsystematically.
引文
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