【作者】 曾庆刚；

【导师】 张彬；

【作者基本信息】 四川大学 ， 光学， 2004， 硕士

【摘要】 激光束的描述、光束传输变换和光束质量控制一直是激光科学技术和激光光学中的重要理论研究工作。国内外的研究工作表明，M~2因子是一个很重要的光束参数，可用来描述光束的传输行为，在某些应用中还可作为判断光束质量优劣的参数之一，具有重要的应用价值。另外，由于高增益、自发辐射等因素，高功率激光器输出的激光通常具有复杂的多模结构，并具有部分相干性，因而研究激光的相干模分解理论具有重要的理论意义和实用价值。在强激光的许多实际应用中，例如，激光材料加工和惯性约束聚变中，常要求空间均匀分布的平顶光束，因此，研究平顶分布光束的传输变换特性具有重要意义。 本论文针对强激光技术中应用较为广泛的平顶光束，对其传输变换特性、光束传输M~2因子以及相干模分解理论进行了研究，主要工作包括： 1 基于广义强度二阶矩方法，推导出了非截断和截断平顶光束在直角坐标系和柱坐标系下的广义M~2因子解析表达式，利用数值计算，对影响平顶光束广义M~2因子的因素作了讨论。 2 建立了激光束的相干模分解理论。以平顶光束模型为例，分别推导出非截断和截断平顶光束的模相关系数的解析表达式，在此基础上，对非截断和截断平顶光束的模结构、模相关以及相干模分解进行了分析。 3 利用Collins公式，对平顶光束通过近轴ABCD光学系统的传输特性作了研究，得到相应的解析传输公式。通过数值计算，详细讨论了平顶光束的聚焦特性。在此基础上，利用无光阑限制的解析传输公式研究了平顶光束通过透镜序列系统的传输特性。4利用Colhns公式，推导出环状平顶光束通过近轴ABCD光学系统的传输公式，以自由空间传输为例，对影响环状平顶光束菲涅尔衍射和夫琅和费衍射的因素作了详细的计算和物理分析。5利用Colhns公式，推导出平顶光束通过含有增益和吸收介质的近轴ABCD光学系统的一般传输公式，在此基础上，应用广义强度二阶矩方法，对平顶光束在线性增益和吸收介质中传输时的矿因子进行了详细的分析。关键词:平顶光束，广义矿因子，激光的相干模分解，ABcD光学系统，传输特性本论文工作得到国家自然科学基金项目(编号:60108004)的资助。更多还原

【Abstract】 Laser beam characterization, beam propagation and beam quality control are the fundamental research subject in laser optics and laser technology. It can be shown from the studies that the M2 factor is a very useful parameter for characterizing various laser beams. In some practical applications, it is a useful parameter for beam quality. On the other hand, laser beams generated from high-power lasers usually result in a complex multi-mode structure and possess partial coherence because of the high gain, amplification of spontaneous emission, etc. Studying on the theory of coherent-mode decomposition of laser beams would be of both theoretical significance and practical interest. Moreover, flat-topped beams are very useful beams in many practical cases of the high-power laser, such as in laser material processing and inertial confinement fusion (ICF). It would be of important significance to study the propagation properties of flat-topped beams.The goal of this thesis is to study the propagation properties, the beam propagation M factor and the theory of coherent-mode decomposition of flat-topped beams. The main results obtained in this thesis can be summarized as follow: 1. Based on the definition of generalized intensity second-order moments, the analytical expressions for the generalized M2 factor of flat-topped beams with andwithout aperture have been derived. The factors that affect the generalized M2 factor have been studied by numerical calculation examples.2. Theory of the coherent-mode decomposition of laser beams was built. The analytical expressions for the mode coherence coefficients of flat-topped beams withand without aperture have been derived, by means of which the mode correlation, mode structure, and coherent-mode decomposition can be analyzed.3. Making use of the Collins formula, the propagation properties of flat-topped light beams passing through a paraxial ABCD optical system have been studied, and the corresponding analytical propagation expressions have been derived. The focusing properties have been analyzed in detail. The propagation properties of flat-topped light beams passing through a lens series have been studied by the analytical propagation expression without aperture.4. The propagation expressions for the annular flat-topped light beams passing through a paraxial ABCD optical system have been derived by using the Collins formula. The factors that affect the Fresnel and Fraunhofer diffractions have been analyzed in detail.5. Making use of the Collins formula, the general propagation expression for flat-topped light beams passing through a paraxial ABCD optical system in gain and absorbing media have been derived. The M1 factor of flat-topped light beams propagating in gain and absorbing media have been analyzed in detail by means of the definition of generalized intensity second-order moments.更多还原