【作者】 文侨；

【导师】 蔡邦维；

【作者基本信息】 四川大学 ， 光学， 2005， 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。由于高增益、大口径、自发辐射、非线性效应、腔镜衍射以及激光控制参数的变化等因素,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。因此,研究部分相干光的传输特性、光束质量和模分解具有重要的理论意义及实用价值。 本论文针就实际工作中具有普遍性的部分相干光束,对其传输变换特性、光束传输M~2因子以及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理论,将矩形函数近似展开为有限项复高斯函数叠加的实部,给出了部分相干光束通过硬边光阑的广义强度二阶矩和广义M~2因子的近似计算公式。以有振幅调制和相位畸变光束为例,推导出相应的广义M~2因子的解析表达式,给出了典型的数值计算结果,并分析了本论文提出近似算法的计算精度。 2.在波数K为复数的情况下,对部分相干光的强度二阶矩及M~2因子的定义进行了修正,使之适用于光束在增益或损耗介质中传输的情况。在此基础上,推导出波数为复数时M~2因子的计算公式。以高斯—谢尔模型(GSM)光束为例,研究了部分相干光束在增益或损耗介质中传输时M~2因子的变化规律。 3.推导出以模式间相互独立的厄米—高斯光束为基底的部分相干平顶光束的模系数和M~2因子的解析式,对部分相干平顶光束的模分解及合成进行了研究。研究表明,光强矩形分布与光束M~2因子二者无法同时兼顾,即若要求空间分布更多还原

【Abstract】 Laser beam characterization, beam propagation, beam transformation and beam quality control are always the fundamental research subjects in laser optics and laser technology. Laser beams generated from high-power lasers usually result in a complex multi-mode structure and possess partial coherence because of the high gain, large aperture, amplification of spontaneous emission, nonlinear optical effects, diffraction of cavity mirror, as well as the variation of laser control parameters. It would be of important significance to study the laser beam characterization, beam propagation, mode decomposition and beam quality control.The goal of this thesis is to study the propagation properties, the beampropagation M2 factor and the theory of mode decomposition of the partially coherentbeams. The main results obtained in this thesis can be summarized as follow:1. Based on the theory of second-order moments and the treatment that the rectangularfunction can be expanded into the real part of an approximate sum of complexGaussian functions with finite numbers, an approximate method for calculating thesecond-order moments and the generalized M2-factor of partially coherent beamspassing through hard-edged apertures has been proposed. A laser beam withamplitude modulation and phase fluctuation was taken as a typical example ofpartially coherent beams. The analytical expression for the generalized M2-factorwas derived. Furthermore, the typical numerical examples have been given and the calculation precision of our method has been analyzed by numerical calculations.2. Considering of the complex wave number, the second-order intensity moments andthe M2-factor of partially coherent beams in gain or absorbing media have been modified. A Guassian Schell-model beam was taken as a typical example of partially coherent beams and the variations of the M2-factor of partially coherent beams in gain or absorbing media have been studied.3. The analytical expressions for the mode coefficients and M2-factor of partiallycoherent flat-topped beams, which can be combined by the independent Hermite-Gaussian beams, have been derived. The mode decomposition and mode composition of partially coherent flat-topped beams have been analyzed. It can be seen from our study that the M2-factor and the rectangular shape of the flat-topped beams combined by the independent Hermite-Gaussian beams are not available at the same time. If an approach rectangular shape of the intensity distribution of partially coherent flat-topped beams is desired, the M2-factor must be large. If the small value of M2-factor is required, the strictly rectangular shape of the intensity distribution is not available.4. The spectral density function of partially coherent flat-topped beams propagatingthrough ABCD optical system including the gain or absorbing media has been derived. The variations the optical spectrum of partially coherent flat-topped beams propagating in gain or absorbing media have been studied in detail. The influence of the parameter characterizing the gain or absorbing media, the real part of wave number, the correlation length and the beam shape on the spectral characteristics in the near zone or in the far zone has been investigated.5. Based on the theory of second-order intensity moments of truncated laser beams inspatial-frequency domain modified by Herrero et al., the theory of measuring the generalized M2-factor of truncated beams and the measuring method have been given. The measurement system has been set up and the experimental results have been analyzed.更多还原