【作者】 李根；

【导师】 唐霞辉；

【作者基本信息】 华中科技大学 ， 光学工程， 2012， 博士

【摘要】 高功率扩散冷却板条CO2激光器被广泛地应用于工业激光加工领域。离轴非稳—波导混合腔是其核心部件之一。本论文针对离轴非稳—波导混合腔腔内光场的空间分布特性作出了系统细致的研究,尤其是利用渐进的方法对非稳方向上场的分布特性进行了详细的论述,包括最低阶模式的虚源法,特征函数法。讨论了模式交叉以及过量噪声因子特性。其主要研究内容如下：(1)研究了平板波导内场沿正向和反向传输的传输特性。利用几何球面波的近似,分别求解了正向传输的均匀平面行波和负向柱面行波在平板波导中的传输特性,指出正向行波在波导内以TE波或TM波的形式存在,且两者不能共存。分析了不同波导材料对传输损耗的影响,指出正向行波损耗最小的材料为氧化铝。分析了负支离轴共焦腔中“热点”处场在波导方向上的分布特性。指出在“热点”处场的六个分量中仅有一个沿波导方向的分量不为0,并分析了电极材料以及电极间距对电极表面场振幅大小的影响。(2)分析了虚源法的数学基础和物理意义。由分析可知虚源法误差来源主要包括：观察点离边界点轴向距离非常近,或者横向距离为零；未考虑各孔阑边界所发出的球面波在观察平面的几何阴影区边界不同；虚源点坐标的几何近似对场分布精细结构的影响。将虚源法扩展到离轴共焦非稳腔的最低阶光场光强模式计算中,给出所取孔阑数在满足自再现模条件下的经验取值。将其应用到千瓦级射频板条激光器所采用的大菲涅尔数离轴腔的模式计算中,得到比较精确的结果。(3)利用均匀渐进的公式,找到了一组特征函数,利用其线性叠加可以比较精确的描述腔内的横模,并给出了自相似分形法的数学基础,得到最低阶模式的近似解析表达式。通过求解一个由该组特征函数构成的特征值多项式就可以得到各阶特征值和对应的本征横模。(4)通过特征向量法的数值计算,指出离轴共焦非稳腔中各阶横模的交叉特性：正支离轴腔模式交叉发生在有效菲涅尔数取为s+0.08处(s为正整数)；而负支离轴腔的交叉发生在s-0.125附近。正支离轴共焦非稳腔中,其最低阶模式并非传统意义上的偶数阶模,而其衍射损耗也明显高于几何衍射损耗值。通过由均匀渐进方法得到的横模特征值多项式,分析了特征值的简并特性,找到了放大率在的区间[1.1,1.9]时对应的复平面内最接近实轴的有效菲涅尔数的取值,其实部大约在75.375附近,并不与模式交叉点重合,而虚部为0。(5)讨论了离轴共焦非稳腔中光场的横向分布与输出激光线宽的问题。说明描述耦合到任意给定模式自发辐射噪声(朗之万噪声)项的统计平均可以用横模的双正交性(即过量噪声K因子)与特征值特性来描述。利用衍射积分方法得到了在放大率一定的条件下,K因子的大小随有效菲涅尔数的变化情况,指出K因子在模式交叉处不存在峰值现象,而是表现出非连续性。通过分析场在腔内的渡越特性,将已有的混合几何法改进,使之能应用于离轴非稳腔,并修正了计算高阶模K因子存在的数量级误差。更多还原

【Abstract】 The high power diffusion-cool slab CO2 laser is widely used for industrial applications. The off-axis unstable-waveguide hybrid resonator is a core component of the laser. Characteristics of the field distribution in the resonator have been studied in this thesis. The transverse modes are analysed by the asymptotic theory, including the virtual source method for the lowest transverse mode and the eigen-function method for all order modes. The mode crossing and the excess noise are also discussed in detail. The main contents are classified as follows.(1) The transmission characteristics of both travelling waves along forward and backward direction have been studied. The approximate solutions for both waves are obtained with the spherical wave theory. The results show that the eigen-solution for forward travelling wave is TE mode or TM mode, the two modes can not exist simultaneously. The effect on transmission loss caused by the dielectric constant of waveguide materials is also discussed; alumina is the optimal material on the loss account. The characteristics of the field distribution along the narrow direction at the "hot spot" in the negative branch unstable resonator are analysed with the formula for the cylindrical wave. At the "hot spot", there is only one component which is along the waveguide direction. The effects on the filed amplitudes on the surface of the electrode caused by the dielectric constant of electrode material and the distance between the electrodes are studied.(2) The mathematic formula and physical meaning of the virtual source method are presented. The analysis shows that the errors are caused by three cases, the axial distance between the observation plane and the aperture, or the transverse distance between the aperture edge and the observation point is too small, the different width of the geometric shadow of the apertures are not considered, the effects on the fine structure of distribution caused by the geometric approximation of the virtual source location are ignored. The virtual source method is extended to the calculation of the lowest mode in the off-axis unstable resonators, the errors are also treated carefully, and the number of the apertures should be small as possible under the condition of the self-produce mode. The numerical result for the kilowatt diffusion-cool slab laser shows good agreement between the virtual source method and FFT.(3) A group of eigen functions have been found by the uniform asymptotic theory. The transverse modes are presented by the linear superposition of the functions. The mathematical validity of the self similar fractal method is proved and the analytic formula for the lowest mode is presented by the functions. To calculate high order modes, a polynomial about the scaled-eigenvalue is obtained.(4) The numerical results by the eigen-vector method show that the mode crossing between the lowest-and the next-lowest-loss modes occurs when the equivalent Fresnel number Neq is close to s+0.08 (s positive integer) for positive branch resonators and is close to s-0.125 for negative branch resonators, the lowest mode in positive branch is not the traditional even mode, the diffraction loss is much larger than the value predicted by the geometric optics. The degeneracy is also determined by the polynomial. The results show that the real part of Neq which is most close to the real axis is equal to about 78.4.(5) The relationship between the laser linewidth and the transverse distribution of the field is discussed. The statistical average of the Langevin noise that describes the spontaneous radiation noise coupling into a given mode is determined by the Biorthogonality of the transverses modes (K factor) and their eigenvalues. The values of K factor varying as a function of Neq are calculated numerically by the eigen-vector method with a fixed magnification. The profile shows discontinuity at mode crossing point instead of the peak. The hybrid-geometry method is modified to calculate the K factor of all order modes, and the magnitude error is corrected.更多还原