非傍轴截断平顶光束的质量因子

 使用功率密度的二阶矩方法和Li提出的平顶光束模型，推导出了非傍轴截断平顶光束的束腰宽度、远场发散角和光束质量因子的解析表达式。计算结果表明：非傍轴截断平顶光束的质量因子不仅与截断参数、光束阶数有关，而且与初始束腰宽度和波长之比有关；当截断参数趋近于0时，远场发散角趋于渐近值63.435°；对于光束阶数为1和截断参数趋于无穷大的特例，计算结果分别退化为非傍轴截断高斯光束和非傍轴无截断平顶光束的结果；功率密度的二阶矩方法可用于截断光束，并克服了光束质量因子的发散困难。

M2 factor of nonparaxial truncated flat-topped beams

By using the second-order moment method of the power density and a new model of flat-topped beams, the waist width，far-field divergence angle and beam quality factor of nonparaxial truncated flat-topped beams are derived analytically. It is shown that the beam quality factor of nonparaxial truncated flat-topped beams depends on the truncation parameter, the beam order and the initial waist-width to wavelength ratio. The far-field divergence angle approaches an asymptotic value of 63.435° when the truncation parameter approaches to 0. For the special case of 1 order beam and the truncation parameter approaching to +∞, the results reduce to those of nonparaxial truncated Gaussian beams and nonparaxial untruncated flat-topped beams, respectively. It is also shown that the second-order mome