非傍轴平顶高斯光束M2因子两种定义的比较研究

基于功率密度的二阶矩方法，推导出了非傍轴平顶高斯(FG)光束束宽和远场发散角的解析表达式.研究表明，当w0/λ→0时，远场发散角趋于渐近值θmax=63.435°，与阶数无关.使用非傍轴高斯光束代替傍轴高斯光束作为理想光束，研究了非傍轴FG光束的M2因子，并与传统定义的M2因子作了比较.在非傍轴范畴，非傍轴FG光束的M2因子不仅与阶数N有关，而且与w0/λ有关.按照定义，当w0/λ→0时，非傍轴FG光束的M2因子不等于0，对阶数N=1, 2, 3时，M2因子分别趋于0.913,0.882和0.886.当N→∞时，M2因子取最小值M2min=0.816.

A Comparative Study on Two Definitions of the M2 Factor of Nonparaxial Flattened Gaussian Beams

Based on the second-order moment of the power density,the explicit expressions for the beam width and far-field divergence angle of nonparaxial flattened Gaussian(FG) beams are derived. It is found that as w0/λ(waist width-to-wavelength ratio)→0,the far-field divergence angle approaches an asymptotic value of θmax=63.435°,indenpent of the beam order. Then,the nonparaxial Gaussian beam instead of the paraxial one is chosen as the ideal beam,the M2 factor of nonparaxial FG beams is studied and compared with the conventional definition of the M2 factor. In the nonparaxial regime,the M2 factor of nonparaxial FG beams depends not only on the beam order,but also on w0/λ. According to our definition,as w0/λ→0,the M2 factor of nonparaxial FG beams does not equal to zero,but approaches 0.913,0.882 and 0.886 for the beam orders N=1,2,3,respectively. In particular,for N→∞ the M2 factor takes its minimum M2min=0.816.