非傍轴平顶高斯光束M^2因子两种定义的比较研究

A Comparative Study on Two Definitions of the M^2 Factor of Nonparaxial Flattened Gaussian Beams

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·

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 ω0/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 M^2 factor of nonparaxial FG beams is studied and compared with the conventional definition of the M^2 factor. In the nonparaxial regime, the M^2 factor of nonparaxial FG beams depends not only on the beam order, but also on ω0/λ. According to our definition, as ω0/λ→0, the M^2 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 M^2 factor takes its minimum M^2min =0.816.