A Comparative Study on Two Definitions of the M2 Factor of Nonparaxial Flattened Gaussian Beams
非傍轴平顶高斯光束M2因子两种定义的比较研究

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.