基于功率密度的二阶矩方法, 数值模拟研究了非傍轴余弦平方-高斯光束的束宽、 远场发散角和M2因子。计算结果表明: 1)束腰宽度W0(0)随w0/λ的增大而增大。 当w0/λ较大 (w0/λ≥0.5) 时, 束腰宽度随着偏心参 数的增大而减小。2) 当w0/λ→0时, 远场发散角趋于渐近值θ0max=63.435°, 与偏心参数α无关。3) 在非傍轴范畴, 余弦平方-高斯光束的M2因子不仅与偏心参数α有关, 而且还与初始束腰宽度和波长之比w0/λ有关。 当w0/λ足够小时, M2因子可小于1。对给定的偏心参数α, M2因子随w0/λ的变化并非总是单调的。 M2因子随w0/λ的增大而增大, 当达到最大值后又逐渐减小, 最后渐近趋于一稳定值。

On the basis of the second-order moment of the power density, beam width, far-field divergence angle and M2 factor nonparaxial cosine-squared Gaussian beams were illustrated and analyzed with numerical simulation. The conclusions are as following. 1) The waist width W0(0) increases with increasing w0/λ parameter. W0(0) decreases with increasing decentred parameter α when w0/λ is relatively large (w0/λ≥0.5). 2) As the parameter w0/λ→0, the far-field divergence angle approaches an asymptotic value of θ0max=63.435°, which is independent of the decentred parameter α. 3) In the nonparaxial regime, the M2 factor of cosine-squared Gaussian beams depends not only on the decentred parameter α, but also on the initial waist-width to wavelength ratio w0/λ, the M2 factor may be less than 1 as w0/λ becomes small enough. The M2 factor does not always vary monotonically with w0/λ for different decentred parameter α, and it increases with increasing w0/λ and reaches the maximum value, then gradually decreases, and finally tends to be a saturated value.