非傍轴矢量高斯光束的光强表示

Intensity representation of nonparaxial vectorial Gaussian beams

基于瑞利-索末菲衍射积分,未使用任何近似,对非傍轴矢量光束的两种光强表示式,即传统光强公式和时间平均坡印廷矢量的z分量进行了研究。对非傍轴矢量高斯光束详细数值计算结果的比较表明,两种表示式之间的差异,即两者的相对误差与束腰宽度及传输距离和波长的比值有关。对非傍轴矢量高斯光束,若传输距离与波长的比值为10,束腰宽度与波长的比值大于等于0.8,则最大相对误差不到1.5%。因此,传统光强公式是可用的。

Based on the vectorial Rayleigh-Sommerfeld diffraction integrals, the two expressions for the intensity of nonparaxial vectorial beams, i.e. , the conventional intensity expression and the z component of the time-averaged Poynting vector, are studied without using any approximation. A detailed numerical comparison for nonparaxial vectorial Gaussian beams shows that the discrepancy between the two expressions, namely, the relative error, depends on the ratio of the waist width to the propagation distance and that of the wavelength to the propagation distance, respectively, and the error decreases with the increase of the two ratios. For nonparaxial vectorial Gaussian beams, if the ratio of the wavelength to the propagation distance is 10, and the ratio of the waist width to the propagation is no less than 0.8, the maxima relative error is no more than 1.5%. Thus, the conventional intensity is applicable.