非傍轴矢量余弦-高斯光束两种光强表示的比较研究

从矢量瑞利-索末菲衍射积分公式出发,以非傍轴矢量余弦－高斯(CoG)光束为例,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分量进行了比较研究.对非傍轴矢量CoG光束轴上和横向光强分布详细的数值计算和比较结果表明,两种光强表示式之间的相对误差η与w0/λ、z/λ和偏心参量b有关,其中w0,λ和z分别为束腰宽度,波长和传输距离.当偏心参量b较小,且束腰宽度与波长相比不很小时,例如,b≤0.8,w0/λ≥0.8,z/λ=10时,二者间的最大相对误差ηmax＜2%,传统光强公式可以使用.

Comparative Study of Two Intensity Expressions of Nonparaxial Vectorial Cosine-Gaussian Beams

Starting from the vectorial Rayleigh-Sommerfeld diffraction integrals and taking the nonparaxial vectorial cosine-Gaussian (CoG) beam as an example, 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. The numerical results and comparison for nonparaxial vectorial CoG beams show that the relative error η between the two intensity expressions depends on the ratios w0/λ,z/λ and decentered parameter b, where w0, λ and z denote the waist width, wavelength and propagation distance, respectively. If the decentered parameter b is smaller, and waist-width to wavelength ratio w0/λ is not very small, for example, if b≤0.8, w0/λ≥0.8 and z/λ=10 the maximum relative error between the two expressions ηmax＜2%. Therefore, the conventional intensity expression can be used.