基于广义瑞利-索末菲衍射积分公式,推导出了非傍轴离轴高斯-谢尔模型(GSM)电磁光束在自由空间传输3×3交叉谱密度矩阵的解析公式,并用以表示电磁光束在z面的光谱密度(光强)、偏振度和光谱相干度。非傍轴共轴GSM电磁光束和非傍轴离轴高斯电磁光束可为特例来处理。着重研究了离轴参数、自相关和互相关长度对电磁光束的光强、偏振度和光谱相干度的影响。对所得结果用数值计算例做了说明。

Based on the generalized Rayleigh-Sommerfeld diffraction integrals,the analytical expression for the 3×3 cross-spectral density matrix of nonparaxial off-axis Gaussian-Schell model (GSM) electromagnetic beams propagating in free space is derived and used to formulate the spectral density (intensity),degree of polarization and spectral degree of coherence of electromagnetic beams at the z plane. Nonparaxial on-axis GSM electromagnetic beams and nonparaxial off-axis Gaussian electromagnetic beams can be treated as special cases of our results. The effect of off-axis parameter,self- and cross-correlation lengths on the intensity,the degree of polarization and the spectral degree of coherence of electromagnetic beams are stressed. The results are illustrated by numerical examples.