从随机电磁光束的相干和偏振性的统一理论出发,利用交叉谱密度矩阵传输公式,推导出随机双曲余弦高斯(ChG)电磁光束通过透镜后2×2交叉谱密度矩阵的传输解析公式,并用以表示任意两点的互偏振度,即纵向互偏振度(LDCP)和横向互偏振度(TDCP)。研究表明,随机ChG电磁光束的互偏振度与透镜焦距及随机ChG电磁光束的参数,例如随机ChG电磁光束系数比、离心参数和自相关长度等有关。随机高斯谢尔模型(GSM)电磁光束通过透镜的互偏振度可作为随机ChG电磁光束离心参数为0的特例得出。对主要结果用数值计算作了说明,并给出相应的物理解释。

Based on the unified theory of coherence and polarization of random electromagnetic beams and the propagation law of cross-spectral density matrix,the closed-form expression for the 2×2 cross-spectral density matrix of random cosh-Gaussian(ChG) electromagnetic beams propagating through a lens is derived,and used to formulate the degrees of cross-polarization,i.e.,the longitudinal degree of cross-polarization (LDCP) and the transverse degrees of the cross-polarization (TDCP) between two arbitrary points upon propagation. It is shown that the degrees ofcross-polarization depend on the focal length of the lens and beam parameters,such as the coefficient ratio,decentered parameter and self-correlation length. The degrees of cross-polarization of radom Gaussion Schell-model (GSM) electromagnetic beams propagating through a lens can be treated as a special case that the decentered parameter of random ChG electromagnetic beams approaches to zero. The main results are illustrated numerically and interpreted physically.