Abstract: Based on the vector angular spectrum representation of optical beam and the method of stationary phase, the analytical TE and TM terms of vector Gaussian beam have been presented in the far field. By using the local polarization matrix, the polarization properties of the TE and TM terms in the far field are investigated, and it is found that the degree of their polarization is only determined by the spatial location. When the source is completely polarized, the TE and TM terms are both completely polarized in the far field. When the source is completely unpolarized, the TE and TM terms in the far field are partially polarized. The whole beam is also partially polarized except on the propagating axis. Moreover, the degrees of polarization of TE and TM terms are both larger than that of the whole beam. 

Key words: vector Gaussian beam, vectorial structure, local polarization matrix, degree of polarization