Structural properties of a TM polarized Gaussian beam in the far-field

In the far-field, the TM polarized Gaussian beam is just a sum of two orthogonal terms: the TE and the TM terms. The analytical expressions for the ratios of the powers of the TE and the TM terms to that of the TM polarized Gaussian beam are obtained without any approximation. The contributions of the powers of the TE and TM terms to the power of the TM polarized Gaussian beam only depend on the f-parameter. The analytical divergence angles of the TE term, the TM term, and the TM polarized Gaussian beam are derived. The formulae of the kurtosis parameters of the TE term, the TM term, and the TM polarized Gaussian beam are also presented. The divergence angles and the kurtosis parameters are only determined by the f-parameter. Relations among the divergence angles and the kurtosis parameters of the TE term, the TM term, and the TM polarized Gaussian beam are presented, respectively. The influence of the f-parameter on the ratios of the powers of the TE and the TM terms to the power of the TM polarized Gaussian beam, the far-field divergence angles, and the kurtosis parameters are numerically analyzed.