Nonparaxial propagation of Gaussian beam in arbitrary linearly polarized state

By applying the vectorial moment theory of nonparaxial beam propagation, the nonparaxial propagation of Gaussian beam with arbitrary linearly polarized state has been systemically investigated. Universal analytical expression, of the beam waist, far field divergence angle and beam propagation factor have been presented, which allow calculating the quintitative contribution of polarization. The formulae can be further simplified in the highly nonparaxial case and paraxial case. As the dimension of Gaussian light source tends to zero, the two transverse maximum divergences are 90 degrees and independent of the polarized state. For the highly nonparaxial case, the anticipated beam propagation charecteristics can be obtained by designing the half width of Gaussian light source and the linearly polarized state. When extending to the paraxial case, the effect of polarization can usually be neglected as its contribution to the beam waist and divergence angle is very slight. The beam propagation factor, however, keeps invariant and is independent of the polarized state. When the value of the half width of Gaussian light source is in between the above cases, the item number of series required to calculate is decided by the half width of Gaussian light source and the expected calculation accuracy. Then, the nonparaxial propagation of Gaussian beam with arbitrary linearly polarized state can be determined.