Vectorial analysis of the collimated beam of a small Gaussian source

A vectorial analysis method to describe the collimated beam is proposed, the formulas of the intensity distribution and divergence angles represented in terms of Bessel functions are derived, and the propagation properties such as the vectorial structure of the collimated field and the shape of the beam spot are discussed in detail. Omitting the vectorial nature of the collimated beam can cause an error of 7.6% in determining the intensity distribution on the optical axis of the collimated beam.