Accurate description of a radially polarized Gaussian beam

An accurate description of a radially polarized fundamental Gaussian beam is presented on the basis of complex-source-point spherical waves (CSPSWs). In contrast to other descriptions based on the perturbative Lax series, the expressions for the electromagnetic field components of this description have explicit and simple mathematical forms. Numerical calculations show that both paraxial and fifth-order corrected beam descriptions have large relative error when the diffraction angle is large, while the accurate description based on the CSPSW approach proposed here can give field expressions which satisfy Maxwell's equations with great accuracy.