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In this paper, the fields of a radially polarized fundamental Gaussian beam are derived with a complex-source-point spherical wave approach and then compared and contrasted with those derived recently from a Lax series to the order of e15, where e is the diffraction angle. It is shown that the domain of validity of the derived fields is restricted by a discontinuity built into the vector potential from which they are obtained. Furthermore, in disagreement with recent experimental observations, the axial field intensity decreases with tighter focusing (decreasing waist radius at focus).

Fields of a tightly focused radially polarized laser beam: the truncated series versus the complex-source-point spherical wave representation