Accurate fields of a radially polarized Gaussian laser beam

Explicit truncated series expressions modelling the fields of a focused radially polarized Gaussian laser beam are derived, accurate to order epsilon(15), where e is the associated fundamental Gaussian beam diffraction angle. The new terms make significant corrections to the known paraxial field components, the corrected fields satisfy Maxwell's equations exactly, and their series converge for epsilon< 1 and diverge for epsilon >= 1.