  The evaluation of vector wave fields can be accurately performed by means of
diffraction integrals, differential equations and also series expansions. In
this paper, a Bessel series expansion which basis relies on the exact solution
of the Helmholtz equation in cylindrical coordinates is theoretically developed
for the straightforward yet accurate description of low-numerical-aperture
focal waves. The validity of this approach is confirmed by explicit application
to Gaussian beams and apertured focused fields in the paraxial regime. Finally
we discuss how our procedure can be favorably implemented in scattering
problems.
