Accurate expansion of cylindrical paraxial waves for its straightforward implementation in electromagnetic scattering

- Paraxial beams are represented in a series expansion in terms of Bessel wave functions.
- The coefficients of the series expansion can be analytically determined by using the pattern in the focal plane.
- In particular, Gaussian beams and apertured wave fields have been critically examined.
- This representation of the wave field is adequate for scattering problems with shaped beams.

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.