title: Nonparaxial and paraxial focusing of azimuthal-variant vector beams.
abstract: Based on the vectorial Rayleigh-Sommerfeld formulas under the weak nonparaxial approximation, we investigate the propagation behavior of a lowest-order Laguerre-Gaussian beam with azimuthal-variant states of polarization. We present the analytical expressions for the radial, azimuthal, and longitudinal components of the electric field with an arbitrary integer topological charge m focused by a nonaperturing thin lens. We illustrate the three-dimensional optical intensities, energy flux distributions, beam waists, and focal shifts of the focused azimuthal-variant vector beams under the nonparaxial and paraxial approximations.
authors.affiliation: Advanced Photonics Center, Southeast University, Nanjing 210096, China.
authors.forename: Bing
authors.initials: B
authors.lastname: Gu
authors.forename: Yiping
authors.initials: Y
authors.lastname: Cui