Far-field properties of a cylindrically polarized vector beam and its beam quality beyond the paraxial approximation

The far-field analytical expressions for the electromagnetic fields of a cylindrically polarized vector beam propagating in free space are obtained based on the vector angular spectrum and the method of stationary phase. The far-field energy flux distributions and the beam quality by the power in the bucket (PIB) in the nonparaxial regime have been investigated. The PIB of the cylindrically polarized beam depends on the ratio of the waist width to wavelength, the order of the Laguerre polynomial, and the angle between the electrical vector and the radial direction. The analyses show that azimuthal polarization compared with radial polarization has better energy focusability in the far field.