Nonparaxial analyses of cylindrical vector beams with arbitrary polarization order in the far field

Based on the vector angular spectrum representation and the method of stationary phase, the analytical expressions for the electromagnetic fields of the cylindrical vector Laguerre-Gaussian beams with arbitrary polarization order are derived in the far field. The radially, anti-vortex and linearly polarized beams can be viewed as the special cases of our general result. The analyses indicate that the beam evolution properties and nonparaxiality are closely related to the radial mode number, the polarization order number and the ratio of the waist width to the wavelength. The high polarization order cylindrical vector beams compared with the radially polarized beams are more influenced by the nonparaxiality. This research provides a convenient approach to manipulate the cylindrical vector Laguerre-Gaussian beams by choosing the special state of polarization.