<p>The arbitrary vector vortex beams on a higher-order Poincaré sphere (HOPS) are generated and manipulated using the combination of a Mach–Zehnder interferometer and a spatial light modulator. In terms of the transfer matrix method, the analytical expressions of the arbitrary vector vortex beams on the HOPS through a paraxial optical system are derived. The characteristics of the transformation of vector vortex beams by three typical optical systems, such as free space, Fourier transform, and fractional Fourier transform system, are investigated theoretically and verified experimentally. The intensity distribution of the vector vortex beams is found to be form-invariant under paraxial transformations. In addition, the intensity and polarization properties of the vector vortex beams are closely related to the several independent complex parameters of the beams and the optical systems. This research provides a reliable and flexible approach to manipulating the vector vortex beams in practical optical systems.</p>
Laser resonator for generating radially polarized beams is designed with aid of a special wire grid polarizer which is used
as the rear mirror in CO<sub>2</sub> lasers. A theoretical model for this resonator with polarization selectivity is established, and the
simulation results show that not only radially polarized modes but also azimuthally polarized modes exist in the laser resonator. In order to guarantee pure radial polarization, the purity of radial polarization needs to be improved by suppressing azimuthal polarization. The purity of radial polarization depends on refractive index of the substrate and grating period of the wire grid polarizer. If the substrate of the wire grid polarizer is ZnSe, the purity of radial polarization can arrive at 85%. When the wire grid polarizer has low refractive index and high ratio of laser wavelength to grating period, pure radial polarization can be obtained.