Currently, cylindrical beams with radial or azimuthal polarization are being used successfully for the optical manipulation of micro-and nano-particles as well as in microscopy, lithography, nonlinear optics, materials processing, and telecommunication applications. The creation of these laser beams is carried out using segmented polarizing plates, subwavelength gratings, interference, or light modulators. Here, we demonstrate the conversion of cylindrically polarized laser beams from a radial to an azimuthal polarization, or vice versa, by introducing a higher-order vortex phase singularity. To simultaneously generate several vortex phase singularities of different orders, we utilized a multiorder diffractive optical element. Both the theoretical and the experimental results regarding the radiation transmitted through the diffractive optical element show that increasing the order of the phase singularity leads to more efficient conversation of the polarization from radial to azimuthal. This demonstrates a close connection between the polarization and phase states of electromagnetic beams, which has important implications in many optical experiments.Phase singularities of a scalar field, which include vortex phases and phase jumps, are important features of various types of waves 1, 2 . Vector fields also exhibit a variety of polarization singularities 3, 4 . The spin angular momentum of photons was detected a long time ago [5][6][7] , and its interrelation with the orbital angular momentum has been discussed in several recent reviews 2,4,[8][9][10][11][12][13][14] . Light beams with defined phase and polarization features are important for many applications, including optical manipulation [15][16][17] , microscopy 18-20 , materials processing 21-24 , and telecommunications [25][26][27] . Cylindrically polarized optical beams, which may have a radial or azimuthal polarization, have attracted the most attention from researchers because of their special properties 12 .In some applications, such as STED (Stimulated Emission Depletion Microscopy) methods 20 , it is important to use a specific combination of laser beam polarization and spatial properties. In other applications, a desired state of polarization during the propagation of the beam must be retained, for example, to increase network throughput by using fibre modes that carry orbital angular momentum 27 . Polarization distribution control of the laser radiation enables some unique methods, like the selective excitation of an anisotropic molecule, focusing on a size smaller than the diffraction limit, and the fabrication of periodic nanostructures with femtosecond laser light 22,23,28 . The conversion of polarization type can take place when beams with a phase singularity are tightly focused [29][30][31] . The transfer of angular momentum from the spin degree of freedom (which is related to the state of polarization) to the orbital (which is relevant to the phase distribution) degree of freedom can also occur in anisotropic media [32][33][34][35] . The inter...

It was shown that the presence of wave aberrations (analyzed in the form of Zernike functions) in high-numerical-aperture focusing systems results in narrowing of the transverse dimension of the focal spot below the diffraction limit. Moreover, for linear polarization, the most common for modern lasers, the results achieved along one direction are better than for the radial polarization, the obtaining of which requires complex or expensive devices. Overcoming of the diffraction limit happens due to a substantial reduction of energy in the central part of the focal region. However, the possibility of the registration of light fields that have a very low intensity provides perspectives on the received results. It was also shown that not only the size of the light spot can be reduced, but also the shadow area, formed by a light ring with very small radius.

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