Vector vortex beams (VVBs), as a new type of structured light with anisotropic spatial polarization and phase, carry orbital angular momentum related to the phase distribution and possess potential application values in fields such as optical manipulation, high-resolution imaging, and optical information transmission. Currently, there are scarce studies on the correlation between the polarization and phase topological charges of VVBs. Additionally, in contrast to scalar vortex beams, research on the interference and diffraction measurement of the orbital angular momentum of VVBs is relatively rare. This paper explores the correlation between the polarization and phase topological charges of VVBs, realizes the determination of topological charges through polarization methods, and investigates the interference and diffraction measurement approaches of the orbital angular momentum of VVBs, which is anticipated to broaden the thinking for the measurement and application of the orbital angular momentum of VVBs.

Based on the field distribution characteristics of VVBs with different polarization orders and phase topological charges, this paper studies the correlation issue between the polarization order and phase topological charge values of VVBs and analyzes the influence of changes in the azimuthal angle and ellipticity angle on the polarization state and orbital angular momentum of VVBs. The orbital angular momentum measurement method of VVBs is analyzed by exploiting the characteristics of double-slit interference fringes, and the diffraction effects of VVBs with different aperture diaphragms are simulated and calculated. By comparing the diffraction spot shapes of different apertures, parameters including the phase topological charge and polarization order are derived, and the orbital angular momentum measurement method of VVBs is studied.

The innovative results of this paper are as follows:

1) According to the intensity and phase distributions of VVBs with different polarization orders and phase topological charges, the relationship of the light intensity and phase with the polarization order and phase topological charge values is analyzed. It is discovered that the phase topological charge and polarization order of VVBs respectively affect the sizes of the phase singularity and polarization singularity of the beams. The numbers of peripheral and central bifurcations of the beam phase distribution correspond to the polarization order and phase topological charge (Figs. 1?3). The ellipticity angle and azimuthal angle in the polarization matrix term of the vector vortex field have an impact on the polarization distribution of the field, the ellipticity angle affects the distribution range of light intensity, and the azimuthal angle causes a related rotation in the distribution direction of polarization state (Figs. 4?7).

2) A double-slit interference simulation experiment of VVBs is carried out. It is found that when the polarization order and the absolute value of the phase topological charge are equal, the central dark core disappears. When the phase topological charge is l, the width of the interference fringe distortion is l stripe, and the direction of the interference fringe distortion is also related to the phase topological charge. When the phase topological charge is positive, the fringes twist to the right, and when the phase topological charge is negative, the fringes twist to the left. Moreover, the double-slit interference of VVBs with different polarization orders changes the size of the polarization singularity (Fig. 8).

3) Through the diffraction calculation of VVBs after passing through single slit, right-angle triangular aperture, etc., the relationship of the diffraction pattern morphology with the phase topological charge value and polarization order of VVBs is compared and analyzed. It is found that when the polarization orders and phase topological charges of VVBs after passing through right-angle triangular hole diaphragms are simultaneously opposite numbers, the diffraction spot undergoes a phase shift related to the absolute value of the polarization order (Figs. 9?14).

The research findings indicate that the polarization order and the phase topological charge value jointly determine the intensity and phase distributions of VVBs. During the transmission process of VVBs under different polarization conditions, the vortex phase distribution remains relatively stable, and the alteration of the ellipticity angle leads to the difference in the polarization state distribution. Based on the regular changes in the fringe distribution after interference, the polarization order and the phase topological charge value of VVBs can be determined. When the VVBs pass through the right-angle triangular aperture diaphragm, the diffraction spot undergoes a phase shift related to the absolute value of the polarization order only when the polarization orders are opposite to each other, which suggests that single-slit diffraction is more conducive to the determination of the polarization order value, while right-angle triangular aperture diffraction is more effective for the determination of the phase topological charge.