In recent years, special optical fields, especially vortex beams, have attracted widespread attention for their unique phase, polarization, and amplitude characteristics, which show great potential for applications in optical information transmission, rotational speed measurement, and quantum optics. Using the grating diffraction method, firstly, the generation of two types of dual-mode vortex beams, namely vortex beam superposition states and polarization vortex beams are explored in this study. The comparison shows that the structural similarity (SSIM) of the experimental and simulated optical fields of the vortex beam superposition state decreases gradually as the orbital angular momentum (OAM) mode increases. The SSIM of l=±5 is 7.78% lower than that of l=±1. Secondly, the study explores the effect of the center offset between the Gaussian beam and spatial light modulator on distortion of the optical field. As offset increases, the correlation coefficient of the light intensity of different OAM modes gradually decreases. The light intensity correlation coefficient of D=0.5 w is 13.91% lower than that of D=0.1 w (w is waist radius). Finally, by adjusting the parameters of two pure phase gratings with orthogonal modulation directions, we generate polarization vortex beams with adjustable topological charges, polarization orders, and diffraction orders in simulations. The polarization analysis shows that the number of spots detected by the polaroid is twice that of the polarization order. Our research has important theoretical and practical value in expanding the application of vortex beams in optical field regulation.