Fig. 1. A tightly focusing system with a X-type vortex beam as the incident field

Fig. 2. Intensity distribution on the focal plane with the different anisotropic parameters $c$，where$\alpha =\mathrm{80}°,n=\mathrm{1}$

Fig. 3. Locations of the intensity maxima on the focal plane with the different anisotropic parameters $c$，where $\alpha =\mathrm{30}°,\mathrm{60}°,\mathrm{80}°,n=\mathrm{1}$

Fig. 4. Locations of the intensity maxima on the focal plane with the different anisotropic parameters $c$ for the case of RCP， where$\alpha =\mathrm{30}°,\mathrm{60}°,\mathrm{80}°,n=\mathrm{1},c<\mathrm{0}$

Fig. 5. Locations of the intensity maxima on the focal plane with the different anisotropic parameters c for the case of linear polarization，where $\alpha =\mathrm{30}°,\mathrm{60}°,\mathrm{80}°,n=\mathrm{1}$

Fig. 6. Intensity distribution on the focal plane changes with the different anisotropic parameters c，where $\alpha =\mathrm{80}°,n=\mathrm{2}$

Fig. 7. Locations of the intensity maxima on the focal plane with the different anisotropic parameters $c$，where$\alpha =\mathrm{30}°,\mathrm{60}°,\mathrm{80}°,n=\mathrm{2}$

Fig. 8. Locations of the intensity maxima on the focal plane with the different anisotropic parameters $c$ for the case of linear polarization，where $\alpha =\mathrm{30}°,\mathrm{60}°,\mathrm{80}°,n=\mathrm{2}$

Fig. 9. Intensity distribution on the transverse planes along the propagation direction，where the unit of $z_{\mathrm{s}}$ is $\lambda$，$\alpha =\mathrm{80}°,n=\mathrm{1},c=\mathrm{0.3}$

Fig. 10. Variation of the azimuthal angles of the intensity maxima along the propagation direction，here$\alpha =\mathrm{80}°,$

Fig. 11. The intensity distribution and the corresponding phase of the main field component with the beam propagation. Here the unit of $z_{\mathrm{s}}$ is $\lambda$，$\alpha =\mathrm{80}°,n=\mathrm{2},c=\mathrm{0.3}$

Fig. 12. Variation of the azimuthal angles of the intensity maxima along the propagation direction，here $\alpha =\mathrm{80}°,n=\mathrm{2},c=\mathrm{0.3}$

Fig. 13. Field component distribution with the beam propagation，here$\alpha =\mathrm{80}°,n=\mathrm{2},c=\mathrm{0.3}$

Fig. 14. Variation of the azimuthal angles of the vortices of $e_l/e_r$ components along the propagation direction for the cases of LCP and RCP，here $\alpha =\mathrm{80}°,n=\mathrm{2},c=\mathrm{0.3}$