Fig. 1. (a) Schematic of the PS in the spherical coordinate system represented by the traditional latitude and longitude circles, (b) the sine-form varying ellipticity ϵA in a range of [−1,1] along δ, and (c) the sine-form varying ellipticity ϵB in a range of [0, 1] along δ.

Fig. 2. Schematic of the experimental setup for generating the desired EV-VOFs. L1 and L2, a pair of lenses; λ/2, half-wave plates; SF, spatial filter; G, Ronchi phase grating; PC, computer.

Fig. 3. Generated EV-VOFs when (m,n)=(1,0), (2, 0), (0, 1), and (1, 1). The first row gives the total intensity patterns and corresponding schematics of the SoPs, and the second and third rows show the simulated and measured x-component intensity patterns, respectively, for the EV-VOFs with the sine-form varying ellipticity in a range of [−1,1].

Fig. 4. Generated EV-VOFs when (m,n)=(1,0), (2, 0), (0, 1), and (1, 1). The first row gives the total intensity patterns and corresponding schematics of the SoPs, and the second and third rows show the simulated and measured x-component intensity patterns, respectively, for the EV-VOFs with the sine-form varying ellipticity in a range of [0, 1].

Fig. 5. Intensity distributions and the Poynting vectors in the focal plane of the tightly focused EV-VOFs with the sine-form varying ellipticity in a range of [−1,1] when (m,n)=(2,0), (4, 0), and (6, 0) (left, middle, and right columns, respectively). The intensity patterns of the tightly focused fields are shown in the first row, and the transverse and longitudinal components of the normalized Poynting vectors in the focal plane are shown in the second and third rows, respectively. The direction of the transverse energy flow is shown by the black arrows. All images have dimensions of 4λ×4λ.

Fig. 6. Schematic structures of the phase masks and the Poynting vectors of the tightly focused EV-VOFs with the sine-form varying ellipticity in a range of [0, 1] when (m,n)=(1,0). The cases of twofold, fourfold, and sixfold fanlike phase masks are shown in the first, second, and third columns, respectively. The schematics of fanlike phase masks are shown in the first row, and the transverse and longitudinal components of the normalized Poynting vectors in the focal plane are shown in the second and third rows, respectively. The direction of the transverse energy flow is shown by the black arrows. All images in the second and third rows have dimensions of 4λ×4λ.

Fig. 7. Transverse components of the Poynting vectors of the tightly focused EV-VOFs with the sine-form varying ellipticity in a range of [0, 1] when (m,n)=(1,0). The cases of twofold, fourfold, and sixfold fanlike phase masks are shown in the first, second, and third rows, respectively. The rotation angles of the phase masks in columns 1–4 are 0, π/4, π/2, and 3π/4, respectively. The insets show the corresponding fanlike phase masks used. The direction of the transverse energy flow is shown by the black arrows. All images have dimensions of 4λ×4λ.

Fig. 8. Intensity distributions and the Poynting vectors of the tightly focused vortex EV-VOFs with the sine-form varying ellipticity in a range of [0, 1] when (m,l)=(3,1), (4, 2), (5, 2), and (6, 3) (columns 1–4, respectively). The intensity patterns of the tightly focused fields are shown in the first row, and the transverse and longitudinal components of the normalized Poynting vectors in the focal plane are shown in the second and third rows, respectively. The direction of the transverse energy flow is shown by the black arrows. All images have dimensions of 4λ×4λ.

Fig. 9. Transverse components of the normalized Poynting vectors of the tightly focused vortex EV-VOFs with the sine-form varying ellipticity in a range of [−1,1] when (m,l)=(1,5),(2,5),(3,5),(4,5),(5,5), and (6, 5). The direction of the transverse energy flow is shown by the black arrows. All images have dimensions of 4λ×4λ.