Fig. 1. Scheme of the ANU-OAM with (a,b)=(0,0) and (m,n)=(2,2). (a), (c), and (e) The intensity, phase, polarization, and energy flow direction for the +1st order, −1st order, and the superposed VOF, respectively. (b) and (d) Dependence of the intensity modulated OAM per photon on the azimuthal coordinate ϕ for the ±1st orders. (f) Dependence of the average OAM per photon on the azimuthal coordinate for the superposed VOF. The blue and red arrows represent the directions of the energy flow, and the white arrows represent the polarization directions. The green and gray-scale patterns represent the intensity and phase distributions of the optical fields, respectively.

Fig. 2. Schematic of the experimental setup for generating and measuring the desired VOFs carrying ANU-OAM. (a) The generating setup. SLM, spatial light modulator; L1 (f=300mm) and L2 (f=200mm), a pair of lenses; λ/4, quarter-wave plate; SF, spatial filter; G, Ronchi phase grating; CCD, charge-coupled device; inset, two-dimensional holographic grating. (b) The interference setup. BS, beam splitter; M, mirror. The white cuboid in (b) represents the setup in (a).

Fig. 3. VOFs carrying ANU-OAM with (a,b)=(0,0) and (m,n)=(2,2). (a) The total intensity pattern and the simulated SoP distribution with linear (white), left-handed (red), and right-handed (yellow) polarizations, respectively. (b) The interference pattern between the +1st order and the horizontally polarized reference beam. (c) The interference pattern between the −1st order and the vertically polarized reference beam. The measured Stokes parameters of (d) S1, (e) S2, and (f) S3 are shown in the second row. The corresponding simulated Stokes parameters are shown in the insets, respectively.

Fig. 4. Numerically simulated OAM spectra of two vortex optical fields with non-uniform amplitude profiles expressed as (a) |cos(2ϕ)|ei4ϕvα and (b) cos(2ϕ)ei4ϕvα, respectively. The spectral intensities are normalized by the maximum intensity of the initial mode.

Fig. 5. Intensity of the perfect VOFs carrying ANU-OAM with m=1,2,3 and n=1,2. All of the pictures have the same size of 1.2mm×1.2mm.

Fig. 6. Dependence of the radius R of the experimentally generated perfect VOFs carrying ANU-OAM with (m,n)=(1,2), (2,1), and (5,2) on the propagation distance z within a propagation range of z∈[−40,40]mm.