Fig. 1. Phases, polarization states and OAM spectra of a single Gaussian beam with different vortex and polarization topological charges. (a), (d), (g): (l, m)=(1, 0); (b), (e), (h): (l, m)=(1, 1); (c), (f), (i): (l, m)=(2, 2). (d), (e), (f): RH (Red) and LH (Blue) elliptical polarizations

Fig. 2. The OAM spectra (d)−(f) and OAM densities (g)−(i) of beam arrays in coherent combinations with radial, rectangular and linear symmetries at z=0. (a), (d), (g): radial symmetry; (b), (e), (h): rectangular symmetry; (c), (f), (i): linear symmetry. The parameters are (l, m)=(1, 1), η=0, N=6 and ρ=5w₀

Fig. 3. (a) Illustration of center optical vortex at (0, 0, z) of beam array in coherent combination with radial symmetry at the output plane. (b) Spiral phase of center optical vortex. (c) OAM-spectra of the corresponding beam arrays. The parameters are (l, m)=(0, 0), η=+1, N=8 and ρ=5w₀

Fig. 4. The correspondence between the topological charge of central optical vortex and maximal modes of OAM-spectra for different l, m, η at z=10z_e. (a)−(d): m=1; (e)−(h): m=2. The parameters are N=8 and ρ=3w₀

Fig. 5. OAM-spectra, spiral phases of central optical vortex and OAM densities for different η. η=−2, η=−1, η=1, and η=2 respectively, from top to bottom.The parameters are (l, m)=(1, 1), N=8, ρ=3w₀ and z=10z_e

Fig. 6. (a) Effect of polarization topological charges and the number of beamlets on weight of maximal mode in OAM-spectra for a fixed l+η=2. (b) The corresponding weight in OAM-spectra for (l, η)=(2, 0). The other parameters are the same as in Fig. 5

Fig. 7. Locations of non-zero weight for OAM-modes with an increasing of the number of beamlet N for different l, η and m. (a): (l, η, m)=(1, 0, 1), (b): (l, η, m)=(2, 0, 1), (c): (l, η, m)=(1, 0, 2), (d): (l, η, m)=(1, −2, 1)