Fig. 1. Principle of generating arbitrary TAM states.

Fig. 2. Holograms to generate multiplexed scalar vortex beams, and their corresponding far-field diffraction patterns and OAM spectra. The OAM state distributions are (a) $(|-1\rangle +|+2\rangle )$, (b) $(|-4\rangle +|-3\rangle +\text{|}+1\rangle )$, and (c) $(|-4\rangle +|-3\rangle +|+1\rangle )e^{i\pi }$.

Fig. 3. The experimental setups for generating and testing arbitrary TAM states. LD, laser diode; PBS, polarized beam splitter; HWP1 & 2, half-wave plate; $\text{SLM}1\text{–}\text{SLM}3$, liquid-crystal spatial light modulator; QWP, quarter wave plate; P, polarizer; L, convex lens; CCD, infrared CCD camera. (a) Generating arbitrary TAM states. (b) Detection of vector polarization properties. (c) Detection of OAM distributions.

Fig. 4. Experimental results of generating separable TAM states. (a) $|L\rangle |+1\rangle$ and (b) $|R\rangle |+3\rangle$.

Fig. 5. Experimental results of generating non-separable TAM states with homogeneous transverse polarizations. (a) $|\mathrm{\Psi }\rangle =|R\rangle (|-3\rangle +|-1\rangle +|+1\rangle +|+3\rangle )+|L\rangle (|-3\rangle +|-1\rangle +|+1\rangle +|+3\rangle )$, and (b) $|\mathrm{\Psi }\rangle =|R\rangle (|-3\rangle +|-1\rangle +|+1\rangle +|+3\rangle )+\exp (i\pi )|L\rangle (|-3\rangle +|-1\rangle +|+1\rangle +|+3\rangle )$.

Fig. 6. Experimental results of generating non-separable TAM states with anisotropic transverse polarizations. The generated TAM state is $|\mathrm{\Psi }\rangle =|R\rangle (|-1\rangle +|+1\rangle )+|L\rangle |+2\rangle$.