Fig. 1. Design of the azimuthal beam shaper. (a) The schematic of the system. The angular shaper consists of a phase-only SLM and a dielectric mirror. The MPLC for sorting and OAM spectral modulation and a combination of the OAM modes are implemented on the SLM. The system works in a sequence of “OAM mode sorting—mode spectral modulation—OAM mode recombination.” The input port also serves as the output port. (b) Inverse-designed phase pattern of the MPLC for transforming the coaxial OAM modes into spatially separated elliptical beams. (c) The compositions of the phase pattern of R5 are static phase for spectral modulation, 2ϕ5 for conjugating the wavefront, and linear phase for inverting the optical axis.

Fig. 2. Characterization of the azimuthal beam shaper. (a) The insertion loss for each OAM mode. (b) The variation of the mode conversion loss with radius of the incident beam r0. (c) The variation of the mode conversion loss with width-radius ratio w0/r0. As the phase pattern is horizontally symmetrical, OAM modes with the same |ℓ| have the same performance. IL, insertion loss; MCL, mode conversion loss; and MDCL, mode-dependent conversion loss.

Fig. 3. Demonstration of rotation of the beam with linear phase applied to the OAM mode spectrum. (a) Rotation of a petal-like beam with an OAM mode spectrum of Aℓ=exp(0.09ℓ2)exp(iℓπ). (b) Rotation of a petal-like beam with an OAM mode spectrum of Aℓ=exp(0.09ℓ2). The rotation is performed at an interval of θ=π/4 across 2π azimuthal space. Sim.: simulation and Exp.: experiment.

Fig. 4. Demonstration of the beam splitting and combining with Talbot phase applied to the OAM spectrum. (a) The initial beam is split into two or three beams as a result of twofold or threefold Talbot self-imaging in azimuth. (b) Combination of two beams by an inverse process of twofold self-imaging. (c) Combination of three beams by an inverse process of threefold self-imaging.

Fig. 5. Demonstration of the OAM mode spectrum filter. (a) By controlling the region of grating, the odd-order OAM modes are filtered out and the even-order OAM modes are preserved. The amplitude modulation is conjunction with a linear phase modulation. (b) OAM mode with ℓ=3k(k∈Z) is preserved.