Fig. 1. OAM separation method with radial varying phase. U0(r,θ),…,U5(x′,y′) are the electric fields, l1,l2 denote different OAM modes, and m1,m2 represent different radial varying phases. Image e is the superposition beam. Image f is the unfolded beam from image e by the coordinate transformation. FSO: free space optical channel. Images a and c are the horizontal distribution phases that unfolded from the vortex phases, and images b and d are the vertical distribution phases unfolded from the radial varying phases.

Fig. 2. Schematic setup for the experiment. L1–L5, lenses; BS, beam splitter; M1 and M2, mirrors; A1 and A2, apertures.

Fig. 3. Demonstration of the propagation properties of the radial varying phase.

Fig. 4. Simulation and experimental results for the proposed separation method with two OAM modes.

Fig. 5. Simulation and experimental results for the proposed separation method with three OAM modes.

Fig. 6. Comparisons of the separation methods based on coordinate transformation and their corresponding separation efficiency. (a) illustrates the method in Ref. [9]; (b) illustrates the method in Ref. [12]; (c) illustrates the proposed method.