Fig. 1. (a) PTC sorting setup, (b) the angle function α1(x,y) of optical geometric transverter (OGT), and (c) α2(x,y) of optical phase corrector (OPC).

Fig. 2. Simulation of the optical geometric transformation of vector beams with m=1. OGT is at z/f=−1, the first lens is at z/f=0 and OPC is at z/f=1.

Fig. 3. Intensity profiles at a distance from the first lens to OPC: z=250, 750, 1000 mm. (a)–(c) are experimental records by CCD camera, while (d)–(f) are simulation results.

Fig. 4. (a) Intensity profile of incident vector beam with m=−2, (b) the horizontal and (c) the vertical polarization components, and the intensity distributions at image plane for the incident beam with PTC values of (d) m=−2, −1, 0, 1, and 2, and (e) m=0 and −2.

Fig. 5. (a) x–directional integral intensity distribution of the vector fields along the y direction with the PTC values of m=−2, −1, 0, 1, and 2 at the image plane. (b) Experimental intensity distribution via different PTC values from −2 to 2 over whole detection regions.