Different orders of optical vortex generation on demand. (a)–(d) A Vortex laser with the first order of orbital angular momentum optical vortex emission, where the magnetic field intensity distributions inside the laser cavity (a), and |H| (b), H_r (c), and arg (H_r) (d) at 4 μm above the lase cavity are depicted. (e)–(h) A Vortex laser with the second order of orbital angular momentum optical vortex emission, where the magnetic field intensity distributions inside the laser cavity (e), and |H| (f), H_r (g), and arg (H_r) (h) at 4 μm above the lase cavity are depicted. (i)–(l) A Vortex laser with the third order of orbital angular momentum optical vortex emission, where the magnetic field intensity distributions inside the laser cavity (i), and |H| (j), H_r (k), and arg (H_r) (l) at 4 μm above the lase cavity are depicted. All systems have the same index modulation (Δn_R = Δn_I = 0.01).