Fig. 1. Dispersion curves of LP01 and LP11; the relationship of the LPG period and the resonance wavelength.

Fig. 2. Converter producing and controlling the OAM modes.

Fig. 3. Experimental setup. WDM: wavelength division multiplexing coupler; EDF: erbium-doped fiber; OC: optical coupler; PC: polarization controller; PD-ISO: polarization-dependent isolator; LPG: long period grating; CCD: charge coupled device, infrared camera; OSA: optical spectrum analyzer.

Fig. 4. (a) Relationship between the pump power and output power of the laser in the continuous state (pentagon) or mode-locked state (circle). (b) The output spectrum of the laser running in the continuous state. (c) The output spectrum of the laser running in the mode-locked state. (d) The mode-locked pulse trains recorded by the oscilloscope. (e) The pulse recorded by autocorrelation and its fitting. (f) The infrared CCD image of the near-field intensity distribution: a1–f1 are when the laser is excited in the continuous state, a2–f2 are when the laser is running in the mode-locked state. a1 and a2 are LP01 modes, b1 and b2 are LP11 modes, c1, c2, e1, and e2 are in OAM modes with topological charges of +1 and −1, respectively; d1, d2, f1, and f2 are interference patterns of the corresponding OAM modes and reference beam.