Fig. 1. The first- and second-order azimuthal mode bases of few-mode fibers in the (a) LP mode, (b) full vector mode, and (c) OAM mode.

Fig. 2. LP and OAM mode fluorescence emission processes in an FM-EDF. (a) Energy-level structure model of a signal carrying photon excitation based on photon–electron interactions, and evolution of the inversion particle distribution in FM-EDF with respect to the fiber length; (b) local analysis model micro-elements in FM-EDF; (c) normalized intensity of the LP and OAM modes; and (d) local normalized particle number of the ground-state energy level.

Fig. 3. Simulation results for different cases. (a) Lower-energy-level particle population distribution for a range of signal power (−20 to 10 dBm) with a pump power of 600 mW; (b) gain and DMBG of LP and OAM modes with a range of signal power from −15 to 15 dBm; and (c) modal gains of the second-order and first-order signals, DMBG, DMG before and after controlling the mode phase profile in the FM-EDF at a wavelength of 1550 nm with a signal power of −10dBm as functions of the pump power.

Fig. 4. (a) Evolution process of particles in the optical fiber as the length changes; (b) lower-energy-level particle population distribution of different fiber lengths of 2 and 4 m with a pump power of 600 mW; and (c) gain and DMBG of LP and OAM modes with different fiber lengths and a signal power of −10dBm.

Fig. 5. (a) Cross section, (b) refractive index profile, and (c) calculated mode phase and intensity distribution of the FM-EDF used. (d) Experimental optical test system setup for the gain test based on space optical components. SLM, spatial light modulator; QWP, quarter-wave plate; HWP, half-wave plate; Col, collimator; DM, dichroic mirror; BS, beam splitter; Obj, objective lens; PP, phase plate; CCD, charge-coupled device; OSA, optical spectrum analyzer.

Fig. 6. (a) Modal intensity distributions and interference patterns of the first- and second-order signal modes at a wavelength of 1550 nm under 150-mW total pump power and (b) modal intensity distributions and interference patterns obtained by shortening the fiber length from 2.2 to 0.2 m.

Fig. 7. Measured modal gains of the second- and first-order signals, DMBG, and DMG before and after controlling the mode phase profile in the FM-EDF at a wavelength of 1550 nm with a signal power of −10dBm as functions of the pump power.

Fig. 8. (a) Modal intensity distributions of the LP (top row) and OAM modes (bottom row) with a range of signal power from −10 to 10 dBm at a wavelength of 1550 nm under 300-mW total pump power. (b) Measured modal gain of the second-order signal between the LP and OAM modes in the FM-EDF under amplification at a 1550-nm wavelength with a range of signal power from −15 to 15 dBm; the red line represents the DMBG.