Fig. 1. Free-space mode multiplexer/demultiplexer. (a) 15-LP mode MPLC device^[19]; (b) 6-LP mode 3D waveguide device^[16]

Fig. 2. Performance comparison of photonic lantern based on different fibers^[20] (GIF—graded-index fiber; SI-DCF—step-index double-cladding fiber; SMF—single-mode fiber). (a) Mode field diameter variation of three fibers during tapering; (b) relationship between loss and taper transition length of 3-LP mode photonic lantern based on different fibers

Fig. 3. All-fiber photonic lantern (PL) ^[20]. (a) Side view of the tapering area of PL; (b) end view of 3-LP mode PL; (c) end view of 4-LP mode PL; (d) end view of 6-LP mode PL; (e) end view of 7-LP mode PL; (f) packaged 3-LP mode PL; (g) packaged 6-LP mode PL

Fig. 4. Schematic of MDM optical transmission system and amplifier based on FM-EDFA

Fig. 5. Schematics of pump scheme. (a) Core-pumping; (b) cladding pumping

Fig. 6. Schematics of cladding-pumping scheme. (a) End-face coupling; (b) side coupling

Fig. 7. DMG manipulation strategy of FM-EDFA

Fig. 8. Core-pumped FM-EDFA based on different mode converters. (a) 6-LP mode FM-EDFA based on phase plate^[27]; (b) 6-LP mode FM-EDFA based on photonic lantern^[28]; (c) 3-LP mode FM-EDFA based on mode selective coupler^[29]

Fig. 9. FM-EDFA with higher-order mode core-pumping. (a) LP₁₁ mode core-pumping ^[30]; (b) bidirectional hybrid core-pumping ^[31]

Fig. 10. Structure diagrams of FM-EDFA based on cladding pumping. (a) 4-LP mode group FM-EDFA with end-face coupling^[24]; (b) 3-LP mode FM-EDFA with side coupling^[32]; (c) 6-LP mode FM-EDFA with end-face coupling^[33]; (d) 6-LP mode Er/Yb co-doped optical fiber amplifier with end-face coupling^[34]

Fig. 11. Two FM-EDFs with different refractive index distributions^[22]. (a) Normal distribution FM-EDF; (b) central depressed FM-EDF

Fig. 12. Design and fabrication of ring-core FM-EDF. (a) Theoretical designed ring-core FM-EDF^[35]; (b) calculated gain of FM-EDFA based on designed ring-core FM-EDF over the C-band^[35]; (c) fabricated 2-LP mode group FM-EDF^[36]; (d) experimental measured DMG of fabricated 2-LP mode group FM-EDF^[36]

Fig. 13. Two kinds of classical design of ring-core FM-EDF. (a) 18-LP mode FM-EDF^[37]; (b) 3-LP mode FM-EDF^[38]

Fig. 14. Cross-section of two kinds of FM-EDF. (a) 10-LP mode group FM-EDF^[39]; (b) 21-LP mode FM-EDF^[40]

Fig. 15. Single-layer ring-core erbium ion doping scheme. (a) 2-LP mode group FM-EDF design with non-uniform erbium ion doping^[42]; (b) refractive index and erbium-doped profile of fabricated 2-LP mode group FM-EDF^[43]

Fig. 16. Multiple-layer ring-core erbium ion doping scheme. (a) 4-LP and 6-LP mode FM-EDF design^[44]; (b) 4-LP mode over-doped FM-EDF^[45]; (c) 6-LP mode double-layer FM-EDF^[46]; (d) 4-LP mode double-layer over-doped FM-EDF^[47]

Fig. 17. Multiple-layer ring-core erbium ion doping scheme. (a) 3-LP mode FM-EDF^[48]; (b) 4-LP mode FM-EDF^[49]; (c) 4-OAM mode FM-EDF^[50]

Fig. 18. Two-LP mode gain equalization based on spatial light modulator^[51]. (a) Top view; (b) side view

Fig. 19. Schematic of DMG reduction through femtosecond laser etching and variation in gain and DMG of different modes with wavelength^[52]

Fig. 20. Mode-dependent loss adjusting device based on femtosecond laser-induced index tailoring^[53]. (a) Microscopic image of the device; (b) relationship between device length and mode loss; (c) relationship between femtosecond laser scanning times and mode loss; (d) differential mode attenuation (DMA) over the C-band

Fig. 21. 2-LP mode group FM-EDFA DMG equalization based on femtosecond laser induced refractive index tailoring^[54]. (a) Mode gain and DMG of FM-EDFA before equalization; (b) evolution of DMG with length; (c) evolution of DMG with femtosecond laser scanning times; (d) mode gain and DMG of FM-EDFA after equalization