Fig. 1. Historical view of microelectronics development, PIC integration (upper), and ASIC integration (lower).

Fig. 2. Optical fiber transmission capacity trend with respect to all kinds of enabling technologies.

Fig. 3. Schematic diagram of MDM optical interface, including vertical coupling with on-chip mode multiplexer (MUX) and edge coupling with 3D asymmetric waveguide. (i)–(iii) Specific progresses of the MDM interface^[35,36,37].

Fig. 4. Schematic diagram of integrated multimode waveguide bends: (a) the Euler curved bend for four TM modes^[49], (b) the dual-mode bend with MC^[54], (c) the pixelated four-mode bend structure^[51], (d) four-mode bend based on a TIR mirror^[56].

Fig. 5. Schematic diagram of integrated multimode waveguide crossing: (a) two-mode crossing based on non-adiabatic tapered waveguide^[58], (b) three-mode crossing based on pixelated mode MUX and single-mode crossing array^[60], (c) ultra-compact multimode crossing for two TE modes^[61], (d) meta-material-based dual-mode star-crossing^[62].

Fig. 6. Schematic diagram of integrated mode MUX/deMUX: (a) 10-channel mode (de)MUX with dual polarizations by adiabatic tapered ADC^[15], (b) asymmetric Y-junction-based mode MUX^[90], (c) MRRs serving as modulators and mode MUXs simultaneously^[79], (d) four-mode MUX based on pixelated waveguides^[86].

Fig. 7. Schematic diagram of universal (a) MC^[94] and (b) mode exchanger^[98].

Fig. 8. Schematic diagram of (a), (b) integrated PBS based on mode conversion^[102,103] and (c) mode-transparent PBS based on TIR mirror^[110].

Fig. 9. Schematic diagram of (a) Si-based MZI modulator with two branches of light propagating in one multimode waveguide^[112], and (b) spatial mode recycling scheme used to reduce the required power consumption^[113].

Fig. 10. Schematic of (a) mode switch based on two micro-rings^[114] and (b) reconfigurable mode switch based on an MZI structure^[115]. (c) Four-mode thermal switch by geometric-optic inspired multimode 3 dB coupler^[56].

Fig. 11. Schematic diagram of Si optical phased array based on multi-pass recycling structure by mode multiplexing^[119].

Fig. 12. Schematic diagram of integrated interconnect system hybrid multiplexed by WDM, MDM, and PDM.

Fig. 13. Schematic diagram of on-chip switching networks ROADM for multiplexing: (a) on-chip typical multimode optical switching system^[125], (b) on-chip ROADM system for hybrid WDM and MDM^[129].

Fig. 14. (a) Optimized step-index profiles of different FMFs^[133], (b) core-cladding difference for seven-LP-mode fibers with step-index and depressed-inner-core profiles^[134], (c) refractive index profile of ring-assisted four-mode fiber^[135], (d) refractive index profile of ring-assisted seven-LP-mode fiber with trench structure^[136].

Fig. 15. (a) Refractive index profile of two-mode graded-index fiber^[137], (b) refractive index profile of nine-mode graded-index fiber with trench-assisted structure^[138], (c) geometry and parameter definitions of the elliptical core fiber^[142].

Fig. 16. Schematic of a multi-core super-mode fiber^[143].

Fig. 17. (a) Flow chart of the proposed NN-assisted inverse design method. (b) The inverse design frame of the NN^[145].

Fig. 18. Schematic diagram of mode MUX based on free-space beam combiner^[148].

Fig. 19. Directional fiber-coupler-based (a) mode MUX and (b) mode deMUX supporting ${\mathrm{LP}}_{01}$, ${\mathrm{LP}}_{11}$_a, and ${\mathrm{LP}}_{11}$_b modes^[148].

Fig. 20. LPFBG-based (a) mode MUX and (b) mode deMUX supporting ${\mathrm{LP}}_{01}$ and ${\mathrm{LP}}_{11}$_a modes. MC is achieved by LPFBG^[148].

Fig. 21. Schematic diagram of a photonics lantern^[151].

Fig. 22. (a) Ring-shaped erbium doping profile^[154]. (b) Refractive index and doping profile (shaded region) of the four-mode EDF^[155]. (c) Overlaps between mode fields and gain media in a small doped area (left) and a large doped area (right)^[156]. (d) Schematic of dual-core fiber with dual-core doping and colored shadings representing erbium doping^[157]. (e) Schematic description of micro-structure^[158].

Fig. 23. Schematic principle of DRA for mitigating the nonlinear distortion and noise over EDFA^[148].

Fig. 24. Quasi-lossless transmission with bidirectional high-order pump^[166].

Fig. 25. Inverse design based on NN for FM-DRA^[170].

Fig. 26. Recent-year MDM experiments and progresses.

Table 1. Photonic Integration Platforms

Table 2. Cutting-Edge Performance of MDM Interface on SOI

Table 3. Benchmark Performance of MDM Bend

Table 4. The Summary of Mode MUX/deMUX