Fig. 1. Light field characteristic of optical vortices carrying OAM modes and CVB modes using high-order Poincaré sphere, where ±1 OAM modes with orthogonal circular polarizations are located at the north and south poles, respectively, whereas CVB modes with varying polarization angles are distributed along the equator.

Fig. 2. Schematic diagram of an OAM/CVB mode-based communication network, with mode (de)modulation, mode processing, and mode transmission as the three main cornerstones.

Fig. 3. Technologies and schemes related to mode (de)modulation, mode processing, and mode transmission.^8–240" target="_self" style="display: inline;">^–240

Fig. 4. OAM modulation technologies and applications. (a) Principle of N-bit multi-state integer-order OAM mode modulation, (b) the method for encoding 8-bit binary sequence using 8 OAM modes, and (c) the corresponding OAM-SK communication link. Figure reproduced with permission from Ref. 27 (CC-BY).

Fig. 5. Measurement-based mode demodulation technologies. (a) Interference patterns of vortex beams with plane waves and spherical waves. (b) Principles and (c) results of OAM mode demodulation using Dammann vortex grating, reproduced with permission from Ref. 12 (CC-BY). (d) OAM mode demodulation using triangular aperture, reproduced with permission from Ref. 54 © 2010 APS.

Fig. 6. Deep learning-based OAM mode demodulation technologies. (a) A 7-layer CNN and (b) its performances for OAM mode detection, reproduced with permission from Ref. 68 © 2017 IEEE. (c) Feature extraction and (d) OAM-SK communication using cylindrical lenses, reproduced with permission from Ref. 69 (CC-BY). (e) Superhigh-resolution fractional-order OAM mode recognition, reproduced with permission from Ref. 17 © 2019 APS. (f) OAM mode spectrum analysis using diffraction optical neural network, reproduced with permission from Ref. 89 (CC-BY).

Fig. 7. Angle-separated gratings for mode (de)multiplexing. (a) Schematic diagram of multiplexing and demultiplexing of four OAM modes (−9,−3,3,9) using Dammann vortex gratings, (b) the corresponding communication experimental setup, and (c) the BER and constellation. Figure reproduced with permission from Ref. 13 (CC-BY).

Fig. 8. Angular lenses for mode sorting. (a) Illustration of the working principle of the angular lens, reproduced with permission from Ref. 108 (CC-BY). (b) Spin-decoupled metasurface-based momentum transformation for simultaneous detection of spin and OAM modes, reproduced with permission from Ref. 110 (CC-BY).

Fig. 9. Coordinate transformation for mode (de)multiplexing. (a) Mode coordinate transformation with high resolution via beam copying, reproduced with permission from Ref. 117 (CC-BY). (b) Compact and high-performance vortex mode sorter and (c) 50 km OAM-MDN-WDM system experimental setup, reproduced with permission from Ref. 120 (CC-BY).

Fig. 10. Multi-plane light conversion. (a) Laguerre-Gaussian mode sorter based on multi-plane light conversion for 210 OAM modes and (b) its measured total crosstalk of LG modes. Figure reproduced with permission from Ref. 132 (CC-BY).

Fig. 11. Multi-dimensional modulation multi-layer mode sorter for simultaneously (de)multiplexing modes and wavelengths or polarizations. (a) Broadband OAM mode multiplexing and demultiplexing, reproduced with permission from Ref. 142 © 2024 Wiley-VCH. (b) CVB mode and wavelength parallel multiplexing and demultiplexing, reproduced with permission from Ref. 146 (CC-BY).

Fig. 12. On-chip devices. (a), (b) Integrated circular phase array for OAM multiplexing and communication performances, reproduced with permission from Ref. 158 (CC-BY). (c), (d) Multi-mode micro-ring emitter for OAM mode multiplexing communication and its performances, reproduced with permission from Ref. 150 (CC-BY). (e), (f) On-chip phase demodulator for high-speed coherent optical and coherent optical communication testing, reproduced with permission from Ref. 160 © 2024 Wiley-VCH.

Fig. 13. Mode exchanging technologies. (a) Mode exchange using helical phase plate, reproduced with permission from Ref. 10 (CC-BY). (b) CVB exchanging via cascaded q-plates, reproduced with permission from Ref. 162 (CC-BY).

Fig. 14. Mode channel add/drop and routing technologies. (a) OAM mode add/drop multiplexer using mode down/up conversion, reproduced with permission from Ref. 231 © 2012 IEEE. (b) Experimental setup and (c) communication performances of regional phase gratings for OAM modes add/drop, reproduced with permission from Ref. 171 (CC-BY).

Fig. 15. OAM mode division and multiplication using optical transformations. (a) Multiplication and division of OAM modes with diffractive transformation optics, reproduced with permission from Ref. 178 (CC-BY). (b), (c) Arbitrary multiplication and division of OAM modes, reproduced with permission from Ref. 181 © 2020 AIP. (d) Multiplication and division of OAM modes by Fermat’s spiral transformation, reproduced with permission from Ref. 182 (CC-BY).

Fig. 16. OAM mode logic operation using optical transformations. (a) High-dimensional quantum gates using OAM modes and radial index, reproduced with permission from Ref. 165 (CC-BY). (b) OAM mode logic operation using optical diffractive deep neural networks, reproduced with permission from Ref. 21 (CC-BY).

Fig. 17. OAM mode channels filtering technologies. (a)–(c) Concept and experimental results of tunable OAM mode filter based on geometrical transformation, reproduced with permission from Ref. 185 © 2014 Optica Publishing Group. (d) OAM mode filter based on azimuthal beam shaper, reproduced with permission from Ref. 187 (CC-BY).

Fig. 18. Free-space propagation of optical vortex beams. (a) Indicators of OAM mode divergence, reproduced with permission from Ref. 28 (CC-BY). (b) OAM mode waist compensation system based on lens set, reproduced with permission from Ref. 189 © 2016 Optica Publishing Group. (c) Quasi-ring Airy vortex beam, reproduced with permission from Ref. 191 (CC-BY).

Fig. 19. Turbulence disturbance of vortex beams. (a) Schematic diagram of OAM mode distortion and crosstalk caused by atmospheric turbulence, reproduced with permission from Ref. 193 © 2014 Optica Publishing Group. (b), (c) OAM mode compensation using optical adaptive systems, reproduced with permission from Refs. 192 and 203 © 2014 Optica Publishing Group. (d) CNN-based compensation for OAM mode multiplexing, reproduced with permission from Ref. 207 © 2020 IEEE.

Fig. 20. Orbital angular momentum mode fibers. (a), (b) Cross-sectional diagram and performances of modulated-refractive-index RCF, reproduced with permission from Ref. 216 (CC-BY). (c), (d) Cross-section and performances of 19-ring MRCF, reproduced with permission from Ref. 228 © 2020 IEEE.

Fig. 21. Mode transmission using fiber. (a) Experimental setup, (b) transmission spectrum, and (c) results of an all-fiber laser for generating CVBs, reproduced with permission from Ref. 252 © 2018 Optica Publishing Group. (d) Experimental setup used for LP11 mode oscillation in an all-FMF laser, reproduced with permission from Ref. 253 (CC-BY).