Fig. 1. Schematic illustration of field distributions (polarization, amplitude, phase) of (a,b) polarization vortex and (c,d) phase vortex beams. (a) Radially polarized beam (TM01). (b) Azimuthally polarized beam (TE01). (c) OAM beam with topological charge value of +1 (OAM+1). (d) OAM beam with topological charge value of −1 (OAM−1).

Fig. 2. Schematic illustration of physical dimensions of photons (frequency/wavelength, time, complex amplitude, polarization, spatial structure) and orthogonal states (multiple wavelengths, time slots, constellation points in the complex plane, X- and Y-polarizations, polarization vortices, phase vortices) in modulation schemes and multiplexing techniques.

Fig. 3. Schematic illustration of optical vortex modulation and optical vortex multiplexing. (a) Polarization vortex modulation. (b) Phase vortex modulation. (c) Polarization vortex multiplexing. (d) Phase vortex multiplexing.

Fig. 4. Experimental setup for generating and detecting polarization vortex beams (radially/azimuthally polarized and high-order vector beams) with a single SLM. Pol., polarizer; M, mirror.

Fig. 5. (a) Phase patterns loaded to SLM for the generation of four polarization vortex beams (radially polarized beam P=1, ϕ0=0, azimuthally polarized beam P=1, ϕ0=π/2, vector beam P=2, ϕ0=0, vector beam P=3, ϕ0=0). (b) Linear polarizer with orientation of 0°, −45°, 90°, 45° with respect to the y direction. (c)–(f) Left column: illustration of spatially variant polarization of four polarization vortex beams. Right four columns: measured multipetal intensity profiles of four polarization vortex beams after linear polarizer.

Fig. 6. Measured multipetal intensity profiles of 16 polarization vortex beams after linear polarizer.

Fig. 7. Schematic illustration of (a) conversion from planar phase fronts to helical ones and (b) backconversion from helical phase fronts to planar ones using spiral phase masks loaded to the SLM.

Fig. 8. Schematic illustration of a controllable all-fiber OAM mode converter.

Fig. 9. Measured (a,c) intensity profiles and (b,d) interferograms (interference with reference Gaussian beam) of the generated (a,b) OAM−1 and (c,d) OAM+1 modes using an all-fiber device.

Fig. 10. Schematic illustration of simultaneous demultiplexing and steering of multiple OAM modes using a single complex phase mask.

Fig. 11. Measured intensity profiles for the demultiplexing of OAM l=±6, ±7, ±8, ±9 with circular-shaped beam steering of demultiplexed beams.

Fig. 12. Schematic illustration of optical communications using polarization vortex modulation.

Fig. 13. Free-space 64×64  pixels Lena gray image transfer through a visible-light communication link using polarization vortex modulation.

Fig. 14. Schematic illustration of optical communications using phase vortex (OAM-carrying Bessel beam) modulation.

Fig. 15. Measured intensity profiles for free-space data information transfer using phase vortex (OAM-carrying Bessel beam) modulation. (a) Hexadecimal coding. (b) Decoding for hexadecimal number 4, 7, and 15. (c) 32-ary coding. (d) Decoding for 32-ary number 14.

Fig. 16. Measured BER for free-space data information transfer using hexadecimal and 32-ary phase vortex (OAM-carrying Bessel beam) modulation.

Fig. 17. Schematic illustration of free-space optical communications using phase vortex (OAM beams) multiplexing combined with other multiplexing techniques (e.g., polarization multiplexing).

Fig. 18. Measured intensity profiles and BER performance for free-space communications using 10 Gbaud 16-QAM signals over four OAM beams (four channels in total).

Fig. 19. Measured intensity profiles and BER performance for free-space communications using 10 Gbaud 16-QAM signals over pol-muxed four OAM beams (eight channels in total).

Fig. 20. Measured intensity profile and BER performance for free-space communications using 20 Gbaud 16-QAM signals over pol-muxed eight OAM beams in two groups of concentric rings (32 channels in total).

Fig. 21. Measured intensity profiles and BER performance for free-space optical communications using 17.9  Gbit/s OFDM/OQAM 64-QAM signals over pol-muxed 22 OAM modes (44 channels in total).

Fig. 22. Schematic illustration of N-dimensional multiplexing for increased spectral efficiency (OAM multiplexing, PDM, Nyquist m-QAM signal).

Fig. 23. Schematic illustration of N-dimensional multiplexing for increased transmission capacity and spectral efficiency (OAM multiplexing, PDM, WDM, multicarrier multilevel modulation signal).

Fig. 24. Schematic illustration of multi-OAM multiring fiber.

Fig. 25. Schematic illustration and simulated intensity/phase distribution of compact trench-assisted multi-OAM multiring fiber.

Fig. 26. Schematic illustration and simulated intensity/phase distribution of multi-OAM multicore supermode fiber.

Fig. 27. Schematic illustration of fiber optical communications using modes modulation (LP01, LP11a, LP11b, and OAM−1).

Fig. 28. Schematic illustration of the proposed OAM-based MDM-TDM-PON architecture (hybrid OAM multiplexing and TDM PON). ODN, optical distribution network; Mux/Demux, multiplexing/demultiplexing; OC, optical coupler.

Fig. 29. (a) Cross section of the FMF. (b) Relative refractive index profile (step-index) of the FMF. (c) Supported six eigenmodes in two mode groups of the FMF.

Fig. 30. (a) Complex phase patterns for the generation of OAM+1 and OAM−1 modes. (b) Measured intensity profiles and interferograms for input OAM modes. (c) Measured intensity profiles and interferograms for output OAM modes after 1.1 km FMF transmission.

Fig. 31. Measured BER performance for OAM-based MDM-TDM-PON (hybrid OAM multiplexing and TDM PON). (a) Downstream transmission link. (b) Upstream transmission link.