Fig. 1. Polarization distribution of (a) natural, unpolarized light, (b) linearly polarized beam, (c) RPB, (d) APB, and (e) hybridly polarized beam.

Fig. 2. Phase evolution of (a) VB, (b) plane wave, and (c) spherical wave.

Fig. 3. Mode distributions of TMF under (a) scalar approximation and (b) corresponding groups of the vector modes. Adapted with permission from Ref. 80 © OSA Publishing.

Fig. 4. (a) Flow diagram and (b) experimental setup for generating CVBs based on an acoustically induced LPFG. SMF, single-mode fiber; EDFA, erbium-doped fiber amplifier; PC, polarization controller; TMF, two-mode fiber; MS, mode stripper; MO, micro-objective; GT, Glan–Taylor prism polarizer; CCD, charge coupled device. (c) Intensity patterns of (c₁), (c₃), (c₅) RPB and (c₂), (c₄), (c₆) APB at (c₁), (c₂) 633 nm, (c₃), (c₄) 532 nm, and (c₅), (c₆) 1550 nm before and after passing a polarizer. Adapted with permission from Ref. 80 © OSA Publishing.

Fig. 5. Mode-selective coupler based on tapered SMF and TMF.

Fig. 6. (a) Configuration of the all-TMF laser for ${\mathrm{LP}}_{11}$ mode oscillation. TM-EDF, two-mode erbium-doped fiber; PC, polarization controller; OSA, optical spectrum analyzer; CCD, charge coupled device; MSC, mode-selective coupler; WDM, wavelength division multiplexer. (b) Spectrum of the TMF laser; the inset shows the near-field pattern of the generated ${\mathrm{LP}}_{11}$ mode. (c) The relationship between the pump and output powers. Adapted with permission from Ref. 101 © OSA Publishing.

Fig. 7. (a) Diagram of the offset-spliced SMF and TMF. Calculated coupling efficiency of the fundamental mode to (b) ${\mathrm{TM}}_{01}$ mode and (c) ${\mathrm{TE}}_{01}$ mode versus mismatch distances $\mathrm{\Delta }R$. The polarization of the fundamental mode is (b) parallel and (c) perpendicular to the mismatch direction $y$, respectively. The insets show the calculated normalized intensities and polarization distributions of the ${\mathrm{TM}}_{01}$ and ${\mathrm{TE}}_{01}$ modes, respectively. (d) Measured images of the SMF and TMF before and after splicing. Adapted with permission from Ref. 105 © AIP Publishing.

Fig. 8. (a) Reflection spectrum of TMFBG and SMFBG. (b) Intensity distribution of radially polarized laser beam before and after passing through a linear polarizer with the transmission axis orientation denoted by arrows. Adapted with permission from Ref. 108 © OSA Publishing.

Fig. 9. Q-switched and mode-locked cylindrical vector beam lasers. Mode-locked (a) RPB and (b) APB before and after passing through a polarizer. (c) Optical spectra and (d) pulse trains of Q-switched and mode-locked cylindrical vector beam lasers. (e) Evolution of Q-switched cylindrical vector beam lasers. (f) Autocorrelation traces of mode-locked cylindrical vector beam lasers. Adapted with permission from Ref. 105 © AIP Publishing.

Fig. 10. Formation mechanism of VBs in TMF. (a₁)–(a₄) mode distribution of ${\mathrm{TM}}_{01}$, ${\mathrm{HE}}_{21}^{\text{even}}$, ${\mathrm{HE}}_{21}^{\text{odd}}$, and ${\mathrm{TE}}_{01}$ modes. Mode distribution, phase, and polarization of (b₁)–(b₃), (c₁)–(c₃) circularly polarized VBs and (d₁)–(e₃), (e₁)–(e₃) linearly polarized VBs.

Fig. 11. Generation of VBs based on an acoustically-induced LPFG. (a) Experiment setup. EDFA, erbium-doped fiber amplifier; SMF, single-mode fiber; PC, polarization controller; MS, mode stripper; TMF, two-mode fiber; MO, micro-objective; NPBS, nonpolarizing beam splitter; CCD, charge coupled device. (b) VBs and coaxial interference patterns at wavelengths of 1540, 1545, 1550, 1555, and 1560 nm. Adapted with permission from Ref. 118 © OSA Publishing.

Fig. 12. (a) Principle of the VB converter based on a mechanical LPFG. Intensity profiles of (b₁) $-1$-order and (b₃) $+1$-order VB. Coaxial interference patterns of (b₂) $-1$-order and (b₄) $+1$-order VB with a Gaussian beam. Adapted with permission from Ref. 120 © OSA Publishing.

Fig. 13. (a) Mode coupling and output elements are the LPFG and fiber mirror, SMF-TMF taper and TMFBG, and LPFG and TMFBG for schemes 1, 2, and 3, respectively. (b) Intensity distributions and interference patterns, (c) optical spectra, and (d) autocorrelation traces of mode-locked vortex lasers. $l$, topological charge. Adapted with permission from Ref. 130 © AIP Publishing.

Table 1. Generation systems and performances of CVBs using different schemes.

Table 2. Generation systems and performances of VBs based on different schemes.