Fig. 1. Transverse intensity and phase distributions of zeroth-order to second-order Bessel beams. (a)-(c) Transverse intensity; (d)-(f) phase distributions

Fig. 2. Generation of Bessel beams. (a) Conical wave vector of Bessel beams; (b) annular aperture method^[4]; (c) axicon method^[42]; (d) hologram method^[48]; (e) dielectric metasurface method^[55]; (f) Fabry-Perot resonator method^[58]

Fig. 3. Self-recovery of Bessel beams. (a) Propagation of obstructed Bessel beam; (b) geometrical explanation of self-recovery of Bessel beams

Fig. 4. Radially self-accelerating beams^[75]. (a)(b) Schematics of accelerations of Airy beam and radially self-accelerating beam; (c) propagation dynamics of radially self-accelerating beam

Fig. 5. Self-accelerating rotating beams produced by superposition of nonlinear vortex beams^[76]. (a) Superposition of Bessel beams with nonlinear vortex phases; (b) simulated (1st row) and measured (2nd row) self-accelerating rotating beams

Fig. 6. Spiral Bessel beam produced by beam cone splicing^[77]. (a) Schematic of cone splicing; (b) schematic of beam trajectory

Fig. 7. Bessel-like beams propagating along arbitrary trajectories based on caustic principle^[78]. (a) Principle diagram; (b) self-recovery of hyperbolic beam; (c) beam propagating around object on propagation axis

Fig. 8. Flexible trajectory control of Bessel beams with pure phase modulation^[79]. (a) Principle diagram; (b) self-accelerating Bessel-like beam with piecewise trajectory

Fig. 9. Controllable spin Hall effect of Bessel beams realized by geometric phase elements^[80]. (a) Schematic of optical path; (b) spiral photonics spin Hall effect

Fig. 10. Nonparaxial self-accelerating beams. (a) Vector solutions of nonparaxial self-accelerating beam^[81]; (b) linear (top) and nonlinear (bottom) propagation of nonparaxial self-accelerating beam^[82]

Fig. 11. Nonparaxial tightly autofocusing beams^[85]. (a) Principle diagram; (b) focusing properties of radially polarized tightly autofocusing beam; (c) intensity distributions of radially (I_r), azimuthally (I_φ), and longitudinally (I_z) polarized components and total field (I) at focal plane

Fig. 12. Axial intensity engineering of Bessel beams based on “frozen waves”^[86]. (a) Axial intensity distribution compared with desired function; (b) 3D-plot of propagation process

Fig. 13. “Frozen waves” following spiral and snake-like trajectories^[91]. (a) Spiral trajectories; (b) snake-like trajectory

Fig. 14. Controlling longitudinal intensity based on spatial spectrum engineering theory. (a) Bessel beams with tunable axial intensity distribution^[92]; (b)(c) longitudinally modulated beam intensity via metasurface^[93]; (d) self-accelerating Bessel beams with on-demand tailored intensity profiles along arbitrary trajectories^[94]

Fig. 15. Bessel beams with polarization state varying with propagation distance^[95]. (a) Experimental optical path; (b) beam propagation results through different analyzers

Fig. 16. Vector Bessel beams with polarization state varying with propagation distance^[97]. (a) Schematic of transverse-to-longitudinal mapping (top) and beam self-recovery (bottom); (b) propagation process and intensity distributions with polarization analyzer at different distances

Fig. 17. Polarization oscillating beams constructed by copropagating optical “frozen waves”^[99]. (a) Optical setup; (b) intensities of right- and left-handed components of zeroth-order “frozen waves” (first and second rows) and transverse polarization states (third row) at different distances

Fig. 18. Self-accelerating propagation rotation in free space induced by Gouy phase^[101]. (a) Schematic of accelerating polarization rotation; (b) beam intensity distributions at different distances; (c) axial polarization orientations (top) and polarization ellipticities (bottom)

Fig. 19. Optical rotation effect in free space induced by Gouy phase. (a) Polarization rotator consisting of a pair of conical wave plates^[103]; (b) spin Hall effect induced by self-accelerating Bessel-like beam^[104]

Fig. 20. Solution of self-similar beam with different scaling factor^[105]. (a) Focal lines of converging cylindrical waves; (b) microscopic image of mask; (c) beam propagation process

Fig. 21. Self-similar arbitrary-order Bessel-like beams based on Fresnel integral^[107]. (a) First-order self-similar Bessel-like beam with beam width varying as hyperbolic secant; (b)(c) maximum intensity and beam width varying with propagation distance

Fig. 22. Constructing arbitrary self-similar Bessel-like beams via transverse-longitudinal mapping^[108]. (a) Principle diagram; (b) zero-order Bessel-like beams with sinusoidal varying beam width