Fig. 1. Cross-section intensity distribution and generation principle of the Bessel beam^{[23, 25]}. (a) Cross-section intensity diagram of Bessel beam of order 0; (b) cross-section intensity diagram of Bessel beam of order 1; (c) diagram of Bessel beam generated by a prism lens; (d) schematic diagram of Bessel beam generation; (e) modulation phase diagram of Bessel beam with transverse bending; (f) intensity diagram of x-z plane; (g) intensity diagram of x-y plane

Fig. 2. Propagation path and cross section distribution of Airy beam^[27,31-32]. (a) Propagation path of the ideal Airy beam; (b) propagation path of "truncated" Airy beam; (c) the intensity distribution of the Airy wave packet; (d)‒(f) the cross-section distribution of the "truncated" Airy beam corresponding to z is 0, 10, 20 cm; (g)‒(i) theoretical simulation results of the relative position between the Gaussian beam and phase plate; (j)(k) the propagation trajectory and cross-sectional distribution of the corresponding Airy beam; (l)‒(n) Airy beam cross-section distribution under frequency-domain modulation

Fig. 3. Application research of diffraction-free beam in light sheet microscope. (a) Structure diagram of the Bessel light sheet microscope; (b) the intensity distribution of the propagation cross section of the Gaussian beam and Bessel beam through the glass sphere; (c)(d)cross sections of Gaussian beam and Bessel beam passing through human skin; (e)(f)epithelial tissue imaging near the basement membrane based on the Gaussian beam and Bessel beam^[41]; (g) the x-z intensity distribution of Gaussian beam, Bessel beam, and Airy beam; (h) the simulation of the three beams corresponds to the results before and after deconvolution; (i) the fluorescent particle experimental image corresponding to Fig. 3(h)^[42]

Fig. 4. Application of non-diffracting beam in two-photon/multi-photon microscope. (a) Two-color 3D structure diagram of young killifish, in which the red image is the blood vessel image and the green image is the lymphatic vessel image; (b)(c) the x-z plane PSF of three-photon and two-photon excitation imaging system; (d)(e) the x-y plane PSF of three-photon excitation and two-photon excitation imaging system; (f) comparison of images of live zebrafish blood vessels; (g) two-photon imaging corresponding to the red line area in Fig. 4(f); (h) three-photon imaging corresponding to the red line area in Fig. 4(f); (i) fluorescence intensity corresponding to the yellow line direction in Fig. 4(g),(h); (j) SLAM volume imaging schematic diagram by adjusting Bessel beam mode; (k) cross-section distribution of Bessel beam with order 0, order 1 and subtraction; (l) projection of mouse brain slices based on Gaussian beam, color corresponding to different depths; (m) projection of mouse brain slices after subtraction of 0-order and 1-order Bessel beams ^{[45, 47-48]}; (n)(o) the PSF experimental images of the Gaussian and Airy for a 1 µm fluorescent particle in the two-photon microscope on the x-y (left) and x-z (right) plane; (p) strength curve corresponding to Fig. 4(n),(o); (q)(r) mouse brain slice imaging, in which the left image corresponds to Gaussian beam z scan imaging, and the depth is color coded, and the right image is a single frame measurement image of Airy beam^[49]

Fig. 5. Application of non-diffracting beam in stimulated Raman microscopy^[50]. (a) Set-up of stimulated Raman projection microscope based on Bessel beam; (b)(c) stimulated Raman imaging and synthetic images of polystyrene ball at various depths; (d)(e) the stimulated Raman projection images of the Raman signal on and off

Fig. 6. Application of non-diffracting beam in stimulated emission loss microscope^[51-52]. (a) Schematic diagram of Bessel-Beam STED microscope; (b) the phase of the 0-order Bessel beam, the intensity distribution of the r-z and x-y planes; (c) the phase of the 1-order Bessel beam, the intensity distribution of the r-z and x-y planes; (d) the phase of double-ring Bessel beam; (e) simulation diagram of Bessel beam corresponding to Fig. 6(d); (f) the beam intensity distribution of r-z plane with different bias distance and average value; (g) scanning image of HeLa cells under traditional Gaussian beam microscope; (h) Bessel beam imaging corresponding to Fig. 6(g); (i)(j) the enlarged view of the yellow line area in Fig. 6(g) and Fig. 6(h); (k) the intensity distribution curve corresponding to the yellow dot line direction in Fig. 6(i) and Fig. 6(j)

Fig. 7. Application of Airy beam in an imaging terminal^[53-55]. (a) Cross section of SB-PSF and Gaussian PSF measured at different depths; (b) single-molecule localization reconstruction at different positions (left) and spatial distribution analysis (right); (c) schematic diagram of the ATM microscope; (d) removing Airy PSF sidelobe; (e) the propagation distance of the Airy beam improved by Chirp; (f) the PSF distribution distorted caused by non-paraxial imaging in a large FOV; (g) schematic diagram of FOV expansion in the ATM microscope; (h) 3D bead reconstruction image; (i) 3D measurement of half peak full width of reconstructed particles