Fig. 1. Dependence of the radial size r on the conical angle α_l.

Fig. 2. Schematics of the setup for generating a helical light field. (a) Diagram of the experimental setup. HWP, half-wave plate; Pol, linear polarizer; SLM, spatial light modulator; L1 and L2, lenses; Iris, aperture diaphragm; MO1 and MO2, microscope objectives; CMOS, complementary metal oxide semiconductor. (b) Phase of the helical light field loaded on the SLM. (c) Generation of the helical light field at the back focal plane of objective MO1 after the 4f system and then the overall transmission of the light field obtained by transverse scanning of objective MO2.

Fig. 3. Radial intensity profiles of the single-lobe helical light fields generated from high-order Bessel beams of different topological charge numbers. (a)–(d) Simulations for m = 1, 3, 5, and 7 and (e)–(h) corresponding experimental results. The white circles (dotted lines) in all the sub-figures share an identical size, corresponding to the 2 µm radius. The scale bars in all the subfigures represent 2 µm.

Fig. 4. Multi-lobe helical light fields with identical radial sizes obtained by changing the topological charge number difference. (a)–(d) Simulations of radial intensity profiles for the topological charge difference (l − m) = 1, 2, 3, and 4 and (e)–(h) corresponding experimental results. All the scale bars represent 4 µm.

Fig. 5. Simulations of the helical light fields with varying chirality and rotational speeds. The radial intensity profiles at (l − m) = 1 with different rotational speeds (a) v = 0.064 rad/µm and (c) v = 0.136 rad/µm. The radial intensity profiles at (l − m) = − 1 with different rotational speeds (b) v = − 0.064 rad/µm and (d) v = − 0.136 rad/µm. The intensity profiles at z = 7 µm and 27 µm are, respectively, shown in the left and in the right column of each subfigure. Dashed circles occur with identical radii, and the scale bars in all the subfigures represent 3 µm.

Fig. 6. Simulated intensity profiles along propagation. High-order Bessel beams with (a) l = 6 and (b) m = 5. Helical light fields with a single lobe (c) in overspeed mode (∼1.0 rad/µm) and (d) in underspeed mode (0.0064 rad/µm). Multi-lobe helical light fields with (e) a single, (f) double, (g) triple, and (h) quadruple lobes corresponding to those in Fig. 4.

Fig. 7. Experimental results of the helical light fields with varying chirality and rotational speeds. The radial intensity profiles at (l − m) = 1 and rotational speeds (a) v = 0.064 rad/µm and (c) v = 0.136 rad/µm. The radial intensity profiles at (l − m) = − 1 with different rotational speeds (b) v = −0.064 rad/µm and (d) v = −0.136 rad/µm. The intensity profiles at z = 7 µm and 27 µm are, respectively, shown in the left and in the right column of each subfigure. Dashed circles occur with identical radii, and the scale bars in all the subfigures represent 3 µm.