Fig. 1. Polarization of incident beams and structure of DOE. (a) CV beams; (b) DOE

Fig. 2. Schematic of 4Pi optical focusing system

Fig. 3. Total intensity distributions of light field. Intensity evolutions of x-y plane in vicinity of z=0 (a) without DOE modulation and (b) with 4 ring DOE modulation; intensity distributions of light field in r-z plane (c) without DOE modulation and (d) with 4 ring DOE modulation; intensity distributions of light field along different directions (e) without DOE modulation and (f) with 4 ring DOE modulation

Fig. 4. Total intensity distributions of focused CV beams with radial polarization and azimuthal polarization. Intensity distributions of light field in r-z plane with (a) radial polarization and (b) azimuthal polarization; intensity linear distributions of light field along different directions with (c) radial polarization and (d) azimuthal polarization

Fig. 5. Generation of optical chain. (a)(b) Intensity distributions of light field in r-z plane; (c)(d) intensity linear distributions of light field along z axis

Fig. 6. Radiation force of light field exerted on Rayleigh particles. (a)-(c) Radiation force of optical spheres exerted on high-refractive-index Rayleigh particles; (d)-(f) radiation force of optical chain exerted on low-refractive-index Rayleigh particles

Fig. 7. Phase distributions of longitudinal component of focused CV beams with different topological charges. (a) m=0; (b) m=1;

Fig. 8. Generation of dark channel by focusing CV vortex beams. (a) Intensity distribution for m=2; (b) line intensity distribution for m=3; (c) intensity linear distribution along r-axis when z=0; (d) width of dark channel for different topological charges

Fig. 9. Moving of focal field by changing Δφ from 0 to 2π (white line is at focus plane z=0). (a) Δφ=0 (downward-facing white arrow), Δφ=2π (upward-facing white arrow); (b) Δφ=π/2; (c) Δφ=π; (d) Δφ=3π/2

Fig. 10. Relationship between moving distance and phase difference and longitudinal radiation force exerted on trapped particles. (a) Moving distance Δz as a function of phase difference Δφ; (b) radiation force for different Δφ