Fig. 1. Polarization patterns of polarized beams and focusing diagrams. (a) Illustrations of the polarization patterns for LPB, RPB, APB and generalized CVB^[28]; (b) focusing diagram of LPB^[29]; (c) focusing diagram of RPB^[29]

Fig. 2. Focal field distribution examples for LPB, RPB and APB^[31]

Fig. 3. Illustration of the polarization pattern at the pupil plane for the radiation from a vertical electric dipole collected by a high-NA objective^[28]

Fig. 4. Comparison of angular spectrum diffraction integral formula and Rayleigh-Sommerfeld diffraction integral formula^[32]

Fig. 5. Example of the VAS design of RPB incident SOL, and comparison of theoretical with experimental results^[33]

Fig. 6. Comparison of COMSOL simulation results and experimental results with SOL focusing^[46]

Fig. 7. Experimental observation of optical superoscillation^[63]. (a) An SEM image of a quasiperiodic metallic nanohole array; (b) corresponding superoscillatory spot at 7.5λ; (c) optical intensity distribution of the superoscillatory spot (marked by the square) along vertical (red) and horizontal (blue) directions in Fig. 7(b)

Fig. 8. Crescent-shaped sharp edge aperture generating superoscillating spot^[66]

Fig. 9. Definition of resolution criterion^[64]. (a) Variation of focal spot size and its evolution; (b) division of resolution region

Fig. 10. Experiment of focusing and imaging with RPB. (a) Experimental setup and result of RPB focusing measurement^[70]; (b) setup of improved CLSM and imaging comparison of improved and conventional CLSM^[72]; (c) PSFs distribution of CLSM, experimental and simulated results of LDOS mapping^[73]

Fig. 11. Focusing of Bessel spot array and superoscillating. (a) Bessel spot array generating device and experimental results^[26]; (b) device and experimental results for generating superoscillating optical spots by Bessel beam^[27]

Fig. 12. Propagation of abruptly autofocusing beams. (a) Transmission diagram of NAAB^[78]; (b) intensity distribution of AAB and transverse intensity patterns of vectorial structured AABs^[79]; (c) intensity profiles of RPCPVB propagating at different propagation distances^[80]

Fig. 13. Binary optical lens of ring structure generates sub-diffraction focal spot. (a)‒(c) SEM diagram of BA binary optical lens and its focal field distribution^[82]; (d)‒(f) SEM diagram of BP binary optical lens and its focal field distribution^[24]; (g)‒(i) schematic diagram, SEM image and focal field distribution of BAP binary optical lens^[35]

Fig. 14. Binary optical lens produces super-diffraction needle. (a)‒(c) Schematic diagram, SEM diagram and the generated super-diffraction solid needle of ONSOL^[83]; (d)‒(f) schematic diagram, SEM image and the generated hollow super-diffraction needle of binary optical lens based on NASC^[85]; (g)‒(i) schematic diagram, SEM image of SCL and the resulting hollow super-diffraction needle^[86]

Fig. 15. Binary optical elements combined with vector beams produce tight focusing. (a) Schematic diagram of tightly focused radially polarized Bessel-Gaussian beam regulated by binary optical elements and focal spot distribution^[30]; (b) schematic diagram of azimuthally polarized beam regulated by a binary vortex phase plate and focal spot distribution of different polarized beams^[87]; (c) the binary optical element regulates the field transmission function of azimuthally polarized beam focusing and focal spot distribution^[88]; (d) the superoscillatory spot generated by radially regulated polarized Laguerre-Gaussian beams with binary optical elements, the confocal spots generated by linearly polarized beam and radially polarized Laguerre-Gaussian beam and the imaging results^[89]

Fig. 16. Schematic diagrams of band plate and photon sieves. (a) Fresnel band plate; (b) amplitude zone photon sieve^[90]; (c) phase zone photon sieve^[91]; (d) binary photon sieve^[93]

Fig. 17. Different photon sieves and their focusing performance. (a) DGPS^[94]; (b) quasi-phase photon sieves^[95]; (c) fractals photon sieves^[96]

Fig. 18. Schematic diagrams of transmission phase, geometric phase and resonance phase^[104]

Fig. 19. Large numerical aperture metalens achieves minimal focal spot. (a)‒(c) Schematic diagrams and the focused light field distribution of the nano-brick structure metalens^[110]; (d)‒(f) working principle diagram, SEM image and focusing field distribution of V-shaped antenna structure metalens^[111]; (g)‒(h) SEM images and focusing properties of nano-brick structure metalens^[112]

Fig. 20. A metalens integrating polarization conversion and subdiffraction focusing. (a)‒(c) Phase modulation principle, working principle and focusing effect diagrams of the transmission metalens^[114]; (d)‒(e) working principle and focusing effect diagrams of reflective metalens^[115]

Fig. 21. Focusing properties of metalens. (a) Schematic diagram of metalens incident by vortex beam and focal spot^[116]; (b) schematic diagram of metalens incident by polarized beam and focal spots^[117]