Superoscillation: from physics to optical applications

Gang Chen; Zhong-Quan Wen; Cheng-Wei Qiu

doi:10.1038/s41377-019-0163-9

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Superoscillation: from physics to optical applications

Review Article

- Superoscillation: from physics to optical applications
- Superoscillation: from physics to optical applications
- LSA 2019年8卷第4期页码：471-493
- Affiliations：
  
  1.College of Optoelectronic Engineering, Chongqing University, 174 Shazheng Street, Chongqing 400044, China
  2.Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117583, Singapore
- Author bio：
  
  Cheng-Wei Qiu (eleqc@nus.edu.sg)
- Funds：
- DOI：10.1038/s41377-019-0163-9
  中图分类号：
- 纸质出版日期：2019，
  
  网络出版日期：2019-06-12，
  
  收稿日期：2019-01-21，
  
  修回日期：2019-05-14，
  
  录用日期：2019-05-21
- Accepted：
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Superoscillation: from physics to optical applications[J]. LSA, 2019,8(4):471-493.

Chen, G., Wen, Z. Q. & Qiu, C. W. Superoscillation: from physics to optical applications. Light: Science & Applications, 8, 471-493 (2019).
Superoscillation: from physics to optical applications[J]. LSA, 2019,8(4):471-493. DOI： 10.1038/s41377-019-0163-9.

Chen, G., Wen, Z. Q. & Qiu, C. W. Superoscillation: from physics to optical applications. Light: Science & Applications, 8, 471-493 (2019). DOI： 10.1038/s41377-019-0163-9.

摘要

Abstract

The resolution of conventional optical elements and systems has long been perceived to satisfy the classic Rayleigh criterion. Paramount efforts have been made to develop different types of superresolution techniques to achieve optical resolution down to several nanometres

such as by using evanescent waves

fluorescence labelling

and postprocessing. Superresolution imaging techniques

which are noncontact

far field and label free

are highly desirable but challenging to implement. The concept of superoscillation offers an alternative route to optical superresolution and enables the engineering of focal spots and point-spread functions of arbitrarily small size without theoretical limitations. This paper reviews recent developments in optical superoscillation technologies

design approaches

methods of characterizing superoscillatory optical fields

and applications in noncontact

far-field and label-free superresolution microscopy. This work may promote the wider adoption and application of optical superresolution across different wave types and application domains.

关键词

Keywords

references

Abbe, E. Beiträge zur theorie des mikroskops und der mikroskopischen wahrnehmung.Arch. f.ür. Mikrosk. Anat.9, 413-418 (1873)..

Goodman, J. W.Introduction to Fourier Optics. 2nd edn. (Mcgraw-Hill, New York, 1996).

Dürig, U., Pohl, D. W.&Rohner, F. Near-field optical-scanning microscopy.J. Appl. Phys.59, 3318-3327 (1986)..

Yang, H. et al. Super-resolution biological microscopy using virtual imaging by a microsphere nanoscope.Small10, 1712-1718 (2014)..

Upputuri, P. K.&Pramanik, M. Microsphere-aided optical microscopy and its applications for super-resolution imaging.Opt. Commun.404, 32-41 (2017)..

Fang, N.et al. Sub-diffraction-limited optical imaging with a silver superlens.Science308, 534-537 (2005)..

Taubner, T. et al. Near-field microscopy through a SiC superlens.Science313, 1595 (2006)..

Kehr, S. C. et al. Near-field examination of perovskite-based superlenses and superlens-enhanced probe-object coupling.Nat. Commun.2, 249 (2011)..

Jacob, Z., Alekseyev, L. V.&Narimanov, E.Optical hyperlens: far-field imaging beyond the diffraction limit.Opt. Express14, 8247-8256 (2006)..

Salandrino, A.&Engheta, N. Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations.Phys. Rev. B74, 075103 (2006)..

Liu, Z. W. et al. Far-field optical hyperlens magnifying sub-diffraction-limited objects.Science315, 1686 (2007)..

Guerra, J. M. Super-resolution through illumination by diffraction-born evanescent waves.Appl. Phys. Lett.66, 3555-3557 (1995)..

Wei, F. F.&Liu, Z. W. Plasmonic structured illumination microscopy.Nano Lett.10, 2531-2536 (2010)..

Liu, X. W. et al. Fluorescent nanowire ring illumination for wide-field far-field subdiffraction imaging.Phys. Rev. Lett.118, 076101 (2017)..

Gustafsson, M. G. L. Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution.Proc. Natl Acad. Sci. USA102, 13081-13086 (2005)..

Hell, S. W. Far-field optical nanoscopy.Science316, 1153-1158 (2007)..

Rust, M. J., Bates, M.&Zhuang, X. W. Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM).Nat. Methods3, 793-796 (2006)..

Betzig, E. et al. Imaging intracellular fluorescent proteins at nanometer resolution.Science313, 1642-1645 (2006)..

Hess, S. T., Girirajan, T. P. K.&Mason, M. D. Ultra-high resolution imaging by fluorescence photoactivation localization microscopy.Biophys. J.91, 4258-4272 (2006)..

Ayas, S. et al. Label-free nanometer-resolution imaging of biological architectures through surface enhanced raman scattering.Sci. Rep.3, 2624 (2013)..

Rivenson, Y. et al. Deep learning microscopy.Optica4, 1437-1443 (2017)..

Nehme, E. et al. Deep-STORM: super-resolution single-molecule microscopy by deep learning.Optica5, 458-464 (2018)..

Wang, H. D. et al. Deep learning enables cross-modality super-resolution in fluorescence microscopy.Nat. Methods16, 103-110 (2019)..

Barakat, R. Application of apodization to increase two-point resolution by the sparrow criterion. Ⅰ. Coherent illumination.J. Opt. Soc. Am.52, 276-283 (1962)..

Barakat, R.&Levin, E. Application of apodization to increase two-point resolution by the sparrow criterion. Ⅱ. Incoherent illumination.J. Opt. Soc. Am.53, 274-282 (1963)..

Ando, H. Phase-shifting apodizer of three or more portions.Jpn. J. Appl. Phys.31, 557-567 (1992)..

Boyer, G. R. Pupil filters for moderate superresolution.Appl. Opt.15, 3089-3093 (1976)..

Boyer, G.&Sechaud, M. Superresolution by taylor filters.Appl. Opt.12, 893-894 (1973)..

Boivin, R.&Boivin, A. Optimized amplitude filtering for superresolution over a restricted field Ⅰ. Achievement of maximum central irradiance under an energy constraint.Opt. Acta.: Int. J. Opt.27, 587-610 (1980)..

Boivin, R.&Boivin, A. Optimized amplitude filtering for superresolution over a restricted field Ⅱ. Application of the impulse-generating filter.Opt. Acta.: Int. J. Opt.27, 1641-1670 (1980)..

Boivin, R.&Boivin, A. Optimized amplitude filtering for superresolution over a restricted field Ⅲ. Effects due to variation of the field extent.Opt. Acta.: Int. J. Opt.30, 681-688 (1983)..

Sales, T. R. M.&Morris, G. M. Fundamental limits of optical superresolution.Opt. Lett.22, 582-584 (1997)..

Guillemin, E. A.The Mathematics of Circuit Analysis: Extensions to the Mathematical Training of Electrical Engineers(John Wiley&Sons, New York, 1949).

Barnes, C. W. Object restoration in a diffraction-limited imaging system.J. Opt. Soc. Am.56, 575-578 (1966)..

Frieden, B. R. On arbitrarily perfect imagery with a finite aperture.Opt. Acta.: Int. J. Opt.16, 795-807 (1969)..

Di Francia, G. T. Super-gain antennas and optical resolving power.Il Nuovo Cim.9, 426-438 (1952)..

Aharonov, Y., Albert, D. Z.&Vaidman, L. How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100.Phys. Rev. Lett.60, 1351-1354 (1988)..

Berry, M. V. Evanescent and real waves in quantum billiards and Gaussian beams.J. Phys. A: Math. Gen.27, L391-L398 (1994)..

Berry, M. V.&Popescu, S. Evolution of quantum superoscillations and optical superresolution without evanescent waves.J. Phys. A: Math. Gen.39, 6965-6977 (2006)..

Berry, M. V.&Dennis, M. R. Natural superoscillations in monochromatic waves in D dimensions.J. Phys. A: Math. Theor.42, 022003 (2009)..

Berry, M. V.&Shukla, P. Pointer supershifts and superoscillations in weak measurements.J. Phys. A: Math. Theor.45, 015301 (2012)..

Berry, M. V. A note on superoscillations associated with Bessel beams.J. Opt.15, 044006 (2013)..

Berry, M. V. Exact nonparaxial transmission of subwavelength detail using superoscillations.J. Phys. A: Math. Theor.46, 205203 (2013)..

Berry, M. V.&Moiseyev, N. Superoscillations and supershifts in phase space: wigner and Husimi function interpretations.J. Phys. A: Math. Theor.47, 315203 (2014)..

Berry, M. V.&Morley-Short, S. Representing fractals by superoscillations.J. Phys. A: Math. Theor.50, 22LT01 (2017)..

Berry, M. V. Suppression of superoscillations by noise.J. Phys. A: Math. Theor.50, 025003 (2017)..

Berry, M. V.&Fishman, S. Escaping superoscillations.J. Phys. A: Math. Theor.51, 025205 (2018)..

Liu, D. M. et al. Diffraction interference induced superfocusing in nonlinear Talbot effect.Sci. Rep.4, 6134 (2014)..

Slepian, D.&Pollak, H. O. Prolate spheroidal wave functions, fourier analysis and uncertainty—Ⅰ.Bell Syst. Tech. J.40, 43-63 (1961)..

Huang, F. M.&Zheludev, N. I. Super-resolution without evanescent waves.Nano Lett.9, 1249-1254 (2009)..

Ferreira, P. J. S. G.&Kempf, A. Superoscillations: faster than the nyquist rate.IEEE Trans. Signal Process.54, 3732-3740 (2006)..

Rogers, E. T. F.&Zheludev, N. I. Optical super-oscillations: sub-wavelength light focusing and super-resolution imaging.J. Opt.15, 094008 (2013)..

Wen, Z. Q. et al. Super-oscillation focusing lens based on continuous amplitude and binary phase modulation.Opt. Express22, 22163-22171 (2014)..

Berry, M. V. Quantum backflow, negative kinetic energy, and optical retro-propagation.J. Phys. A: Math. Theor.43, 415302 (2010)..

Kempf, A.&Ferreira, P. J. S. G. Unusual properties of superoscillating particles.J. Phys. A: Math. Gen.37, 12067-12076 (2004)..

Berry, M. V.Faster Than Fourier in Quantum Coherence and Reality. (World Scientific, Singapore, 1994).

Yuan, G. H., Rogers, E. T. F.&Zheludev, N. I. "Plasmonics" in free space: observation of giant wavevectors, vortices, and energy backflow in superoscillatory optical fields.Light.: Sci. Appl.8, 2 (2019)..

Huang, K. et al. Optimization-free superoscillatory lens using phase and amplitude masks.Laser Photonics Rev.8, 152-157 (2014)..

Zheludev, N. I. What diffraction limit?Nat. Mater.7, 420-422 (2008)..

Huang, F. M. et al. Focusing of light by a nanohole array.Appl. Phys. Lett.90, 091119 (2007)..

Wang, T. T. et al. Experimental verification of the far-field subwavelength focusing with multiple concentric nanorings.Appl. Phys. Lett.97, 231105 (2010)..

Rogers, E. T. F. et al. A super-oscillatory lens optical microscope for subwavelength imaging.Nat. Mater.11, 432-435 (2012)..

Li, M. Y. et al. Controllable design of super-oscillatory lenses with multiple sub-diffraction-limit foci.Sci. Rep.7, 1335 (2017)..

Grosjean, T.&Courjon, D. Polarization filtering induced by imaging systems: effect on image structure.Phys. Rev. E67, 046611 (2003)..

Chen, G. et al. Super-oscillatory focusing of circularly polarizedlight by ultra-long focal length planar lens based on binary amplitude-phase modulation.Sci. Rep.6, 29068 (2016)..

Liu, T. et al. Subwavelength focusing by binary multi-annular plates: design theory and experiment.J. Opt.17, 035610 (2015)..

Wan, X. W., Shen, B.&Menon, R. Diffractive lens design for optimized focusing.J. Opt. Soc. Am. A31, B27-B33 (2014)..

Chen, G. et al. Super-oscillation far-field focusing lens based on ultra-thin width-varied metallic slit array.IEEE Photonics Technol. Lett.28, 335-338 (2016)..

Chen, G. et al. Far-field sub-diffraction focusing lens based on binary amplitude-phase mask for linearly polarized light.Opt. Express24, 11002-11008 (2016)..

He, Y. H. et al. Double-layer metallic holes lens based on continuous modulation of phase and amplitude.IEEE Photonics Technol. Lett.26, 1801-1804 (2014)..

Huang, K. et al. Ultrahigh-capacity non-periodic photon sieves operating in visible light.Nat. Commun.6, 7059 (2015)..

Dorn, R., Quabis, S.&Leuchs, G. Sharper focus for a radially polarized light beam.Phys. Rev. Lett.91, 233901 (2003)..

Hao, X. et al. Phase encoding for sharper focus of the azimuthally polarized beam.Opt. Lett.35, 3928-3930 (2010)..

Kuga, T. et al. Novel optical trap of atoms with a doughnut beam.Phys. Rev. Lett.78, 4713-4716 (1997)..

Zhan, Q. W. Trapping metallic Rayleigh particles with radial polarization.Opt. Express12, 3377-3382 (2004)..

Terakado, G., Watanabe, K.&Kano, H. Scanning confocal total internal reflection fluorescence microscopy by using radial polarization in the illumination system.Appl. Opt.48, 1114-1118 (2009)..

Xue, Y. et al. Sharper fluorescent super-resolution spot generated by azimuthally polarized beam in STED microscopy.Opt. Express20, 17653-17666 (2012)..

Hulteen, J. C. et al. Nanosphere lithography: size-tunable silver nanoparticle and surface cluster arrays.J. Phys. Chem. B103, 3854-3863 (1999)..

Niziev, V. G.&Nesterov, A. V. Influence of beam polarization on laser cutting efficiency.J. Phys. D: Appl. Phys.32, 1455-1461 (1999)..

Hafizi, B., Esarey, E.&Sprangle, P. Laser-driven acceleration with Bessel beams.Phys. Rev. E55, 3539-3545 (1997)..

Quabis, S. et al. Focusing light to a tighter spot.Opt. Commun.179, 1-7 (2000)..

Zhang, M. G. et al. Three-dimensional nanoscale far-field focusing of radially polarized light by scattering the SPPs with an annular groove.Opt. Express18, 14664-14670 (2010)..

Venugopalan, P. et al. Focusing dual-wavelength surface plasmons to the same focal plane by a far-field plasmonic lens.Opt. Lett.39, 5744-5747 (2014)..

Zakharian, A. R., Moloney, J. V.&Mansuripur, M. Surface plasmon polaritons on metallic surfaces.Opt. Express15, 183-197 (2007)..

Liu, Y. X. et al. Far-field superfocusing with an optical fiber based surface plasmonic lens made of nanoscale concentric annular slits.Opt. Express19, 20233-20243 (2011)..

Liu, T. et al. Vectorial design of super-oscillatory lens.Opt. Express21, 15090-15101 (2013)..

Ye, H. P. et al. Creation of a longitudinally polarized subwavelength hotspot with an ultra-thin planar lens: vectorial Rayleigh-Sommerfeld method.Laser Phys. Lett.10, 065004 (2013)..

Yu, A. P. et al. Creation of Sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens.Sci. Rep.6, 38859 (2016)..

Kozawa, Y.&Sato, S. Sharper focal spot formed by higher-order radially polarized laser beams.J. Opt. Soc. Am. A24, 1793-1798 (2007)..

Kozawa, Y.&Sato, S. Focusing of higher-order radially polarized Laguerre-Gaussian beam.J. Opt. Soc. Am. A29, 2439-2443 (2012)..

Jiang, Y. S., Li, X. P.&Gu, M. Generation of sub-diffraction-limited pure longitudinal magnetization by the inverse Faraday effect by tightly focusing an azimuthally polarized vortex beam.Opt. Lett.38, 2957-2960 (2013)..

Gu, Z. T. et al. Methods for generating a dark spot using phase and polarization modulation light.Optik124, 650-654 (2013)..

Gan, Z. S. et al. Three-dimensional deep sub-diffraction optical beam lithography with 9nm feature size.Nat. Commun.4, 2061 (2013)..

Singh, R. K., Senthilkumaran, P.&Singh, K. Tight focusing of vortex beams in presence of primary astigmatism.J. Opt. Soc. Am. A26, 576-588 (2009)..

Chen, G. et al. Generation of a sub-diffraction hollow ring by shaping an azimuthally polarized wave.Sci. Rep.6, 37776 (2016)..

Wu, Z. X. et al. Binary-amplitude modulation based super-oscillatory focusing planar lens for azimuthally polarized wave.Opto-Electron. Eng.45, 170660 (2018)..

Li, Z. Y.&Yu, N. F. Modulation of mid-infrared light using graphene-metal plasmonic antennas.Appl. Phys. Lett.102, 131108 (2013)..

Yu, N. F. et al. Light propagation with phase discontinuities: generalized laws of reflection and refraction.Science334, 333-337 (2011)..

Huang, L. L. et al. Dispersionless phase discontinuities for controlling light propagation.Nano Lett.12, 5750-5755 (2012)..

Sun, S. L. et al. High-efficiency broadband anomalous reflection by gradient meta-surfaces.Nano Lett.12, 6223-6229 (2012)..

Li, X. et al. Catenary nanostructures as compact Bessel beam generators.Sci. Rep.6, 20524 (2016)..

Yu, N. F. et al. A broadband, background-free quarter-wave plate based on plasmonic metasurfaces.Nano Lett.12, 6328-6333 (2012)..

Zhao, Y.&Alù, A. Tailoring the dispersion of plasmonic nanorods to realize broadband optical meta-waveplates.Nano Lett.13, 1086-1091 (2013)..

Luo, J. et al. Tight focusing of radially and azimuthally polarized light with plasmonic metalens.Opt. Commun.356, 445-450 (2015)..

Wang, S. Y.&Zhan, Q. W. Reflection type metasurface designed for high efficiency vectorial field generation.Sci. Rep.6, 29626 (2016)..

Li, Y. Y. et al. Broadband quarter-wave birefringent meta-mirrors for generating sub-diffraction vector fields.Opt. Lett.44, 110-113 (2019)..

Zuo, R. Z. et al. Breaking the diffraction limit with radially polarized light based on dielectric metalenses.Adv. Opt. Mater.6, 1800795 (2018)..

McLeod, J. H. The axicon: a new type of optical element.J. Opt. Soc. Am.44, 592-597 (1954)..

Hatakoshi, G. et al. Grating axicon for collimating Čerenkov radiation waves.Opt. Lett.15, 1336-1338 (1990)..

García-Martínez, P. et al. Generation of bessel beam arrays through dammann gratings.Appl. Opt.51, 1375-1381 (2012)..

Herman, R. M.&Wiggins, T. A. Production and uses of diffractionless beams.J. Opt. Soc. Am. A8, 932-942 (1991)..

Sabatyan, A.&Meshginqalam, B. Generation of annular beam by a novel class of Fresnel zone plate.Appl. Opt.53, 5995-6000 (2014)..

Rogers, E. T. F. et al. Super-oscillatory optical needle.Appl. Phys. Lett.102, 031108 (2013)..

Yuan, G. H. et al. Planar super-oscillatory lens for sub-diffraction optical needles atviolet wavelengths.Sci. Rep.4, 6333 (2014)..

Liu, T. et al. Focusing far-field nanoscale optical needles by planar nanostructured metasurfaces.Opt. Commun.372, 118-122 (2016)..

Qin, F. et al. Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light.Sci. Rep.5, 09977 (2015)..

Ruan, D. S. et al. Realizing a terahertz far-field sub-diffraction optical needle with sub-wavelength concentric ring structure array.Appl. Opt.57, 7905-7909 (2018)..

Wang, H. F. et al. Creation of a needle of longitudinally polarized light in vacuum using binary optics.Nat. Photonics2, 501-505 (2008)..

Kitamura, K., Sakai, K.&Noda, S. Sub-wavelength focal spot with long depth of focus generated by radially polarized, narrow-width annular beam.Opt. Express18, 4518-4525 (2010)..

Peng, R. B. et al. Super-resolution long-depth focusing by radially polarized light irradiation through plasmonic lens in optical meso-field.Plasmonics9, 55-60 (2014)..

Qin, F. et al. A supercritical lens optical label-free microscopy: sub-diffraction resolution and ultra-long working distance.Adv. Mater.29, 1602721 (2017)..

Yu, W. T. et al. Super-resolution deep imaging with hollow Bessel beam STED microscopy.Laser Photonics Rev.10, 147-152 (2016)..

Lin, J. et al. Generation of hollow beam with radially polarized vortex beam and complex amplitude filter.J. Opt. Soc. Am. A31, 1395-1400 (2014)..

Chen, G. et al. Planar binary-phase lens for super-oscillatory optical hollow needles.Sci. Rep.7, 4697 (2017)..

Zhu, M. N., Cao, Q.&Gao, H. Creation of a 50, 000λ long needle-like field with 0.36λ width.J. Opt. Soc. Am. A31, 500-504 (2014)..

Dehez, H., April, A.&Piché, M. Needles of longitudinally polarized light: guidelines for minimum spot size and tunable axial extent.Opt. Express20, 14891-14905 (2012)..

Khonina, S. N., Kazanskiy, N. L.&Volotovsky, S. G. Vortex phase transmission function as a factor to reduce the focal spot of high-aperture focusing system.J. Mod. Opt.58, 748-760 (2011)..

Makris, K. G.&Psaltis, D. Superoscillatory diffraction-free beams.Opt. Lett.36, 4335-4337 (2011)..

Zhang, S. et al. Synthesis of sub-diffraction quasi-non-diffracting beams by angular spectrum compression.Opt. Express25, 27104-27118 (2017)..

Wu, Z. X. et al. Optimization-free approach for generating sub-diffraction quasi-non-diffracting beams.Opt. Express26, 16585-16599 (2018)..

Greenfield, E. et al. Experimental generation of arbitrarily shaped diffractionless superoscillatory optical beams.Opt. Express21, 13425-13435 (2013)..

Wu, J. et al. Creating a nondiffracting beam with sub-diffraction size by a phase spatial light modulator.Opt. Express25, 6274-6282 (2017)..

Bokor, N.&Davidson, N. Generation of a hollow dark spherical spot by 4πfocusing of a radially polarized Laguerre-Gaussian beam.Opt. Lett.31, 149-151 (2006)..

Bokor, N.&Davidson, N. Tight parabolic dark spotwith high numerical aperture focusing with a circular π phase plate.Opt. Commun.270, 145-150 (2007)..

Kozawa, Y.&Sato, S. Focusing property of a double-ring-shaped radially polarized beam.Opt. Lett.31, 820-822 (2006)..

Xue, Y. et al. A method for generating a three-dimensional dark spot using a radially polarized beam.J. Opt.13, 125704 (2011)..

Li, S. et al. Generation of a 3D isotropic hollow focal spot for single-objective stimulated emission depletion microscopy.J. Opt.14, 085704 (2012)..

Wan, C. et al. Three-dimensinal visible-light capsule enclosing perfect supersized darkness via antiresolution.Laser Photonics Rev.8, 743-749 (2014)..

Wu, Z. X. et al. Generating a three-dimensional hollow spot with sub-diffraction transverse size by a focused cylindrical vector wave.Opt. Express26, 7866-7875 (2018)..

Tang, D. L. et al. Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing.Laser Photonics Rev.9, 713-719 (2015)..

Yuan, G. H., Rogers, E. T. F.&Zheludev, N. I. Achromatic super-oscillatory lenses with sub-wavelength focusing.Light.: Sci. Appl.6, e17036 (2017)..

Khorasaninejad, M. et al. Achromatic metalens over 60nm bandwidth in the visible and metalens with reverse chromatic dispersion.Nano Lett.17, 1819-1824 (2017)..

Arbabi, E. et al. Controlling the sign of chromatic dispersion in diffractive optics with dielectric metasurfaces.Optica4, 625-632 (2017)..

Wang, S. M. et al. A broadband achromatic metalens in the visible.Nat. Nanotechnol.13, 227-232 (2018)..

Yuan, G. H. et al. Quantum super-oscillation of a single photon.Light.: Sci. Appl.5, e16127 (2016)..

Jin, N. B.&Rahmat-Samii, Y. Advances in particle swarm optimization for antenna designs: real-number, binary, single-objective and multiobjective implementations.IEEE Trans. Antennas Propag.55, 556-567 (2007)..

Lin, J. et al. New hybrid genetic particle swarm optimization algorithm to design multi-zone binary filter.Opt. Express24, 10748-10758 (2016)..

Li, W. L., Yu, Y. T.&Yuan, W. Z. Flexible focusing pattern realization of centimeter-scale planar super-oscillatory lenses in parallel fabrication.Nanoscale11, 311-320 (2019)..

Li, J. L., Zhu, S. F.&Lu, B. D. The rigorous electromagnetic theory of the diffraction of vector beams by a circular aperture.Opt. Commun.282, 4475-4480 (2009)..

Carter, W. H. Electromagnetic field of a gaussian beam with an elliptical cross section.J. Opt. Soc. Am.62, 1195-1201 (1972)..

Wolf, E. Electromagnetic diffraction in optical systems-Ⅰ. An integral representation of the image field.Proc. R. Soc. A253, 349-357 (1959)..

Magni, V., Cerullo, G.&de Silvestri, S. High-accuracy fast Hankel transform for optical beam propagation.J. Opt. Soc. Am. A9, 2031-2033 (1992)..

Landau, H. J.&Pollak, H. O. Prolate spheroidal wave functions, Fourier analysis and uncertainty—Ⅱ.Bell Syst. Tech. J.40, 65-84 (1961)..

Landau, H. J.&Pollak, H. O. Prolate spheroidal wave functions, Fourier analysis and uncertainty—Ⅲ: the dimension of the space of essentially time- and band-limited signals.Bell Syst. Tech. J.41, 1295-1336 (1962)..

Slepian, D. Prolate spheroidal wave functions, Fourier analysis and uncertainty—Ⅳ: extensions to many dimensions; generalized prolate spheroidal functions.Bell Syst. Tech. J.43, 3009-3057 (1964)..

Slepian, D. Prolate spheroidal wave functions, Fourier analysis, and uncertainty—Ⅴ: the discrete case.Bell Syst. Tech. J.57, 1371-1430 (1978)..

Rogers, K. S. et al. Optimising superoscillatory spots for far-field super-resolution imaging.Opt. Express26, 8095-8112 (2018)..

Karoui, A.&Moumni, T. Spectral analysis of the finite Hankel transform and circular prolate spheroidal wave functions.J. Comput. Appl. Math.233, 315-333 (2009)..

Diao, J. S. et al. Controllable design of super-oscillatory planar lenses for sub-diffraction-limit optical needles.Opt. Express24, 1924-1933 (2016)..

Yu, Y. Z.&Zhan, Q. W. Optimization-free optical focal field engineering through reversing the radiation pattern from a uniform line source.Opt. Express23, 7527-7534 (2015)..

Liu, T., Yang, S. M.&Jiang, Z. D. Electromagnetic exploration of far-field super-focusing nanostructured metasurfaces.Opt. Express24, 16297-16308 (2016)..

Khosrofian, J. M.&Garetz, B. A. Measurement of a Gaussian laser beam diameter through the direct inversion of knife-edge data.Appl. Opt.22, 3406-3410 (1983)..

Born, M.&Wolf, E.Principles of Optics(Cambridge University Press, New York, 1999).

Pernick, B. J. Two-dimensional light-distribution measurement with a 90° cornered knife edge.Appl. Opt.32, 3610-3613 (1993)..

Xie, X. S. et al. Three-dimensional measurement of a tightly focused laser beam.AIP Adv.3, 022110 (2013)..

Yang, L. X. et al. Minimized spot of annular radially polarized focusing beam.Opt. Lett.38, 1331-1333 (2013)..

Huang, F. M. et al. Nanohole array as a lens.Nano Lett.8, 2469-2472 (2008)..

Roy, T. et al. Point spread function of the optical needle super-oscillatory lens.Appl. Phys. Lett.104, 231109 (2014)..

Wang, C. T. et al. Super-resolution optical telescopes with local light diffraction shrinkage.Sci. Rep.5, 18485 (2015)..

Wong, A. M. H.&Eleftheriades, G. V. Superoscillations without sidebands: power-efficient sub-diffraction imaging with propagating waves.Sci. Rep.5, 08449 (2015)..

Dong, X. H. et al. Superresolution far-field imaging of complex objects using reduced superoscillating ripples.Optica4, 1126-1133 (2017)..

Li, Z. et al. Achromatic broadband super-resolution imaging by super-oscillatory metasurface.Laser Photonics Rev.12, 1800064 (2018)..

Fahrbach, F. O., Simon, P.&Rohrbach, A. Microscopy with self-reconstructing beams.Nat. Photonics4, 780-785 (2010)..

Wong, A. M. H.&Eleftheriades, G. V. An optical super-microscope for far-field, real-time imaging beyond the diffraction limit.Sci. Rep.3, 01715 (2013)..

Matsunaga, D., Kozawa, Y.&Sato, S. Super-oscillation by higher-order radially polarized Laguerre-Gaussian beams. Proceedings of 2016 Conference on Lasers and Electro-Optics. (IEEE, San Jose, 2016).

Yuan, G. H. et al. Flat super-oscillatory lens for heat-assisted magnetic recording with sub-50nm resolution.Opt. Express22, 6428-6437 (2014)..

Eliezer, Y. et al. Breaking the temporal resolution limit by superoscillating optical beats.Phys. Rev. Lett.119, 043903 (2017)..

Eliezer, Y. et al. Experimental realization of structured super-oscillatory pulses.Opt. Express26, 4933-4941 (2018)..

Eliezer, Y.&Bahabad, A. Super defocusing of light by optical sub-oscillations.Optica4, 440-446 (2017)..

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