[1] Berry, M. V. & Dennis, M. R. Knotted and linked phase singularities in monochromatic waves. Proc. R. Soc. Lond. A 457, 2251–2263 (2001). doi: 10.1098/rspa.2001.0826
[2] Leach, J., Dennis, M. R., Courtial, J. & Padgett, M. J. Knotted threads of darkness. Nature 432, 165 (2004).
[3] Soskin, M. S. & Vasnetsov, M. V. Singular optics. Prog. Opt. 42, 219–276 (2001). doi: 10.1016/S0079-6638(01)80018-4
[4] Dennis, M. R., O'Holleran, K. & Padgett, M. J. Singular optics: optical vortices and polarization singularities. Prog. Opt. 53, 293–363 (2009). doi: 10.1016/S0079-6638(08)00205-9
[5] Soskin, M. S., Boriskina, S. V., Chong, Y. D., Dennis, M. R. & Desyatnikov, A. Singular optics and topological photonics. J. Opt. 19, 010401 (2017). doi: 10.1088/2040-8986/19/1/010401
[6] Stockman, M. I. Nanofocusing of optical energy in tapered plasmonic waveguides. Phys. Rev. Lett. 93, 137404 (2004). doi: 10.1103/PhysRevLett.93.137404
[7] Berry, M. V. Geometry of phase and polarization singularities illustrated by edge diffraction and the tides. eds. Soskin, M. S. and Vasnetsov, M. V. In: Proc. SPIE 4403, Second International Conference on Singular Optics (Optical Vortices), (SPIE, Crimea, Ukraine, 2001).
[8] Bashevoy, M. V., Fedotov, V. A. & Zheludev, N. I. Optical whirlpool on an absorbing metallic nanoparticle. Opt. Express 13, 8372–8379 (2005). doi: 10.1364/OPEX.13.008372
[9] Tribelsky, M. I. & Luk'yanchuk, B. S. Anomalous light scattering by small particles. Phys. Rev. Lett. 97, 263902 (2006). doi: 10.1103/PhysRevLett.97.263902
[10] Kuznetsov, A. I., Miroshnichenko, A. E., Brongersma, M. L., Kivshar, Y. S. & Luk'yanchuk, B. Optically resonant dielectric nanostructures. Science 354, aag2472 (2016). doi: 10.1126/science.aag2472
[11] Luk'yanchuk, B. S., Miroshnichenko, A. E. & Kivshar, Y. S. Fano resonances and topological optics: an interplay of far- and near-field interference phenomena. J. Opt. 15, 073001 (2013). doi: 10.1088/2040-8978/15/7/073001
[12] Aharonov, Y., Colombo, F., Sabadini, I., Struppa, D. C. & Tollaksen, J. Some mathematical properties of superoscillations. J. Phys. A 44, 365304 (2011). doi: 10.1088/1751-8113/44/36/365304
[13] Berry, M. V. & Popescu, S. Evolution of quantum superoscillations and optical superresolution without evanescent waves. J. Phys. A 39, 6965–6977 (2006). doi: 10.1088/0305-4470/39/22/011
[14] Berry, M. V. & Moiseyev, N. Superoscillations and supershifts in phase space: Wigner and Husimi function interpretations. J. Phys. A 47, 315203 (2014). doi: 10.1088/1751-8113/47/31/315203
[15] Rogers, E. T. F. & Zheludev, N. I. Optical super-oscillations: sub-wavelength light focusing and super-resolution imaging. J. Opt. 15, 094008 (2013). doi: 10.1088/2040-8978/15/9/094008
[16] Berry, M. V. Five momenta. Eur. J. Phys. 34, 1337–1348 (2013). doi: 10.1088/0143-0807/34/6/1337
[17] Hell, S. W. Far-field optical nanoscopy. Science 316, 1153–1158 (2007). doi: 10.1126/science.1137395
[18] Betzig, E. et al. Imaging intracellular fluorescent proteins at nanometer resolution. Science 313, 1642–1645 (2006). doi: 10.1126/science.1127344
[19] Rust, M. J., Bates, M. & Zhuang, X. W. Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM). Nat. Methods 3, 793–796 (2006). doi: 10.1038/nmeth929
[20] Huang, F. M. & Zheludev, N. I. Super-resolution without evanescent waves. Nano Lett. 9, 1249–1254 (2009). doi: 10.1021/nl9002014
[21] Rogers, E. T. F. et al. A super-oscillatory lens optical microscope for subwavelength imaging. Nat. Mater. 11, 432–435 (2012). doi: 10.1038/nmat3280
[22] Qin, F. et al. A supercritical lens optical label-free microscopy: sub-diffraction resolution and ultra-long working distance. Adv. Mater. 29, 1602721 (2017). doi: 10.1002/adma.201602721
[23] Wong, A. M. H. & Eleftheriades, G. V. An optical super-microscope for far-field, real-time imaging beyond the diffraction limit. Sci. Rep. 3, 1715 (2013). doi: 10.1038/srep01715
[24] Wong, A. M. H. & Eleftheriades, G. V. Advances in imaging beyond the diffraction limit. IEEE Photon. J. 4, 586–589 (2012). doi: 10.1109/JPHOT.2012.2189615
[25] Yuan, G. H., Rogers, E. T. F. & Zheludev, N. I. Achromatic super-oscillatory lenses with sub-wavelength focusing. Light Sci. Appl. 6, e17036 (2017). doi: 10.1038/lsa.2017.36
[26] PJSG, Ferreira & Kempf, A. Superoscillations: faster than the Nyquist rate. IEEE Trans. Signal Process. 54, 3732–3740 (2006). doi: 10.1109/TSP.2006.877642
[27] Remez, R. et al. Superoscillating electron wave functions with subdiffraction spots. Phys. Rev. A 95, 031802 (2017). R. doi: 10.1103/PhysRevA.95.031802
[28] Yuan, G. H. et al. Quantum super-oscillation of a single photon. Light Sci. Appl. 6, e16127 (2016).
[29] Singh, B. K., Nagar, H., Roichman, Y. & Arie, A. Particle manipulation beyond the diffraction limit using structured super-oscillating light beams. Light Sci. Appl. 6, e17050 (2017). doi: 10.1038/lsa.2017.50
[30] Eliezer, Y., Hareli, L., Lobachinsky, L., Froim, S. & Bahabad, A. Breaking the temporal resolution limit by superoscillating optical beats. Phys. Rev. Lett. 119, 043903 (2017). doi: 10.1103/PhysRevLett.119.043903
[31] Dennis, M. R., Hamilton, A. C. & Courtial, J. Superoscillation in speckle patterns. Opt. Lett. 33, 2976–2978 (2008). doi: 10.1364/OL.33.002976
[32] Berry, M. V. Quantum backflow, negative kinetic energy, and optical retro-propagation. J. Phys. A 43, 415302 (2010). doi: 10.1088/1751-8113/43/41/415302
[33] Dändliker, R., Märki, I., Salt, M. & Nesci, A. Measuring optical phase singularities at subwavelength resolution. J. Opt. A 6, S189–S196 (2004). doi: 10.1088/1464-4258/6/5/009
[34] Denisenko, V. G. et al. Mapping phases of singular scalar light fields. Opt. Lett. 33, 89–91 (2008). doi: 10.1364/OL.33.000089
[35] O'Holleran, K., Flossmann, F., Dennis, M. R. & Padgett, M. J. Methodology for imaging the 3D structure of singularities in scalar and vector optical fields. J. Opt. A 11, 094020 (2009). doi: 10.1088/1464-4258/11/9/094020
[36] Lin, D. M., Fan, P. Y., Hasman, E. & Brongersma, M. L. Dielectric gradient metasurface optical elements. Science 345, 298–302 (2014). doi: 10.1126/science.1253213
[37] Zheng, G. X. et al. Metasurface holograms reaching 80% efficiency. Nat. Nanotech. 10, 308–312 (2015). doi: 10.1038/nnano.2015.2
[38] Wu, P. C. et al. Versatile polarization generation with an aluminum plasmonic metasurface. Nano Lett. 17, 445–452 (2017). doi: 10.1021/acs.nanolett.6b04446
[39] Wang, H. F., Shi, L. P., Lu$\mathop {\rm{k}}\limits^{、} $yanchuk, B., Sheppard, C. & Chong, C. T. Creation of a needle of longitudinally polarized light in vacuum using binary optics. Nat. Photon. 2, 501–505 (2008). doi: 10.1038/nphoton.2008.127
[40] García de Abajo, F. J. Light transmission through a single cylindrical hole in a metallic film. Opt. Express 10, 1475–1484 (2002). doi: 10.1364/OE.10.001475
[41] Fan, X. F., Zheng, W. T. & Singh, D. J. Light scattering and surface plasmons on small spherical particles. Light Sci. Appl. 3, e179 (2014). doi: 10.1038/lsa.2014.60