Citation:

"Plasmonics" in free space: observation of giant wavevectors, vortices, and energy backflow in superoscillatory optical fields

• Light: Science & Applications  8, Article number: 2 (2019)
• Corresponding author:
Nikolay I. Zheludev (nzheludev@ntu.edu.sg)
Revised: 29 November 2018
Accepted: 03 December 2018
Published online: 03 January 2019
• Evanescent light can be localized at the nanoscale by resonant absorption in a plasmonic nanoparticle or taper or by transmission through a nanohole. However, a conventional lens cannot focus free-space light beyond half of the wavelength λ. Nevertheless, precisely tailored interference of multiple waves can form a hotspot in free space of an arbitrarily small size, which is known as superoscillation. Here, we report a new type of integrated metasurface interferometry that allows for the first time mapping of fields with a deep subwavelength resolution ~λ/100. The findings reveal that an electromagnetic field near the superoscillatory hotspot has many features similar to those found near resonant plasmonic nanoparticles or nanoholes: the hotspots are surrounded by nanoscale phase singularities and zones where the phase of the superoscillatory field changes more than tenfold faster than a free-propagating plane wave. Areas with high local wavevectors are pinned to phase vortices and zones of energy backflow (~λ/20 in size) that contribute to tightening of the main focal spot size beyond the Abbe–Rayleigh limit. Our observations reveal some analogy between plasmonic nanofocusing of evanescent waves and superoscillatory nanofocusing of free-space waves and prove the fundamental link between superoscillations and superfocusing, offering new opportunities for nanoscale metrology and imaging.
•  [1] Berry, M. V. & Dennis, M. R. Knotted and linked phase singularities in monochromatic waves. Proc. R. Soc. Lond. A 457, 2251–2263 (2001). [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). [4] Dennis, M. R., O'Holleran, K. & Padgett, M. J. Singular optics: optical vortices and polarization singularities. Prog. Opt. 53, 293–363 (2009). [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). [6] Stockman, M. I. Nanofocusing of optical energy in tapered plasmonic waveguides. Phys. Rev. Lett. 93, 137404 (2004). [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). [9] Tribelsky, M. I. & Luk'yanchuk, B. S. Anomalous light scattering by small particles. Phys. Rev. Lett. 97, 263902 (2006). [10] Kuznetsov, A. I., Miroshnichenko, A. E., Brongersma, M. L., Kivshar, Y. S. & Luk'yanchuk, B. Optically resonant dielectric nanostructures. Science 354, aag2472 (2016). [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). [12] Aharonov, Y., Colombo, F., Sabadini, I., Struppa, D. C. & Tollaksen, J. Some mathematical properties of superoscillations. J. Phys. A 44, 365304 (2011). [13] Berry, M. V. & Popescu, S. Evolution of quantum superoscillations and optical superresolution without evanescent waves. J. Phys. A 39, 6965–6977 (2006). [14] Berry, M. V. & Moiseyev, N. Superoscillations and supershifts in phase space: Wigner and Husimi function interpretations. J. Phys. A 47, 315203 (2014). [15] Rogers, E. T. F. & Zheludev, N. I. Optical super-oscillations: sub-wavelength light focusing and super-resolution imaging. J. Opt. 15, 094008 (2013). [16] Berry, M. V. Five momenta. Eur. J. Phys. 34, 1337–1348 (2013). [17] Hell, S. W. Far-field optical nanoscopy. Science 316, 1153–1158 (2007). [18] Betzig, E. et al. Imaging intracellular fluorescent proteins at nanometer resolution. Science 313, 1642–1645 (2006). [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). [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). [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). [24] Wong, A. M. H. & Eleftheriades, G. V. Advances in imaging beyond the diffraction limit. IEEE Photon. J. 4, 586–589 (2012). [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). [26] PJSG, Ferreira & Kempf, A. Superoscillations: faster than the Nyquist rate. IEEE Trans. Signal Process. 54, 3732–3740 (2006). [27] Remez, R. et al. Superoscillating electron wave functions with subdiffraction spots. Phys. Rev. A 95, 031802 (2017). R. [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). [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). [31] Dennis, M. R., Hamilton, A. C. & Courtial, J. Superoscillation in speckle patterns. Opt. Lett. 33, 2976–2978 (2008). [32] Berry, M. V. Quantum backflow, negative kinetic energy, and optical retro-propagation. J. Phys. A 43, 415302 (2010). [33] Dändliker, R., Märki, I., Salt, M. & Nesci, A. Measuring optical phase singularities at subwavelength resolution. J. Opt. A 6, S189–S196 (2004). [34] Denisenko, V. G. et al. Mapping phases of singular scalar light fields. Opt. Lett. 33, 89–91 (2008). [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). [36] Lin, D. M., Fan, P. Y., Hasman, E. & Brongersma, M. L. Dielectric gradient metasurface optical elements. Science 345, 298–302 (2014). [37] Zheng, G. X. et al. Metasurface holograms reaching 80% efficiency. Nat. Nanotech. 10, 308–312 (2015). [38] Wu, P. C. et al. Versatile polarization generation with an aluminum plasmonic metasurface. Nano Lett. 17, 445–452 (2017). [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). [40] García de Abajo, F. J. Light transmission through a single cylindrical hole in a metallic film. Opt. Express 10, 1475–1484 (2002). [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).
通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

Figures(4)

Article Metrics

Article views(85) PDF downloads(3) Citation(0) Citation counts are provided from Web of Science. The counts may vary by service, and are reliant on the availability of their data.

"Plasmonics" in free space: observation of giant wavevectors, vortices, and energy backflow in superoscillatory optical fields

• 1. Centre for Disruptive Photonic Technologies, The Photonic Institute, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
• 2. Optoelectronics Research Centre and Centre for Photonic Metamaterials, University of Southampton, Highfield, Southampton SO17 1BJ, UK
• 3. Institute for Life Sciences, University of Southampton, Highfield, Southampton SO17 1BJ, UK
• Corresponding author: Nikolay I. Zheludev, nzheludev@ntu.edu.sg

Abstract: Evanescent light can be localized at the nanoscale by resonant absorption in a plasmonic nanoparticle or taper or by transmission through a nanohole. However, a conventional lens cannot focus free-space light beyond half of the wavelength λ. Nevertheless, precisely tailored interference of multiple waves can form a hotspot in free space of an arbitrarily small size, which is known as superoscillation. Here, we report a new type of integrated metasurface interferometry that allows for the first time mapping of fields with a deep subwavelength resolution ~λ/100. The findings reveal that an electromagnetic field near the superoscillatory hotspot has many features similar to those found near resonant plasmonic nanoparticles or nanoholes: the hotspots are surrounded by nanoscale phase singularities and zones where the phase of the superoscillatory field changes more than tenfold faster than a free-propagating plane wave. Areas with high local wavevectors are pinned to phase vortices and zones of energy backflow (~λ/20 in size) that contribute to tightening of the main focal spot size beyond the Abbe–Rayleigh limit. Our observations reveal some analogy between plasmonic nanofocusing of evanescent waves and superoscillatory nanofocusing of free-space waves and prove the fundamental link between superoscillations and superfocusing, offering new opportunities for nanoscale metrology and imaging.

• Reference (41)

/