Review Article

Nonlinear photonic metasurfaces

  • Nature Reviews Materials 2, Article number: 17010 (2017)
  • doi:10.1038/natrevmats.2017.10
  • Download Citation
Published online:

Abstract

Compared with conventional optical elements, 2D photonic metasurfaces, consisting of arrays of antennas with subwavelength thickness (the ‘meta-atoms’), enable the manipulation of light–matter interactions on more compact platforms. The use of metasurfaces with spatially varying arrangements of meta-atoms that have subwavelength lateral resolution allows control of the polarization, phase and amplitude of light. Many exotic phenomena have been successfully demonstrated in linear optics; however, to meet the growing demand for the integration of more functionalities into a single optoelectronic circuit, the tailorable nonlinear optical properties of metasurfaces will also need to be exploited. In this Review, we discuss the design of nonlinear photonic metasurfaces — in particular, the criteria for choosing the materials and symmetries of the meta-atoms — for the realization of nonlinear optical chirality, nonlinear geometric Berry phase and nonlinear wavefront engineering. Finally, we survey the application of nonlinear photonic metasurfaces in optical switching and modulation, and we conclude with an outlook on their use for terahertz nonlinear optics and quantum information processing.

  • Subscribe to Nature Reviews Materials for full access:

    $59

    Subscribe

Additional access options:

Already a subscriber?  Log in  now or  Register  for online access.

References

  1. 1.

    & Past achievements and future challenges in the development of three-dimensional photonic metamaterials. Nat. Photonics 5, 523–530 (2011).

  2. 2.

    et al. Active nanoplasmonic metamaterials. Nat. Mater. 11, 573–584 (2012).

  3. 3.

    & From metamaterials to metadevices. Nat. Mater. 11, 917–924 (2012).

  4. 4.

    , & Transforming the optical landscape. Science 348, 521–524 (2015).

  5. 5.

    et al. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science 334, 333–337 (2011).

  6. 6.

    , & Planar photonics with metasurfaces. Science 339, 1232009 (2013).

  7. 7.

    , & Plasmonic meta-atoms and metasurfaces. Nat. Photonics 8, 889–898 (2014).

  8. 8.

    & Flat optics with designer metasurfaces. Nat. Mater. 13, 139–150 (2014).

  9. 9.

    , , , & Broadband light bending with plasmonic nanoantennas. Science 335, 427 (2012).

  10. 10.

    et al. Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves. Nat. Mater. 11, 426–431 (2012).

  11. 11.

    et al. Dual-polarity plasmonic metalens for visible light. Nat. Commun. 3, 1198 (2012).

  12. 12.

    et al. High-efciency broadband meta-hologram with polarization controlled dual images. Nano Lett. 14, 225–230 (2013).

  13. 13.

    , & Metasurface holograms for visible light. Nat. Commun. 4, 2807 (2013).

  14. 14.

    et al. Three-dimensional optical holography using a plasmonic metasurface. Nat. Commun. 4, 2808 (2013).

  15. 15.

    et al. Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light. Nano Lett. 13, 4148–4151 (2013).

  16. 16.

    , , , & Photonic spin Hall effect at metasurfaces. Science 339, 1405–1407 (2013).

  17. 17.

    , , & Dielectric gradient metasurface optical elements. Science 345, 298–302 (2014).

  18. 18.

    & Silicon nanon grating as a miniature chirality-distinguishing beam-splitter. Nat. Commun. 5, 5386 (2014).

  19. 19.

    et al. Aluminum plasmonic multicolor meta-hologram. Nano Lett. 15, 3122–3127 (2015).

  20. 20.

    et al. Polarization-independent silicon metadevices for efcient optical wavefront control. Nano Lett. 15, 5369–5374 (2015).

  21. 21.

    et al. Metasurface holograms reaching 80% efciency. Nat. Nanotechnol. 10, 308–312 (2015).

  22. 22.

    , , & Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission. Nat. Nanotechnol. 10, 937–943 (2015).

  23. 23.

    et al. Broadband hybrid holographic multiplexing with geometric metasurfaces. Adv. Mater. 27, 6444–6449 (2015).

  24. 24.

    et al. Helicity multiplexed broadband metasurface holograms. Nat. Commun. 6, 8241 (2015).

  25. 25.

    , , & Multiwavelength achromatic metasurfaces by dispersive phase compensation. Science 347, 1342–1345 (2015).

  26. 26.

    et al. Metalenses at visible wavelengths: diffraction-limited focusing and subwavelength resolution imaging. Science 352, 1190–1194 (2016).

  27. 27.

    et al. Optically reconfigurable metasurfaces and photonic devices based on phase change materials. Nat. Photonics 10, 60–65 (2016).

  28. 28.

    et al. Photonic spin-controlled multifunctional shared-aperture antenna array. Science 352, 1202–1206 (2016).

  29. 29.

    , , , & Geometric metasurface fork gratings for vortex beam generation and manipulation. Laser Photonics Rev. 2, 322–326 (2016).

  30. 30.

    The Principles of Nonlinear Optics (Wiley, 1984).

  31. 31.

    Nonlinear Optics 3rd edn (Academic, 2008).

  32. 32.

    & Amplified reflection, phase conjugation, and oscillation in degenerate four-wave mixing. Opt. Lett. 1, 16–18 (1977).

  33. 33.

    & Frequency comb generation by four-wave mixing and the role of fiber dispersion. J. Lightwave Technol. 16, 1596–1605 (1998).

  34. 34.

    & Nonlinear plasmonics. Nat. Photonics 6, 737–748 (2012).

  35. 35.

    , & Colloquium: nonlinear metamaterials. Rev. Mod. Phys. 86, 1093–1123 (2014).

  36. 36.

    , , & Second-harmonic generation from magnetic metamaterials. Science 313, 502–504 (2006).

  37. 37.

    , , , & Multipole interference in the second-harmonic optical radiation from gold nanoparticles. Phys. Rev. Lett. 98, 167403 (2007).

  38. 38.

    , , & Three-dimensional nanostructures as highly efficient generators of second harmonic light. Nano Lett. 11, 5519–5523 (2011).

  39. 39.

    et al. Multiresonant broadband optical antennas as efficient tunable nanosources of second harmonic light. Nano Lett. 12, 4997–5002 (2012).

  40. 40.

    et al. Metamaterials with tailored nonlinear optical response. Nano Lett. 12, 673–677 (2012).

  41. 41.

    et al. Collective effects in second-harmonic generation from split-ring-resonator arrays. Phys. Rev. Lett. 109, 015502 (2012).

  42. 42.

    , , , & Enhancement of second-harmonic generation from metal nanoparticles by passive elements. Phys. Rev. Lett. 110, 093902 (2013).

  43. 43.

    et al. Polarization-controlled circular second-harmonic generation from metal hole arrays with threefold rotational symmetry. Phys. Rev. Lett. 112, 135502 (2014).

  44. 44.

    et al. Predicting nonlinear properties of metamaterials from the linear response. Nat. Mater. 14, 379–383 (2015).

  45. 45.

    , , & Controlling light with metamaterial-based nonlinear photonic crystals. Nat. Photonics 9, 180–184 (2015).

  46. 46.

    et al. Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation. Nat. Nanotechnol. 10, 412–417 (2015).

  47. 47.

    et al. Enhanced magnetic second-harmonic generation from resonant metasurfaces. ACS Photonics 2, 1007–1012 (2015).

  48. 48.

    et al. Ultrafast optical modulation of second- and third-harmonic generation from cut-disk-based metasurfaces. ACS Photonics 3, 1517–1522 (2016).

  49. 49.

    et al. Nonlinear generation of vector beams from AlGaAs nanoantennas. Nano Lett. 16, 7191–7197 (2016).

  50. 50.

    et al. Efficient nonlinear light emission of single gold optical antennas driven by few-cycle near-infrared pulses. Phys. Rev. Lett. 103, 257404 (2009).

  51. 51.

    et al. Towards the origin of the nonlinear response in hybrid plasmonic systems. Phys. Rev. Lett. 106, 133901 (2011).

  52. 52.

    et al. Linear and nonlinear Fano resonance on two-dimensional magnetic metamaterials. Phys. Rev. B 84, 235437 (2011).

  53. 53.

    , , & Third-harmonic upconversion enhancement from a single semiconductor nanoparticle coupled to a plasmonic antenna. Nat. Nanotechnol. 9, 290–294 (2014).

  54. 54.

    , , , & Third harmonic mechanism in complex plasmonic Fano structures. ACS Photonics 1, 471–476 (2014).

  55. 55.

    et al. Symmetry selective third harmonic generation from plasmonic metacrystals. Phys. Rev. Lett. 113, 033901 (2014).

  56. 56.

    , , , & Enhanced third harmonic generation in single germanium nanodisks excited at the anapole mode. Nano Lett. 16, 4635–4640 (2016).

  57. 57.

    , , & Multipolar third-harmonic generation driven by optically induced magnetic resonances. ACS Photonics 3, 1468–1476 (2016).

  58. 58.

    , , & Surface-enhanced nonlinear four-wave mixing. Phys. Rev. Lett. 104, 046803 (2010).

  59. 59.

    & Subwavelength imaging using phase-conjugating nonlinear nanoantenna arrays. Nano Lett. 11, 5514–5518 (2011).

  60. 60.

    et al. Optical negative refraction by four-wave mixing in thin metallic nanostructures. Nat. Mater. 11, 34–38 (2012).

  61. 61.

    et al. Phase mismatch-free nonlinear propagation in optical zero-index materials. Science 342, 1223–1226 (2013).

  62. 62.

    , , , & Coherent Fano resonances in a plasmonic nanocluster enhance optical four-wave mixing. Proc. Natl Acad. Sci. USA 110, 9215–9219 (2013).

  63. 63.

    , , , & Circular dichroism of four-wave mixing in nonlinear metamaterials. Phys. Rev. B 88, 195148 (2013).

  64. 64.

    & Plasmon-enhanced four-wave mixing for super resolution applications. Phys. Rev. Lett. 112, 056802 (2014).

  65. 65.

    et al. Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions. Nature 511, 65–69 (2014).

  66. 66.

    et al. Ultrathin gradient nonlinear metasurface with a giant nonlinear response. Optica 3, 283–288 (2016).

  67. 67.

    et al. Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response. Nano Lett. 14, 6488–6492 (2014).

  68. 68.

    et al. Nonlinear Fano-resonant dielectric metasurfaces. Nano Lett. 15, 7388–7393 (2015).

  69. 69.

    , & Optical harmonic generation in calcite. Phys. Rev. Lett. 8, 404–406 (1962).

  70. 70.

    , & Nonlinear electroreflectance in silicon and silver. Phys. Rev. Lett. 18, 167–170 (1967).

  71. 71.

    , & Electrically controlled nonlinear generation flight with plasmonics. Science 333, 1720–1723 (2011).

  72. 72.

    et al. Electrifying photonic metamaterials for tunable nonlinear optics. Nat. Commun. 5, 4680 (2014).

  73. 73.

    et al. Backward phase-matching for nonlinear optical generation in negative-index materials. Nat. Mater. 14, 807–811 (2015).

  74. 74.

    et al. Electrical control of second harmonic generation in a WSe2 monolayer transistor. Nat. Nanotechnol. 10, 407–411 (2015).

  75. 75.

    & Electrically tunable nonlinear plasmonics in graphene nanoislands. Nat. Commun. 5, 5725 (2014).

  76. 76.

    & Plasmon-enhanced nonlinear wave mixing in nanostructured graphene. ACS Photonics 2, 306–312 (2015).

  77. 77.

    & Third-harmonic generation in absorbing media of cubic or isotropic symmetry. Phys. Rev. B 4, 3437–3450 (1971).

  78. 78.

    & Harmonic generation and selection rules in nonlinear optics. Proc. Indian Acad. Sci. A 76, 13–20 (1972).

  79. 79.

    & Phase matched second harmonic generation from nanostructured metallic surfaces. J. Opt. A 6, 26–28 (2004).

  80. 80.

    , & Controlling the second harmonic in a phase matched negative-index metamaterial. Phys. Rev. Lett. 107, 063902 (2011).

  81. 81.

    , & Nonlinear interference and unidirectional wave mixing in metamaterials. Phys. Rev. Lett. 110, 063901 (2013).

  82. 82.

    , , & Interactions between light waves in a nonlinear dielectric. Phys. Rev. 127, 1918–1939 (1962).

  83. 83.

    & Phase matched nonlinear interaction between circularly polarized waves. Appl. Phys. Lett. 15, 189–191 (1969).

  84. 84.

    & Phase matched third harmonic generation in cholesteric liquid crystals. Phys. Rev. Lett. 25, 23–26 (1970).

  85. 85.

    , , & Quasi-phase-matched second harmonic generation: tuning and tolerances. IEEE J. Quantum Electron. 28, 2631–2654 (1992).

  86. 86.

    et al. Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3. Phys. Rev. Lett. 78, 2752–2755 (1997).

  87. 87.

    & Chiral selection on inorganic crystalline surfaces. Nat. Mater. 2, 367–374 (2003).

  88. 88.

    Molecular chirality at surfaces. Phys. Status Solidi B 249, 20572088 (2012).

  89. 89.

    A chiral route to negative refraction. Science 306, 1353–1355 (2004).

  90. 90.

    et al. Giant optical activity in quasi-two-dimensional planar nanostructures. Phys. Rev. Lett. 95, 227401 (2005).

  91. 91.

    , , & Giant gyrotropy due to electromagnetic-field coupling in a bilayered chiral structure. Phys. Rev. Lett. 97, 177401 (2006).

  92. 92.

    , & Optical activity in extrinsically chiral metamaterial. Appl. Phys. Lett. 93, 191911 (2008).

  93. 93.

    et al. Gold helix photonic metamaterial as broadband circular polarizer. Science 325, 1513–1515 (2009).

  94. 94.

    et al. Ultrasensitive detection and characterization of biomolecules using superchiral fields. Nat. Nanotechnol. 5, 783–787 (2010).

  95. 95.

    et al. Photoinduced handedness switching in terahertz chiral metamolecules. Nat. Commun. 3, 942 (2012).

  96. 96.

    et al. Spectrally selective chiral silicon metasurfaces based on infrared Fano resonances. Nat. Commun. 5, 3892 (2014).

  97. 97.

    et al. Enantiomeric switching of chiral metamaterial for terahertz polarization modulation employing vertically deformable MEMS spirals. Nat. Commun. 6, 8422 (2015).

  98. 98.

    , & Light-polarization-induced optical activity. Phys. Rev. Lett. 82, 3601–3604 (1999).

  99. 99.

    , , , & Circular dichroism spectroscopy at interfaces: a surface second harmonic generation study. J. Phys. Chem. 97, 1383–1388 (1993).

  100. 100.

    , & A second harmonic generation analog of optical rotatory dispersion for the study of chiral monolayers. J. Chem. Phys. 101, 6233–6241 (1994).

  101. 101.

    , & Surface second-harmonic generation from chiral materials. Phys. Rev. B 51, 1425–1434 (1995).

  102. 102.

    , , & Optical activity of anisotropic achiral surfaces. Phys. Rev. Lett. 77, 1456–1459 (1996).

  103. 103.

    et al. Plasmonic ratchet wheels: switching circular dichroism by arranging chiral nanostructures. Nano Lett. 9, 3945–3948 (2009).

  104. 104.

    et al. Asymmetric optical second-harmonic generation from chiral G-shaped gold nanostructures. Phys. Rev. Lett. 104, 127401 (2010).

  105. 105.

    , , , & Circular dichroism in the optical second-harmonic emission of curved gold metal nanowires. Phys. Rev. Lett. 107, 257401 (2011).

  106. 106.

    et al. Nonlinear chiral imaging of subwavelength-sized twisted-cross gold nanodimers. Opt. Mater. Express 1, 46–56 (2011).

  107. 107.

    , , , & Nonlinear imaging and spectroscopy of chiral metamaterials. Adv. Mater. 26, 6157–6162 (2014).

  108. 108.

    et al. Nonlinear superchiral meta-surfaces: tuning chirality and disentangling non-reciprocity at the nanoscale. Adv. Mater. 26, 4074–4081 (2014).

  109. 109.

    , , , & Octupolar plasmonic meta-molecules for nonlinear chiral watermarking at subwavelength scale. ACS Photonics 2, 899–906 (2015).

  110. 110.

    et al. Giant nonlinear optical activity of achiral origin in planar metasurfaces with quadratic and cubic nonlinearities. Adv. Mater. 28, 2992–2999 (2016).

  111. 111.

    , , & Giant nonlinear optical activity in a plasmonic metamaterial. Nat. Commun. 3, 833 (2012).

  112. 112.

    Generalized theory of interference, and its applications. Part I. Coherent pencils. Proc. Indian Acad. Sci. A 44, 247–262 (1956).

  113. 113.

    Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. A 392, 45–57 (1984).

  114. 114.

    , , & Space-variant Pancharatnam Berry phase optical elements with computer-generated subwavelength gratings. Opt. Lett. 27, 1141–1143 (2002).

  115. 115.

    , , & Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics. Appl. Phys. Lett. 82, 328–330 (2003).

  116. 116.

    et al. Continuous control of the nonlinearity phase for harmonic generations. Nat. Mater. 14, 607–612 (2015).

  117. 117.

    et al. Gradient nonlinear Pancharatnam–Berry metasurfaces. Phys. Rev. Lett. 115, 207403 (2015).

  118. 118.

    , & Subwavelength nonlinear phase control and anomalous phase matching in plasmonic metasurfaces. Nat. Commun. 7, 10367 (2016).

  119. 119.

    The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light. Proc. R. Soc. A 82, 560–567 (1909).

  120. 120.

    Mechanical detection and measurement of the angular momentum of light. Phys. Rev. 50, 115–125 (1936).

  121. 121.

    A radiation torque experiment. Am. J. Phys. 34, 1185–1192 (1966).

  122. 122.

    & Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate. Opt. Commun. 31, 1–3 (1979).

  123. 123.

    Angular Doppler effect. J. Opt. Soc. Am. 71, 609–611 (1980).

  124. 124.

    , & Evolving geometric phase and its dynamical manifestation as a frequency shift: an optical experiment. Phys. Rev. Lett. 61, 19–22 (1988).

  125. 125.

    An experiment to demonstrate the angular Doppler effect on laser light. Am. J. Phys. 66, 1007–1010 (1998).

  126. 126.

    , & Rotational Doppler effect in nonlinear optics. Nat. Phys. 12, 736–740 (2016).

  127. 127.

    , , , & Plasmonic airy beam generated by in-plane diffraction. Phys. Rev. Lett. 107, 126804 (2011).

  128. 128.

    , & Surface-plasmon holographic beam shaping. Phys. Rev. Lett. 109, 203903 (2012).

  129. 129.

    A new microscopic principle. Nature 161, 777–778 (1948).

  130. 130.

    Time reversal and negative refraction. Science 332, 71–73 (2008).

  131. 131.

    Nonlinear photonic crystals. Phys. Rev. Lett. 81, 4136–4139 (1998).

  132. 132.

    , , , & Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal. Phys. Rev. Lett. 84, 4345–4348 (2000).

  133. 133.

    , , & Nonlinear generation and manipulation of Airy beams. Nat. Photonics 3, 395–398 (2009).

  134. 134.

    , , , & Nonlinear volume holography for wave-front engineering. Phys. Rev. Lett. 113, 163902 (2014).

  135. 135.

    , , , & Third harmonic generation of optical vortices using holography based gold-fork microstructure. Adv. Opt. Mater. 2, 389–393 (2014).

  136. 136.

    et al. Phased-array sources based on nonlinear metamaterial nanocavities. Nat. Commun. 6, 7667 (2015).

  137. 137.

    , , & Nonlinear beam shaping with plasmonic metasurfaces. ACS Photonics 3, 117–123 (2016).

  138. 138.

    , & Nonlinear metamaterials for holography. Nat. Commun. 7, 12533 (2016).

  139. 139.

    et al. Spin and wavelength multiplexed nonlinear metasurface holography. Nat. Commun. 7, 11930 (2016).

  140. 140.

    et al. All optical high speed signal processing with silicon organic hybrid slot waveguides. Nat. Photonics 3, 216–219 (2009).

  141. 141.

    et al. Sub-femtojoule all-optical switching using a photonic-crystal nanocavity. Nat. Photonics 4, 477–483 (2010).

  142. 142.

    , , & Silicon optical modulators. Nat. Photonics 4, 518–526 (2010).

  143. 143.

    , & Nonlinear silicon photonics. Nat. Photonics 4, 535–544 (2010).

  144. 144.

    , & Ultrafast relaxation of electrons probed by surface plasmons at a thin silver film. Phys. Rev. Lett. 12, 784–787 (1990).

  145. 145.

    , , & Direct measurement of nonequilibrium electron energy distributions in subpicosecond laser heated gold films. Phys. Rev. Lett. 68, 2834–2837 (1992).

  146. 146.

    , , & Nonequilibrium electron interactions in metal films. Phys. Rev. Lett. 81, 922–925 (1998).

  147. 147.

    , , & Resonant and off-resonant light driven plasmons in metal nanoparticles studied by femtosecond resolution third harmonic generation. Phys. Rev. Lett. 83, 4421–4424 (1999).

  148. 148.

    , & Ultrafast dynamics of electron thermalization in gold. Phys. Rev. Lett. 86, 1638–1641 (2001).

  149. 149.

    , , & Ultrafast active plasmonics. Nat. Photonics 3, 55–58 (2009).

  150. 150.

    , & Ultrafast all-optical coupling of light to surface plasmon polaritons on plain metal surfaces. Phys. Rev. Lett. 105, 017402 (2010).

  151. 151.

    et al. Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality. Nat. Nanotechnol. 6, 106–110 (2011).

  152. 152.

    et al. Eliminating material constraints for nonlinearity with plasmonic metamaterials. Nat. Commun. 6, 7757 (2015).

  153. 153.

    et al. Nanostructured plasmonic medium for terahertz bandwidth all-optical switching. Adv. Mater. 23, 5540–5544 (2011).

  154. 154.

    et al. An actively ultrafast tunable giant slow-light effect in ultrathin nonlinear metasurfaces. Light Sci. Appl. 4, e302 (2015).

  155. 155.

    , , , & A magneto-electro-optical effect in a plasmonic nanowire material. Nat. Commun. 6, 7021 (2015).

  156. 156.

    Anomalous ultrafast dynamics of hot plasmonic electrons in nanostructures with hot spots. Nat. Nanotechnol. 10, 770–774 (2015).

  157. 157.

    et al. Sub-picosecond optical switching with a negative index metamaterial. Nano Lett. 9, 3565–3569 (2009).

  158. 158.

    , , & Hotspot-mediated ultrafast nonlinear control of multifrequency plasmonic nanoantennas. Nat. Commun. 5, 4869 (2014).

  159. 159.

    et al. Liquid crystal based nonlinear fishnet metamaterials. Appl. Phys. Lett. 100, 121113 (2012).

  160. 160.

    et al. Real-time observation of ultrafast Rabi oscillations between excitons and plasmons in metal nanostructures with J-aggregates. Nat. Photonics 7, 128–132 (2013).

  161. 161.

    et al. Ultrafast all-optical switching with magnetic resonances in nonlinear dielectric nanostructures. Nano Lett. 15, 6985–6990 (2015).

  162. 162.

    , , & Ultrafast switching of tunable infrared plasmons in indium tin oxide nanorod arrays with large absolute amplitude. Nat. Photonics 10, 267–273 (2016).

  163. 163.

    et al. Structural tunability in metamaterials. Appl. Phys. Lett. 95, 084105 (2009).

  164. 164.

    et al. Reconfigurable terahertz metamaterials. Phys. Rev. Lett. 103, 147401 (2009).

  165. 165.

    , , , & Highly strained compliant optical metamaterials with large frequency tunability. Nano Lett. 10, 4222–4227 (2010).

  166. 166.

    , , & Giant nonlinearity of an optically reconfigurable plasmonic metamaterial. Adv. Mater. 28, 729–733 (2015).

  167. 167.

    , , , & Nano-optomechanical nonlinear dielectric metamaterials. Appl. Phys. Lett. 107, 191110 (2015).

  168. 168.

    & Reconfigurable nanomechanical photonic metamaterials. Nat. Nanotechnol. 11, 16–22 (2016).

  169. 169.

    , & Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region. Science 352, 795–797 (2016).

  170. 170.

    et al. Enhanced nonlinear refractive index in ε-near-zero materials. Phys. Rev. Lett. 116, 233901 (2016).

  171. 171.

    , , , & Strong-field physics with singular light beams. Nat. Phys. 8, 743–746 (2012).

  172. 172.

    , , , & Spin angular momentum and tunable polarization in high-harmonic generation. Nat. Photonics 8, 543–549 (2014).

  173. 173.

    et al. Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations. Nat. Photonics 8, 119–123 (2014).

  174. 174.

    et al. Noncollinear generation of angularly isolated circularly polarized high harmonics. Nat. Photonics 9, 743–750 (2015).

  175. 175.

    et al. Real-time observation of interfering crystal electrons in high-harmonic generation. Nature 523, 572–575 (2015).

  176. 176.

    , , & Bicircular high-harmonic spectroscopy reveals dynamical symmetries of atoms and molecules. Phys. Rev. Lett. 116, 123001 (2016).

  177. 177.

    Quantum optics: science and technology in a new light. Science 348, 525–530 (2015).

Download references

Acknowledgements

This work was financially supported by the Deutsche Forschungsgemeinschaft (grants DFG TRR142/A05 and ZE953/7-1). G.X. acknowledges support from China's Recruitment Program of Global Experts and Peacock program of Shenzhen. S.Z. acknowledges support from European Research Council consolidator grant (TOPOLOGICAL).

Author information

Affiliations

  1. Department of Materials Science and Engineering, Southern University of Science and Technology, 518055, Shenzhen, China.

    • Guixin Li
  2. Department of Physics, University of Paderborn, Warburger Strasse 100, D-33098 Paderborn, Germany.

    • Guixin Li
    •  & Thomas Zentgraf
  3. School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK.

    • Shuang Zhang

Authors

  1. Search for Guixin Li in:

  2. Search for Shuang Zhang in:

  3. Search for Thomas Zentgraf in:

Competing interests

The authors declare no competing interests.

Corresponding authors

Correspondence to Guixin Li or Shuang Zhang or Thomas Zentgraf.