Near-zero refractive index photonics

Journal name:
Nature Photonics
Volume:
11,
Pages:
149–158
Year published:
DOI:
doi:10.1038/nphoton.2017.13
Received
Accepted
Published online
Corrected online

Abstract

Structures with near-zero parameters (for example, media with near-zero relative permittivity and/or relative permeability, and thus a near-zero refractive index) exhibit a number of unique features, such as the decoupling of spatial and temporal field variations, which enable the exploration of qualitatively different wave dynamics. This Review summarizes the underlying principles and salient features, physical realizations and technological potential of these structures. In doing so, we revisit their distinctive impact on multiple optical processes, including scattering, guiding, trapping and emission of light. Their role in emphasizing secondary responses of matter such as nonlinear, non-reciprocal and non-local effects is also discussed.

At a glance

Figures

  1. Tunnelling through distorted channels.
    Figure 1: Tunnelling through distorted channels.

    a, Conceptual sketch of stretching the wavelength (left) and power flow concentration (right) in waveguide channels filled with media with near-zero parameters. b,c, Power flow (real part of the Poynting vector field (b) normalized to its maximal value Smax) and snapshot of the magnetic field Hz obtained via numerical simulations (c; see Methods) for ENZ (ε 0, narrow channel, left), MNZ (μ 0, wide channel, centre) and EMNZ (ε 0 and μ 0, arbitrarily shaped channel, right) supercoupling/tunnelling effects. d, Experimental demonstrations of tunnelling, near-unity transmission coefficient T with zero phase advance, in waveguide set-ups. Left: ENZ tunnelling implemented by using a microwave metallic waveguide supporting the TE10 mode with cut-off frequency f10 = 1.47 GHz for relative permittivity εr = 1 (see Box I), and revealing full transmission independently of the length of the channel L; centre: MNZ coupling implemented by using a waveguide filled with split-ring resonators; right: sketch of the possible set-up for EMNZ coupling implemented by using a waveguide at cut-off filled with a dielectric rod (experimental results to be reported in a future publication). Figure adapted with permission from: d (left), ref. 16, APS; d (centre), ref. 19, APS.

  2. Highly directive emission and geometry-invariant phenomena.
    Figure 2: Highly directive emission and geometry-invariant phenomena.

    a, Numerical simulations (see Methods) of the 2D electric field magnitude, |Ez|, and normalized radiation intensity, Wrad(ϕ) = ½Re{E × H*}, excited by an insulated 2D current line source immersed in 2D EMNZ cylinders of rectangular and triangular cross-sections. The current line is insulated from the EMNZ medium by a vacuum circular cylinder. Highly directive beams are generated perpendicular to the sides of the EMNZ body. b, Experimental realization and measured radiation pattern based on a wire mesh fed by a monopole antenna at GHz frequencies. c, ENZ metallic lens (implemented as waveguides at cut-off) and measured electric field distribution, evidencing high directivity (centred case, top) and beamforming (displaced case, bottom). d, Sketch and numerical prediction (see Methods) of the electric and magnetic field distributions for 3D 'open' ENZ cavities containing a dielectric particle of relative permittivity εp and supporting a bound (non-radiating or embedded) eigenmode, independently of the geometry of the external boundary, which is touching the vacuum. Figure adapted with permission from: b, ref. 7, APS; c, ref. 30, IEEE.

  3. Nonlinear phenomena in structures with near-zero parameters.
    Figure 3: Nonlinear phenomena in structures with near-zero parameters.

    a, Phase matching in zero-index media leading to efficient four-wave mixing (FWM) in both the forward and backward directions. DFWM, degenerate four-wave mixing. Sketch (left), geometry (centre) and measured data (right) of the experimental realization with a fishnet metamaterial at near-infrared frequencies. The measured FWM signal in the forward (purple) and backward (blue) directions are shown (right). b, Strong nonlinear response in ENZ thin films. Measured nonlinear effective refractive index, n2(eff), and effective nonlinear attenuation constant, β(eff), of an ITO film of 310 nm thickness. The ENZ point ε(λp) 0 occurs at λp 1,240 nm, centre of the shaded region). c, Frozen light. Self-sustained 3D confinement of light in an ENZ medium with Kerr nonlinearity. Electric field iso-surface (left) and intensity distribution (centre) as well as dielectric permittivity profile (right) are shown. Blue plane (right) corresponds to the zero-permittivity points. All positions normalized with respect to the inverse of the wavevector at the plasma frequency kp−1. Figure adapted with permission from: a, ref. 64, AAAS; b, ref. 71, AAAS; c, ref. 85, under a Creative Commons licence (http://creativecommons.org/licenses/by/4.0/).

  4. Different realizations of structures with near-zero parameters.
    Figure 4: Different realizations of structures with near-zero parameters.

    a, Continuous media including polaritonic materials such as SiC at mid-infrared frequencies (left), doped semiconductors such as transparent conducting oxides (TCOs) at near-infrared frequencies (centre) and topological insulators such as Bi1.5Sb0.5Te1.8Se1.2 (BSTS) at ultraviolet frequencies (right). b, Synthetic implementations including waveguides at cut-off (i), wire media (ii), multilayered structures (iii), arrays of dielectric rods (iv) and/or photonic crystals (v). c, Hybrid implementation of continuous and synthetic media such as dielectric particles immersed in a continuous ENZ medium. Figure adapted with permission from: a (left and centre), ref. 113, OSA; a (right), ref. 117, Macmillan Publishers Ltd.; b (i, SEM inset), ref. 36, APS; b (ii, SEM inset), ref. 95, APS; b (iii, SEM inset), ref. 128, Macmillan Publishers Ltd.; b (iv), ref. 22, Macmillan Publishers Ltd.; b (v), ref. 131, Macmillan Publishers Ltd.

Change history

Corrected online 06 March 2017
Owing to technical problems, this Review Article was published online later than the date given in the print version. The published date should read '1 March 2017', and is correct in the online versions.

References

  1. Engheta, N. & Ziolkowski, R. W. Metamaterials: Physics and Engineering Explorations (Wiley, 2006).
  2. Eleftheriades, G. V. & Balmain, K. G. Negative-Refraction Metamaterials: Fundamental Principles and Applications (Wiley, 2005).
  3. Cai, W. & Shalaev, V. M. Optical Metamaterials: Fundamentals and Applications (Springer, 2010).
  4. Ziolkowski, R. W. Propagation in and scattering from a matched metamaterial having a zero index of refraction. Phys. Rev. E 70, 046608 (2004).
  5. Silveirinha, M. G. & Engheta, N. Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials. Phys. Rev. Lett. 97, 157403 (2006).
  6. Engheta, N. Pursuing near-zero response. Science 340, 286287 (2013).
  7. Enoch, S., Tayeb, G., Sabouroux, P., Guérin, N. & Vincent, P. A metamaterial for directive emission. Phys. Rev. Lett. 89, 213902 (2002).
  8. Graciá-Salgado, R., García-Chocano, V. M., Torrent, D. & Sánchez-Dehesa, J. Negative mass density and ρ-near-zero quasi-two-dimensional metamaterials: design and applications. Phys. Rev. B 88, 224305 (2013).
  9. Wei, Q., Cheng, Y. & Liu, X. J. Acoustic total transmission and total reflection in zero-index metamaterials with defects. Appl. Phys. Lett. 102, 174104 (2013).
  10. Fleury, R. & Alù, A. Extraordinary sound transmission through density-near-zero ultranarrow channels. Phys. Rev. Lett. 111, 055501 (2013).
  11. Gu, Y., Cheng, Y., Wang, J. & Liu, X. Controlling sound transmission with density-near-zero acoustic membrane network. J. Appl. Phys. 118, 024505 (2015).
  12. Silveirinha, M. G. & Engheta, N. Metamaterial-inspired model for electron waves in bulk semiconductors. Phys. Rev. B 86, 245302 (2012).
  13. Silveirinha, M. G. & Engheta, N. Spatial delocalization and perfect tunneling of matter waves: electron perfect lens. Phys. Rev. Lett. 110, 213902 (2013).
  14. Fleury, R. & Alù, A. Manipulation of electron flow using near-zero index semiconductor metamaterials. Phys. Rev. B 90, 035138 (2014).
  15. Silveirinha, M. G. & Engheta, N. Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials. Phys. Rev. B 76, 245109 (2007).
  16. Edwards, B., Alù, A., Young, M. E., Silveirinha, M. G. & Engheta, N. Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide. Phys. Rev. Lett. 100, 033903 (2008).
  17. Edwards, B., Alù, A., Silveirinha, M. G. & Engheta, N. Reflectionless sharp bends and corners in waveguides using epsilon-near-zero effects. J. Appl. Phys. 105, 044905 (2009).
  18. Alù, A., Silveirinha, M. G. & Engheta, N. Transmission-line analysis of ε-near-zero-filled narrow channels. Phys. Rev. E 78, 016604 (2008).
  19. Marcos, J. S., Silveirinha, M. G. & Engheta, N. μ-near-zero supercoupling. Phys. Rev. B 91, 195112 (2015).
  20. Mahmoud, A. M. & Engheta, N. Wave–matter interactions in epsilon-and-mu-near-zero structures. Nat. Commun. 5, 5638 (2014).
  21. Silveirinha, M. G. & Engheta, N. Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media. Phys. Rev. B 75, 075119 (2007).
  22. Huang, X., Lai, Y., Hang, Z. H., Zheng, H. & Chan, C. T. Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials. Nat. Mater. 10, 582586 (2011).
  23. Nguyen, V. C., Chen, L. & Halterman, K. Total transmission and total reflection by zero index metamaterials with defects. Phys. Rev. Lett. 105, 233908 (2010).
  24. Hao, J., Yan, W. & Qiu, M. Super-reflection and cloaking based on zero index metamaterial. Appl. Phys. Lett. 96, 101109 (2010).
  25. Alù, A., Silveirinha, M. G., Salandrino, A. & Engheta, N. Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern. Phys. Rev. B 75, 155410 (2007).
  26. Navarro-Cía, M., Beruete, M., Campillo, I. & Sorolla, M. Enhanced lens by ε and μ near-zero metamaterial boosted by extraordinary optical transmission. Phys. Rev. B 83, 115112 (2011).
  27. Navarro-Cía, M., Beruete, M., Sorolla, M. & Engheta, N. Lensing system and Fourier transformation using epsilon-near-zero metamaterials. Phys. Rev. B 86, 165130 (2012).
  28. Torres, V. et al. Experimental demonstration of a millimeter-wave metallic ENZ lens based on the energy squeezing principle. IEEE Trans. Antennas Propag. 63, 231239 (2015).
  29. Pacheco-Peña, V. et al. Mechanical 144 GHz beam steering with all-metallic epsilon-near-zero lens antenna. Appl. Phys. Lett. 105, 243503 (2014).
  30. Soric, J. C. & Alù, A. Longitudinally independent matching and arbitrary wave patterning using ε-near-zero channels. IEEE Trans. Microw. Theory Tech. 63, 35583567 (2015).
  31. Alù, A. & Engheta, N. Boosting molecular fluorescence with a plasmonic nanolauncher. Phys. Rev. Lett. 103, 043902 (2009).
  32. Fleury, R. & Alù, A. Enhanced superradiance in epsilon-near-zero plasmonic channels. Phys. Rev. B 87, 201101 (2013).
  33. Sokhoyan, R. & Atwater, H. A. Quantum optical properties of a dipole emitter coupled to an ε-near-zero nanoscale waveguide. Opt. Express 21, 3227932290 (2013).
  34. Sokhoyan, R. & Atwater, H. A. Cooperative behavior of quantum dipole emitters coupled to a zero-index nanoscale waveguide. Preprint at http://arxiv.org/abs/1510.07071 (2015).
  35. Liberal, I. & Engheta, N. Nonradiating and radiating modes excited by quantum emitters in open epsilon-near-zero cavities. Sci. Adv. 2, e1600987 (2016).
  36. Vesseur, E. J. R., Coenen, T., Caglayan, H., Engheta, N. & Polman, A. Experimental verification of n = 0 structures for visible light. Phys. Rev. Lett. 110, 013902 (2013).
  37. Alù, A. & Engheta, N. Coaxial-to-waveguide matching with ε-near-zero ultranarrow channels and bends. IEEE Trans. Antennas Propag. 58, 328339 (2010).
  38. Soric, J. C., Engheta, N., Maci, S. & Alù, A. Omnidirectional metamaterial antennas based on ε-near-zero channel matching. IEEE Trans. Antennas Propag. 61, 3344 (2013).
  39. Shahmoon, E. & Kurizki, G. Nonradiative interaction and entanglement between distant atoms. Phys. Rev. A 87, 033831 (2013).
  40. Engheta, N., Salandrino, A. & Alù, A. Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors. Phys. Rev. Lett. 95, 095504 (2005).
  41. Engheta, N. Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials. Science 317, 16981702 (2007).
  42. Alù, A. & Engheta, N. All optical metamaterial circuit board at the nanoscale. Phys. Rev. Lett. 103, 143902 (2009).
  43. Alù, A. & Engheta, N. Optical 'shorting wires'. Opt. Express 15, 1377313782 (2007).
  44. Edwards, B. & Engheta, N. Experimental verification of displacement-current conduits in metamaterials-inspired optical circuitry. Phys. Rev. Lett. 108, 193902 (2012).
  45. Li, Y., Liberal, I., Della Giovampaola, C. & Engheta, N. Waveguide metatronics: lumped circuitry based on structural dispersion. Sci. Adv. 2, e1501790 (2016).
  46. Liu, R., Roberts, C. M., Zhong, Y., Podolskiy, V. A. & Wasserman, D. Epsilon-near-zero photonics wires. ACS Photon. 3, 10451052 (2016).
  47. Rodríguez-Fortuño, F. J., Vakil, A. & Engheta, N. Electric levitation using epsilon-near-zero metamaterials. Phys. Rev. Lett. 112, 033902 (2014).
  48. Lindell, I. V & Sihvola, A. H. Electromagnetic boundary and its realization with anisotropic metamaterial. Phys. Rev. E 79, 026604 (2009).
  49. Rumsey, V. Some new forms of Huygens' principle. IRE Trans. Antennas Propag. 7, 103116 (1959).
  50. Yaghjian, A. D. & Maci, S. Alternative derivation of electromagnetic cloaks and concentrators. New J. Phys. 10, 115022 (2008).
  51. von Neumann, J. & Wigner, E. Über merkwürdige diskrete eigenwerte. Phys. Z. 30, 465467 (1929).
  52. Capasso, F. et al. Observation of an electronic bound state above a potential well. Nature 358, 565567 (1992).
  53. Devaney, A. J. & Wolf, E. Radiating and nonradiating classical current distributions and the fields they generate. Phys. Rev. D 8, 10441047 (1973).
  54. Marengo, E. A. & Ziolkowski, R. W. On the radiating and nonradiating components of scalar, electromagnetic and weak gravitational sources. Phys. Rev. Lett. 83, 33453349 (1999).
  55. Marinica, D. C., Borisov, A. G. & Shabanov, S. V. Bound states in the continuum in photonics. Phys. Rev. Lett. 100, 183902 (2008).
  56. Lee, J. et al. Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs. Phys. Rev. Lett. 109, 067401 (2012).
  57. Erentok, A. & Ziolkowski, R. W. A hybrid optimization method to analyze metamaterial-based electrically small antennas. IEEE Trans. Antennas Propag. 55, 731741 (2007).
  58. Silveirinha, M. G. Trapping light in open plasmonic nanostructures. Phys. Rev. A 89, 023813 (2014).
  59. Monticone, F. & Alù, A. Embedded photonic eigenvalues in 3D nanostructures. Phys. Rev. Lett. 112, 213903 (2014).
  60. Lannebère, S. & Silveirinha, M. G. Optical meta-atom for localization of light with quantized energy. Nat. Commun. 6, 8766 (2015).
  61. Liberal, I., Mahmoud, A. M. & Engheta, N. Geometry-invariant resonant cavities. Nat. Commun. 7, 10989 (2016).
  62. Boyd, R. W. Nonlinear Optics (Academic, 2003).
  63. Shen, Y. R. The Principles of Nonlinear Optics (Wiley, 1984).
  64. Suchowski, H. et al. Phase mismatch—free nonlinear propagation in optical zero-index materials. Science 342, 12231226 (2013).
  65. Mattiucci, N., Bloemer, M. J. & D'Aguanno, G. Phase-matched second harmonic generation at the Dirac point of a 2-D photonic crystal. Opt. Express 22, 63816390 (2014).
  66. Powell, D. A. et al. Nonlinear control of tunneling through an epsilon-near-zero channel. Phys. Rev. B 79, 245135 (2009).
  67. Argyropoulos, C., Chen, P. Y., D'Aguanno, G., Engheta, N. & Alù, A. Boosting optical nonlinearities in ε-near-zero plasmonic channels. Phys. Rev. B 85, 045129 (2012).
  68. Argyropoulos, C., D'Aguanno, G. & Alù, A. Giant second-harmonic generation efficiency and ideal phase matching with a double ε-near-zero cross-slit metamaterial. Phys. Rev. B 89, 235401 (2014).
  69. Capretti, A., Wang, Y., Engheta, N. & Dal Negro, L. Enhanced third-harmonic generation in Si-compatible epsilon-near-zero indium tin oxide nanolayers. Opt. Lett. 40, 15001503 (2015).
  70. Capretti, A., Wang, Y., Engheta, N. & Dal Negro, L. Comparative study of second-harmonic generation from epsilon-near-zero indium tin oxide and titanium nitride nanolayers excited in the near-infrared spectral range. ACS Photon. 2, 15841591 (2015).
  71. Alam, M. Z., De Leon, I. & Boyd, R. W. Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region. Science 352, 795797 (2016).
  72. Caspani, L. et al. Enhanced nonlinear refractive index in ε-near-zero materials. Phys. Rev. Lett. 116, 233901 (2016).
  73. Vincenti, M. A., De Ceglia, D., Ciattoni, A. & Scalora, M. Singularity-driven second- and third-harmonic generation at epsilon-near-zero crossing points. Phys. Rev. A 84, 063826 (2011).
  74. Vassant, S., Hugonin, J.-P., Marquier, F. & Greffet, J.-J. Berreman mode and epsilon near zero mode. Opt. Express 20, 2397123977 (2012).
  75. Vassant, S. et al. Epsilon-near-zero mode for active optoelectronic devices. Phys. Rev. Lett. 109, 237401 (2012).
  76. Campione, S., Brener, I. & Marquier, F. Theory of epsilon-near-zero modes in ultrathin films. Phys. Rev. B 91, 121408(R) (2015).
  77. Jun, Y. C. et al. Epsilon-near-zero strong coupling in metamaterial–semiconductor hybrid structures. Nano Lett. 13, 53915396 (2013).
  78. Campione, S. et al. Epsilon-near-zero modes for tailored light–matter interaction. Phys. Rev. Appl. 4, 044011 (2015).
  79. Molesky, S., Dewalt, C. J. & Jacob, Z. High temperature epsilon-near-zero and epsilon-near-pole metamaterial emitters for thermophotovoltaics. Opt. Express 21, A96A110 (2013).
  80. Ciattoni, A., Marini, A., Rizza, C., Scalora, M. & Biancalana, F. Polariton excitation in epsilon-near-zero slabs: transient trapping of slow light. Phys. Rev. A 87, 053853 (2013).
  81. Ciattoni, A., Rizza, C. & Palange, E. Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity. Phys. Rev. A 81, 043839 (2010).
  82. Krauss, T. F. Why do we need slow light? Nat. Photon. 2, 448450 (2008).
  83. Boyd, R. W. Slow and fast light: fundamentals and applications. J. Mod. Opt. 56, 19081915 (2009).
  84. Rizza, C., Ciattoni, A. & Palange, E. Two-peaked and flat-top perfect bright solitons in nonlinear metamaterials with epsilon near zero. Phys. Rev. A 83, 053805 (2011).
  85. Marini, A. & Garcia de Abajo, F. J. Self-organization of frozen light in near-zero-index media with cubic nonlinearity. Sci. Rep. 6, 20088 (2016).
  86. Tretyakov, S. A., Nefedov, I. S., Sihvola, A. H., Maslovski, S. & Simovski, C. R. Waves and energy in chiral nihility. J. Electromagn. Waves Appl. 17, 695706 (2003).
  87. Davoyan, A. R. & Engheta, N. Theory of wave propagation in magnetized near-zero-epsilon metamaterials: evidence for one-way photonic states and magnetically switched transparency and opacity. Phys. Rev. Lett. 111, 257401 (2013).
  88. Haldane, F. & Raghu, S. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett. 100, 013904 (2008).
  89. Wang, Z., Chong, Y., Joannopoulos, J. D. & Soljačić, M. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772775 (2009).
  90. Rechtsman, M. C. et al. Photonic floquet topological insulators. Nature 496, 196200 (2013).
  91. Lumer, Y., Plotnik, Y., Rechtsman, M. C. & Segev, M. Self-localized states in photonic topological insulators. Phys. Rev. Lett. 111, 243905 (2013).
  92. Lu, L., Joannopoulos, J. D. & Soljačić, M. Topological photonics. Nat. Photon. 8, 821829 (2014).
  93. Davoyan, A. R., Mahmoud, A. & Engheta, N. Optical isolation with epsilon-near-zero metamaterials. Opt. Express 21, 32793286 (2013).
  94. Belov, P. A. et al. Strong spatial dispersion in wire media in the very large wavelength limit. Phys. Rev. B 67, 113103 (2003).
  95. Pollard, R. J. et al. Optical nonlocalities and additional waves in epsilon-near-zero metamaterials. Phys. Rev. Lett. 102, 127405 (2009).
  96. Krishnamoorthy, H. N. S., Jacob, Z., Narimanov, E. E., Kretzschmar, I. & Menon, V. M. Topological transitions in metamaterials. Science 336, 205209 (2012).
  97. Smith, D. R., Schurig, D., Mock, J. J., Kolinko, P. & Rye, P. Partial focusing of radiation by a slab of indefinite media. Appl. Phys. Lett. 84, 22442246 (2004).
  98. Poddubny, A. N., Iorsh, I., Belov, P. A. & Kivshar, Y. Hyperbolic metamaterials. Nat. Photon. 7, 958967 (2013).
  99. Hoffman, A. J. et al. Negative refraction in semiconductor metamaterials. Nat. Mater. 6, 946950 (2007).
  100. Yao, J. et al. Optical negative refraction in bulk metamaterials of nanowires. Science 321, 930 (2008).
  101. Fang, A., Koschny, T. & Soukoulis, C. M. Optical anisotropic metamaterials: negative refraction and focusing. Phys. Rev. B 79, 245127 (2009).
  102. Liu, Y., Bartal, G. & Zhang, X. All-angle negative refraction and imaging in a bulk medium made of metallic nanowires in the visible region. Opt. Express 16, 1543915448 (2008).
  103. Salandrino, A. & Engheta, N. Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations. Phys. Rev. B 74, 075103 (2006).
  104. Jacob, Z., Alekseyev, L. V & Narimanov, E. E. Optical hyperlens: far-field imaging beyond the diffraction limit. Opt. Express 14, 82478256 (2006).
  105. Liu, Z., Lee, H., Xiong, Y., Sun, C. & Zhang, X. Far-field optical hyperlens magnifying sub-diffraction-limited objects. Science 315, 1686 (2007).
  106. Smolyaninov, I. I., Hung, Y. J. & Davis, C. C. Magnifying superlens in the visible frequency range. Science 315, 16991701 (2007).
  107. Belov, P. A., Simovski, C. R. & Ikonen, P. M. T. Canalization of subwavelength images by electromagnetic crystals. Phys. Rev. B 71, 193105 (2005).
  108. Belov, P. A., Hao, Y. & Sudhakaran, S. Subwavelength microwave imaging using an array of parallel conducting wires as a lens. Phys. Rev. B 73, 033108 (2006).
  109. Anderegg, M., Feuerbacher, B. & Fitton, B. Optically excited longitudinal plasmons in potassium. Phys. Rev. Lett. 27, 15651568 (1971).
  110. Spitzer, W. G., Kleinman, D. & Walsh, D. Infrared properties of hexagonal silicon carbide. Phys. Rev. 113, 127132 (1959).
  111. Korobkin, D., Urzhumov, Y. & Shvets, G. Enhanced near-field resolution in midinfrared using metamaterials. J. Opt. Soc. Am. B 23, 468478 (2006).
  112. Caldwell, J. D. et al. Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons. Nanophotonics 4, 4468 (2015).
  113. Kim, J. et al. Role of epsilon-near-zero substrates in the optical response of plasmonic antennas. Optica 3, 339346 (2016).
  114. Naik, G. V., Kim, J. & Boltasseva, A. Oxides and nitrides as alternative plasmonic materials in the optical range. Opt. Mater. Express 1, 10901099 (2011).
  115. Naik, G. V., Shalaev, V. M. & Boltasseva, A. Alternative plasmonic materials: beyond gold and silver. Adv. Mater. 25, 32643294 (2013).
  116. Kinsey, N. et al. Epsilon-near-zero Al-doped ZnO for ultrafast switching at telecom wavelengths. Optica 2, 616622 (2015).
  117. Ou, J. Y. et al. Ultraviolet and visible range plasmonics of a topological insulator. Nat. Commun. 5, 5139 (2014).
  118. Khurgin, J. B. How to deal with the loss in plasmonics and metamaterials. Nat. Nanotech. 10, 26 (2015).
  119. Brown, J. Artificial dielectrics having refractive indices less than unity. Proc. IEEE 100, 5162 (1953).
  120. Rotman, W. Plasma simulation by artificial dielectrics and parallel-plate media. IRE Trans. Antennas Propag. 10, 1719 (1962).
  121. King, R. J., Thiel, D. V. & Park, K. S. The synthesis of surface reactance using an artificial dielectric. IEEE Trans. Antennas Propag. 31, 471476 (1983).
  122. Della Giovampaola, C. & Engheta, N. Plasmonics without negative dielectrics. Phys. Rev. B 93, 195152 (2016).
  123. Pendry, J. B., Holden, A. J., Stewart, W. J. & Youngs, I. Extremely low frequency plasmons in metallic mesostructures. Phys. Rev. Lett. 76, 47734776 (1996).
  124. Moses, C. A. & Engheta, N. Electromagnetic wave propagation in the wire medium: a complex medium with long thin inclusions. Wave Motion 34, 301317 (2001).
  125. Belov, P. A., Tretyakov, S. A. & Viitanen, A. Dispersion and reflection properties of artificial media formed by regular lattices of ideally conducting wires. J. Electromagn. Waves Appl. 16, 11531170 (2002).
  126. Maslovski, S. I., Tretyakov, S. A. & Belov, P. A. Wire media with negative effective permittivity: a quasi-static model. Microw. Opt. Technol. Lett. 35, 4751 (2002).
  127. Smith, D. R., Padilla, W. J., Vier, D. C., Nemat-Nasser, S. C. & Schultz, S. Composite medium with simultaneously negative permeability and permittivity. Phys. Rev. Lett. 84, 184184 (2000).
  128. Maas, R., Parsons, J., Engheta, N. & Polman, A. Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths. Nat. Photon. 7, 907912 (2013).
  129. Wu, Y., Li, J., Zhang, Z. Q. & Chan, C. T. Effective medium theory for magnetodielectric composites: beyond the long-wavelength limit. Phys. Rev. B 74, 085111 (2006).
  130. Moitra, P. et al. Realization of an all-dielectric zero-index optical metamaterial. Nat. Photon. 7, 791795 (2013).
  131. Li, Y. et al. On-chip zero-index metamaterials. Nat. Photon. 9, 738742 (2015).
  132. Li, J., Zhou, L., Chan, C. T. & Sheng, P. Photonic band gap from a stack of positive and negative index materials. Phys. Rev. Lett. 90, 083901 (2003).
  133. Zhou, L., Song, Z., Huang, X. & Chan, C. T. Physics of the zero-n photonic gap: fundamentals and latest developments. Nanophotonics 1, 181198 (2012).
  134. Ziolkowski, R. W. & Heyman, E. Wave propagation in media having negative permittivity and permeability. Phys. Rev. E 64, 056625 (2001).
  135. Javani, M. H. & Stockman, M. I. Real and imaginary properties of epsilon-near-zero materials. Phys. Rev. Lett. 117, 107404 (2016).

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  1. Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

    • Iñigo Liberal &
    • Nader Engheta

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The authors declare no competing financial interests.

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