The Fano resonance in plasmonic nanostructures and metamaterials

Journal name:
Nature Materials
Year published:
Published online


Since its discovery, the asymmetric Fano resonance has been a characteristic feature of interacting quantum systems. The shape of this resonance is distinctively different from that of conventional symmetric resonance curves. Recently, the Fano resonance has been found in plasmonic nanoparticles, photonic crystals, and electromagnetic metamaterials. The steep dispersion of the Fano resonance profile promises applications in sensors, lasing, switching, and nonlinear and slow-light devices.

At a glance


  1. Trajectories of the three first optical electric resonances a[lambda].
    Figure 1: Trajectories of the three first optical electric resonances aλ.

    The lower (solid) branches present the narrow surface plasmon modes and upper (dashed) branches present the broad volume Mie resonances. These two branches converge at certain negative values of ε, for example, at ε −5 and q 1.2 for the dipole resonance λ = 1. Insets show plots of dipole (red) and quadrupole resonances (blue) versus size parameter at ε −2.1 and a three-dimensional plot of quadrupole λ = 2 electric amplitude on the plane of parameters {ε, q}.

  2. Mie scattering against a solid metallic sphere.
    Figure 2: Mie scattering against a solid metallic sphere.

    Radar back scattering (RBS; red) and forward scattering (FS; blue) cross-sections versus normalized frequency ω/ωp. The dielectric permittivity ε is described by the Drude formula, γ/ωp = 10−3 (weak dissipation), where ωp is the plasma frequency and γ is the collision frequency. Parameter q = ωpa/c = 0.7. Calculations using equation (3) and the simplified equation (4) differ less than the thickness of the lines. Inset shows polar scattering diagrams in the x–z plane (azimuthal angle φ = 0 in Mie theory) near the quadrupole resonance of a plasmonic particle. Red lines shows linearly polarized light; blue lines represent non-polarized light.

  3. Higher-order multipolar Fano resonances in Mie scattering against a solid metallic sphere.
    Figure 3: Higher-order multipolar Fano resonances in Mie scattering against a solid metallic sphere.

    a, Radar back scattering (red) and forward scattering (blue) cross-sections calculated using equation (3) versus normalized frequency ω/ωp. The dielectric permittivity ε is described by the Drude formula, γ/ωp = 10−3. The size parameter q = ωpa/c = 1.7. b, Magnetic Fano resonance for a particle with negative μ, ε = 1 and size parameter q = 0.7. c,d, Contour plots of radar back scattering (c) and forward scattering (d) cross-sections in the vicinity of electric and magnetic quadrupole on the plane {ε, μ} parameters in the material with negative refractive index. The size parameter (q) is equal to 0.7. The insets shows corresponding three-dimensional plots.

  4. Extinction spectra of non-concentric ring/disk cavity and a plasmonic dolmen structure.
    Figure 4: Extinction spectra of non-concentric ring/disk cavity22 and a plasmonic dolmen structure25.

    a,b, Effect on extinction spectrum of partial (a) and complete (b) filling of the cavity (yellow areas in the inset) with a dielectric medium of permittivity 1 (black solid), 1.5 (blue dashed) and 3 (red dotted). The structure is placed on a glass substrate modelled using a permittivity of 2.04. Note that the wavelength scale is different in the two panels. c, Experimentally observed single-dolmen structure extinction spectra for the two polarizations indicated in the inset. d, Numerically calculated extinction spectra. e, Surface charge distribution for the two Fano resonances in the extinction spectrum for perpendicular polarization and for the extinction peak for parallel polarization. f, Measured extinction spectra as the polarization of the incoming light beam is continuously rotated between the two principal directions. Figure reproduced with permission from ref. 22: a,b, © 2008 ACS; ref. 25: cf, © 2009 ACS.

  5. Fano resonances in plasmonic nanoparticle clusters.
    Figure 5: Fano resonances in plasmonic nanoparticle clusters.

    a, Calculated dipole amplitudes of the bonding and antibonding collective dipolar plasmon modes in a gold nanoshell heptamer73. b,c, Measured (b) and calculated (c) scattering spectra of a gold nanoshell heptamer73. d, Transmission spectra showing the effects of coupling in lithographically fabricated gold nanodisk heptamers74. e, Extinction spectra showing how the Fano resonance in silver nanosphere hexamers and octumers depend on the size of the central particle75. f, Effect of a surrounding dielectric medium on the extinction spectrum of a silver nanosphere heptamer. g, Example of a large-scale substrate consisting of lithographically fabricated gold nanodisk heptamers74. Scale bar: 1 μm. Figure reproduced with permission from ref. 73: ac, © 2010 AAAS; ref. 74: d,g, © 2010 ACS; ref. 75: e, © 2010 Springer; ref. 24: f, © 2010 ACS.

  6. Fano resonances in a metallic photonic crystal, consisting of a gold nanowire grating on a single-mode indium tin oxide (ITO) slab waveguide, in which the light is incident normal to the structure.
    Figure 6: Fano resonances in a metallic photonic crystal, consisting of a gold nanowire grating on a single-mode indium tin oxide (ITO) slab waveguide, in which the light is incident normal to the structure.

    a, Extinction in TE polarization (E-field parallel to the gold wires). A single Fano resonance owing to grating coupling into the waveguide is visible. b, Extinction in TM polarization (E-field perpendicular to the wires). Two polariton branches that exhibit a Fano lineshape owing to the coupling of the narrow waveguide resonance to the broad particle plasmon in the gold wires are visible.

  7. Fano resonances in metamaterials.
    Figure 7: Fano resonances in metamaterials.

    a,b, In a microwave metamaterial — an array of wire asymmetric split rings (a) — Fano reflection resonance (b) is formed by the interference of the high-Q magnetic dipole mode of excitation (II) and low-Q electric dipole modes (I and III)30. Black arrows indicate instantaneous directions of the current flow. c, A photonic Fano metamaterial, in the form of an array of asymmetric slits in a gold film manufactured by focused ion beam. This structure is complementary to a and is simplified for nanofabrication. d, A unit cell of such a photonic metamaterial functionalized with a 'nanoscale feature' of single-walled carbon nanotubes and imaged with a helium-ion microscope shows enhanced ultrafast nonlinear response owing to plasmon–exciton coupling89. e, Conceptual design of the lasing spaser83, a lasing device fuelled by plasmonic oscillations at the Fano resonance. Figure reproduced with permission from ref. 30: a,b, © 2007 APS; ref. 89: c,d, © 2010 APS; ref. 83: e, © 2008 NPG.

  8. EIT in metamaterials.
    Figure 8: EIT in metamaterials.

    a, Scanning electron microscope image of the stacked plasmonic EIT analogue structure. The red colour represents the gold bar in the top layer and the green colour represents the gold wire pair in the bottom layer. Inset: enlarged view. b, Experimental transmittance spectrum of the sample. The fitting curve was calculated from a Fano-type EIT model simulation. Figure reproduced with permission from ref. 28: a, © 2009 NPG.


  1. Rabinovitch, M. I. & Trubetskov, D. I. Oscillations and Waves in Linear and Nonlinear Systems (Kluwer Academic Publishers, 1989).
  2. Fano, U. Effects of configuration interaction on intensities and phase shifts. Phys. Rev. 124, 18661878 (1961).
  3. Miroshnichenko, A. E., Flach, S. & Kivshar, Y. S. Fano resonances in nanoscale structures. Preprint at (2009).
  4. Luo, H. G., Xiang, T., Wang, X. Q., Su, Z. B. & Yu, L. Fano resonance for Anderson impurity systems. Phys. Rev. Lett. 92, 256602 (2004).
  5. Johnson, A. C., Marcus, C. M., Hanson, M. P. & Gossard, A. C. Coulomb-modified Fano resonance in a one-lead quantum dot. Phys. Rev. Lett. 93, 106803 (2004).
  6. Kobayashi, K., Aikawa, H., Sano, A., Katsumoto, S. & Iye, Y. Fano resonance in a quantum wire with a side-coupled quantum dot. Phys. Rev. B 70, 035319 (2004).
  7. Hessel, A. & Oliner, A. A. A new theory of Wood's anomalies on optical gratings. Appl. Opt. 4, 12751297 (1965).
  8. Sarrazin, M., Vigneron, J. P. & Vigoureux, J. M. Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes. Phys. Rev. B 67, 085415 (2003).
  9. Lee, H-T. & Poon, A. W. Fano resonances in prism-coupled square micropillars. Opt. Lett. 29, 57 (2004).
  10. Rybin, M. V. et al. Fano resonance between Mie and Bragg scattering in photonic crystals. Phys. Rev. Lett. 103, 023901 (2009).
  11. Fan, S. H. Sharp asymmetric line shapes in side-coupled waveguide-cavity systems. Appl. Phys. Lett. 80, 908910 (2002).
  12. Fan, S. H. & Joannopoulos, J. D. Analysis of guided resonances in photonic crystal slabs. Phys. Rev. B 65, 235112 (2002).
  13. Genet, C., van Exter, M. P. & Woerdman, J. P. Fano-type interpretation of red shifts and red tails in hole array transmission spectra. Opt. Commun. 225, 331336 (2003).
  14. Fan, S. H., Suh, W. & Joannopoulos, J. D. Temporal coupled-mode theory for the Fano resonance in optical resonators. J. Opt. Soc. Am. A 20, 569572 (2003).
  15. Christ, A., Tikhodeev, S. G., Gippius, N. A., Kuhl, J. & Giessen, H. Waveguide-plasmon polaritons: Strong coupling of photonic and electronic resonances in a metallic photonic crystal slab. Phys. Rev. Lett. 91, 183901 (2003).
  16. Christ, A. et al. Optical properties of planar metallic photonic crystal structures: Experiment and theory. Phys. Rev. B 70, 125113 (2004).
  17. Sarrazin, M. & Vigneron, J-P. Bounded modes to the rescue of optical transmission. Europhys. News 38, 2731 (2007).
  18. Catrysse, P. B. & Fan, S. H. Near-complete transmission through subwavelength hole arrays in phonon-polaritonic thin films. Phys. Rev. B 75, 075422 (2007).
  19. Ruan, Z. & Fan, S. Temporal coupled-mode theory for Fano resonance in light scattering by a single obstacle. J. Phys. Chem. C 114, 73247329 (2009).
  20. Tribelsky, M. I., Flach, S., Miroshnichenko, A. E., Gorbach, A. V. & Kivshar, Y. S. Light scattering by a finite obstacle and Fano resonances. Phys. Rev. Lett. 100, 043903 (2008).
  21. Miroshnichenko, A. E. et al. Fano resonances: A discovery that was not made 100 years ago. Opt. Phot. News 19, 48 (2008).
  22. Hao, F. et al. Symmetry breaking in plasmonic nanocavities: Subradiant LSPR sensing and a tunable Fano resonance. Nano Lett. 8, 39833988 (2008).
  23. Hao, F., Nordlander, P., Sonnefraud, Y., Van Dorpe, P. & Maier, S. A. Tunability of subradiant dipolar and Fano-type plasmon resonances in metallic ring/disk cavities: Implications for nanoscale optical sensing. ACS Nano 3, 643652 (2009).
  24. Mirin, N. A., Bao, K. & Nordlander, P. Fano resonances in plasmonic nanoparticle aggregates. J. Phys. Chem. A 113, 40284034 (2009).
  25. Verellen, N. et al. Fano resonances in individual coherent plasmonic nanocavities. Nano Lett. 9, 16631667 (2009).
  26. Maier, S. A. The benefits of darkness. Nature Mater. 8, 699700 (2009).
  27. Sonnefraud, Y. et al. Experimental realization of subradiant, superradiant, and Fano resonances in ring/disk plasmonic nanocavities. ACS Nano 4, 16641670 (2010).
  28. Liu, N. et al. Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit. Nature Mater. 8, 758762 (2009).
  29. Shvets, G. & Urzhumov, Y. A. Engineering the electromagnetic properties of periodic nanostructures using electrostatic resonances. Phys. Rev. Lett. 93, 243902 (2004).
  30. Fedotov, V. A., Rose, M., Prosvirnin, S. L., Papasimakis, N. & Zheludev, N. I. Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry. Phys. Rev. Lett. 99, 147401 (2007).
  31. Christ, A. et al. Controlling the Fano interference in a plasmonic lattice. Phys. Rev. B 76, 201405 (2007).
  32. Auguié, B. & Barnes, W. L. Collective resonances in gold nanoparticle arrays. Phys. Rev. Lett. 101, 143902 (2008).
  33. Bachelier, G. et al. Fano profiles induced by near-field coupling in heterogeneous dimers of gold and silver nanoparticles. Phys. Rev. Lett. 101, 197401 (2008).
  34. Le, F. et al. Metallic nanoparticle arrays: A common substrate for both surface-enhanced Raman scattering and surface-enhanced infrared absorption. ACS Nano 2, 707718 (2008).
  35. Yan, J-Y., Zhang, W., Duan, S., Zhao, X-G. & Govorov, A. O. Optical properties of coupled metal-semiconductor and metal-molecule nanocrystal complexes: Role of multipole effects. Phys. Rev. B 77, 165301 (2008).
  36. Kivshar, Y. S. Nonlinear optics: The next decade. Opt. Express 16, 2212622128 (2008).
  37. Ekinci, Y. et al. Electric and magnetic resonances in arrays of coupled gold nanoparticle in-tandem pairs. Opt. Express 16, 1328713295 (2008).
  38. Neubrech, F. et al. Resonant plasmonic and vibrational coupling in a tailored nanoantenna for infrared detection. Phys. Rev. Lett. 101, 157403 (2008).
  39. Nygaard, N., Piil, R. & Mølmer, K. Feshbach molecules in a one-dimensional optical lattice. Phys. Rev. A 77, 021601 (2008).
  40. Pistolesi, F., Blanter, Y. M. & Martin, I. Self-consistent theory of molecular switching. Phys. Rev. B 78, 085127 (2008).
  41. Cho, D. J., Wang, F., Zhang, X. & Shen, Y. R. Contribution of the electric quadrupole resonance in optical metamaterials. Phys. Rev. B 78, 121101 (2008).
  42. Christ, A., Martin, O. J. F., Ekinci, Y., Gippius, N. A. & Tikhodeev, S. G. Symmetry breaking in a plasmonic metamaterial at optical wavelength. Nano Lett. 8, 21712175 (2008).
  43. Petschulat, J. et al. Multipole approach to metamaterials. Phys. Rev. A 78, 043811 (2008).
  44. Naether, U., Rivas, D. E., Larenas, M. A., Molina, M. I. & Vicencio, R. A. Fano resonances in waveguide arrays with saturable nonlinearity. Opt. Lett. 34, 27212723 (2009).
  45. Chen, C-Y., Un, I-W., Tai, N-H. & Yen, T-J. Asymmetric coupling between subradiant and superradiant plasmonic resonances and its enhanced sensing performance. Opt. Express 17, 1537215380 (2009).
  46. Cubukcu, E., Zhang, S., Park, Y. S., Bartal, G. & Zhang, X. Split ring resonator sensors for infrared detection of single molecular monolayers. Appl. Phys. Lett. 95, 043113 (2009).
  47. Kanté, B., de Lustrac, A. & Lourtioz, J. M. In-plane coupling and field enhancement in infrared metamaterial surfaces. Phys. Rev. B 80, 035108 (2009).
  48. Miroshnichenko, A. E. et al. Dynamics and instability of nonlinear Fano resonances in photonic crystals. Phys. Rev. A 79, 013809 (2009).
  49. Liu, N. et al. Planar metamaterial analogue of electromagnetically induced transparency for plasmonic sensing. Nano Lett. 10, 11031107 (2010).
  50. Miroshnichenko, A. E. Non-rayleigh limit of the lorenz-Mie solution and suppression of scattering by spheres of negative refractive index. Phys. Rev. A 80, 013808 (2009).
  51. Miroshnichenko, A. E. Instabilities and quasi-localized states in nonlinear Fano-like systems. Phys. Lett. A 373, 35863590 (2009).
  52. Miroshnichenko, A. E. Nonlinear Fano-Feshbach resonances. Phys. Rev. E 79, 026611 (2009).
  53. Pakizeh, T., Langhammer, C., Zoric, I., Apell, P. & Käll, M. Intrinsic Fano interference of localized plasmons in Pd nanoparticles. Nano Lett. 9, 882886 (2009).
  54. Pakizeh, T. & Käll, M. Unidirectional ultracompact optical nanoantennas. Nano Lett. 9, 23432349 (2009).
  55. Parsons, J. et al. Localized surface-plasmon resonances in periodic nondiffracting metallic nanoparticle and nanohole arrays. Phys. Rev. B 79, 073412 (2009).
  56. Li, Z-P., Shegai, T., Haran, G. & Xu, H-X. Multiple-particle nanoantennas for enormous enhancement and polarization control of light emission. ACS Nano 3, 637642 (2009).
  57. Papasimakis, N. & Zheludev, N. I. Metamaterial-induced transparency: Sharp Fano resonances and slow light. Opt. Phot. News 20, 2227 (2009).
  58. Urzhumov, Y. A., Korobkin, D., Neuner, B., Zorman, C. & Shvets, G. Optical properties of sub-wavelength hole arrays in SiC membranes. J. Opt. A 9, S322S333 (2007).
  59. Ebbesen, T. W., Lezec, H. J., Ghaemi, H. F., Thio, T. & Wolff, P. A. Extraordinary optical transmission through sub-wavelength hole arrays. Nature 391, 667669 (1998).
  60. Garcia-Vidal, F. J., Martin-Moreno, L., Ebbesen, T. W. & Kuipers, L. Light passing through subwavelength apertures. Rev. Mod. Phys. 82, 729787 (2010).
  61. Stockman, M. I., Faleev, S. V. & Bergman, D. J. Localization versus delocalization of surface plasmons in nanosystems: Can one state have both characteristics? Phys. Rev. Lett. 87, 167401 (2001).
  62. Born, M. & Wolf, E. Principles of Optics 7th edn (Cambridge Univ. Press, 1999).
  63. Bohren, C. F. & Huffman, D. R. Absorption and Scattering of Light by Small Particles (Wiley, 1998).
  64. Tribelsky, M. I. & Luk'yanchuk, B. S. Anomalous light scattering by small particles. Phys. Rev. Lett. 97, 263902 (2006).
  65. Luk'yanchuk, B. S. et al. Peculiarities of light scattering by nanoparticles and nanowires near plasmon resonance frequencies in weakly dissipating materials. J. Opt. A 9, S294S300 (2007).
  66. Bystrov, A. M. & Gildenburg, V. B. Dipole resonances of an ionized cluster. J. Exp. Theor. Phys. 100, 428439 (2005).
  67. Wang, Z. B., Luk'yanchuk, B. S., Hong, M. H., Lin, Y. & Chong, T. C. Energy flow around a small particle investigated by classical Mie theory. Phys. Rev. B 70, 035418 (2004).
  68. Luk'yanchuk, B. S. et al. Extraordinary scattering diagram for nanoparticles near plasmon resonance frequencies. Appl. Phys. A 89, 259264 (2007).
  69. Luk'yanchuk, B. S. & Qiu, C-W. Enhanced scattering efficiencies in spherical particles with weakly dissipating anisotropic materials. Appl. Phys. A 92, 773776 (2008).
  70. Brown, L. V., Sobhani, H., Lassiter, J. B., Nordlander, P. & Halas, N. J. Heterodimers: Plasmonic properties of mismatched nanoparticle pairs. ACS Nano 4, 819832 (2010).
  71. Hu, Y., Noelck, S. J. & Drezek, R. A. Symmetry breaking in gold-silica-gold multilayer nanoshells. ACS Nano 4, 15211528 (2010).
  72. Zhang, S., Genov, D. A., Wang, Y., Liu, M. & Zhang, X. Plasmon-induced transparency in metamaterials. Phys. Rev. Lett. 101, 047401 (2008).
  73. Fan, J. A. et al. Self-assembled plasmonic nanoparticle clusters. Science 328, 11351138 (2010).
  74. Hentschel, M. et al. Transition from isolated to collective modes in plasmonic oligomers. Nano Lett. 10, 27212726 (2010).
  75. Bao, K., Mirin, N. & Nordlander, P. Fano resonances in planar silver nanosphere clusters. Appl. Phys. A 100, 333339 (2010).
  76. Zentgraf, T., Christ, A., Kuhl, J. & Giessen, H. Tailoring the ultrafast dephasing of quasiparticles in metallic photonic crystals. Phys. Rev. Lett. 93, 243901 (2004).
  77. Klein, M. W., Tritschler, T., Wegener, M. & Linden, S. Lineshape of harmonic generation by metallic nanoparticles and metallic photonic crystal slabs. Phys. Rev. B 72, 115113 (2005).
  78. Nau, D. et al. Correlation effects in disordered metallic photonic crystal slabs. Phys. Rev. Lett. 98, 133902 (2007).
  79. Plum, E. et al. Metamaterials: Optical activity without chirality. Phys. Rev. Lett. 102, 113902 (2009).
  80. Papasimakis, N. et al. Metamaterial with polarization and direction insensitive resonant transmission response mimicking electromagnetically induced transparency. Appl. Phys. Lett. 94, 211902 (2009).
  81. Fedotov, V. A. et al. Temperature control of Fano resonances and transmission in superconducting metamaterials. Opt. Express 18, 90159019 (2010).
  82. Fedotov, V. A. et al. Spectral collapse in ensembles of meta-molecules. Phys. Rev. Lett. 104, 223901 (2010).
  83. Zheludev, N. I., Prosvirnin, S. L., Papasimakis, N. & Fedotov, V. A. Lasing spaser. Nature Photon. 2, 351354 (2008).
  84. Debus, C. & Bolivar, P. H. Terahertz biosensors based on double split ring arrays. Proc. SPIE 6987, 6987OU (2008).
  85. Lahiri, B., Khokhar, A. Z., De La Rue, R. M., McMeekin, S. G. & Johnson, N. P. Asymmetric split ring resonators for optical sensing of organic materials. Opt. Express 17, 11071115 (2009).
  86. Papasimakis, N. et al. Graphene in a photonic metamaterial. Opt. Express 18, 83538359 (2010).
  87. Dicken, M. J. et al. Frequency tunable near-infrared metamaterials based on VO2 phase transition. Opt. Express 17, 1833018339 (2009).
  88. Sámson, Z. L. et al. Metamaterial electro-optic switch of nanoscale thickness. Appl. Phys. Lett. 96, 143105 (2010).
  89. Nikolaenko, A. E. et al. Carbon nanotubes in a photonic metamaterial. Phys. Rev. Lett. 104, 153902 (2010).
  90. Maier, S. A. et al. Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides. Nature Mater. 2, 229232 (2003).
  91. Kawata, S., Ono, A. & Verma, P. Subwavelength colour imaging with a metallic nanolens. Nature Photon. 2, 438442 (2008).
  92. Liu, M., Lee, T-W., Gray, S. K., Guyot-Sionnest, P. & Pelton, M. Excitation of dark plasmons in metal nanoparticles by a localized emitter. Phys. Rev. Lett. 102, 107401 (2009).

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Author information


  1. Data Storage Institute, Agency for Science, Technology and Research, DSI Building, 5 Engineering Drive 1, Singapore 117608, Singapore

    • Boris Luk'yanchuk &
    • Chong Tow Chong
  2. Optoelectronics Research Centre, University of Southampton, Southampton SO17 1BJ, UK

    • Nikolay I. Zheludev
  3. Physics Department, Imperial College London, South Kensington, London SW7 2AZ, UK

    • Stefan A. Maier
  4. Department of Electrical and Computer Engineering, Rice University, Houston, Texas 77005-1892, USA

    • Naomi J. Halas
  5. Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA

    • Peter Nordlander
  6. 4th Physics Institute, University of Stuttgart, D-70569 Stuttgart, Germany

    • Harald Giessen
  7. Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576, Singapore.

    • Chong Tow Chong


B.L. and C.T.C. initiated the section The Fano resonance'. N.I.Z. initiated the section 'Fano resonances in metamaterials'. S.A.M., N.J.H. and P.N. initiated the section 'Fano resonances in plasmonic nanostructures'. H.G. initiated the sections 'Fano resonances in metallic photonic crystals' and 'Plasmon-induced transparency in metamaterials'. All authors contributed equally to the 'Applications' section and to editing. B.L., P.N. and N.J.H. carried out the main final edits.

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