The Fano resonance in plasmonic nanostructures and metamaterials

Journal name:
Nature Materials
Volume:
9,
Pages:
707–715
Year published:
DOI:
doi:10.1038/nmat2810
Published online

Abstract

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

Figures

  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.

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Affiliations

  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

Contributions

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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