Abstract

We reveal that the resonant Mie scattering by high-index dielectric nanoparticles can be presented through cascades of Fano resonances. We employ the exact solution of Maxwell’s equations and demonstrate that the Lorenz-Mie coefficients of the Mie problem can be expressed generically as infinite series of Fano functions as they describe interference between the background radiation originated from an incident wave and narrow-spectrum Mie scattering modes that lead to Fano resonances.

© 2013 Optical Society of America

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  3. P. Garcia, M. Ibisate, R. Sapienza, D. Wiersma, and C. López, “Mie resonances to tailor random lasers,” Phys. Rev. A80, 013833 (2009).
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  4. M. V. Rybin, P. V. Kapitanova, D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, Y. S. Kivshar, and M. F. Limonov, “Fano resonances in antennas: General control over radiation patterns,” Phys. Rev. B88, 205106 (2013).
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    [CrossRef]
  11. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev.124, 1866–1878 (1961).
    [CrossRef]
  12. V. Madhavan, W. Chen, T. Jamneala, M. F. Crommie, and N. S. Wingreen, “Tunneling into a single magnetic atom: Spectroscopic evidence of the Kondo resonance,” Science280, 567–569 (1998).
    [CrossRef] [PubMed]
  13. M. F. Limonov, A. I. Rykov, S. Tajima, and A. Yamanaka, “Raman scattering study on fully oxygenated YBa2CuO7single crystals: x-y anisotropy in the superconductivity-induced effects,” Phys. Rev. Lett.80, 825–828 (1998).
    [CrossRef]
  14. M. Limonov, S. Lee, S. Tajima, and A. Yamanaka, “Superconductivity-induced resonant raman scattering in multilayer high-Tc superconductors,” Phys. Rev. B66, 054509 (2002).
    [CrossRef]
  15. M. I. Tribelsky, S. Flach, A. E. Miroshnichenko, A. V. Gorbach, and Y. S. Kivshar, “Light scattering by a finite obstacle and Fano resonances,” Phys. Rev. Lett.100, 043903 (2008).
    [CrossRef] [PubMed]
  16. M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg scattering in photonic crystals,” Phys. Rev. Lett.103, 023901 (2009).
    [CrossRef] [PubMed]
  17. M. V. Rybin, A. B. Khanikaev, M. Inoue, A. K. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Bragg scattering induces Fano resonance in photonic crystals,” Photonics Nanostruct. Fundam. Appl.8, 86–93 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  21. A. N. Poddubny, M. V. Rybin, M. F. Limonov, and Y. S. Kivshar, “Fano interference governs wave transport in disordered systems,” Nat. Commun.3, 914 (2012).
    [CrossRef] [PubMed]
  22. A. E. Miroshnichenko and Y. S. Kivshar, “Fano resonances in all-dielectric oligomers,” Nano Lett.12, 6459–6463 (2012).
    [CrossRef] [PubMed]
  23. Y. Francescato, V. Giannini, and S. A. Maier, “Plasmonic systems unveiled by Fano resonances,” ACS Nano6, 1830–1838 (2012).
    [CrossRef] [PubMed]
  24. M. Tribelsky, A. Miroshnichenko, and Y. Kivshar, “Unconventional Fano resonances in light scattering by small particles,” Europhys. Lett.97, 44005 (2012).
    [CrossRef]
  25. C. P. Burrows and W. L. Barnes, “Large spectral extinction due to overlap of dipolar and quadrupolar plasmonic modes of metallic nanoparticles in arrays,” Opt. Express18, 3187–3198 (2010).
    [CrossRef] [PubMed]
  26. J.-P. Connerade and A. M. Lane, “Interacting resonances in atomic spectroscopy,” Rep. Prog. Phys.51, 1439–1478 (1988).
    [CrossRef]

2013 (1)

M. V. Rybin, P. V. Kapitanova, D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, Y. S. Kivshar, and M. F. Limonov, “Fano resonances in antennas: General control over radiation patterns,” Phys. Rev. B88, 205106 (2013).
[CrossRef]

2012 (4)

A. N. Poddubny, M. V. Rybin, M. F. Limonov, and Y. S. Kivshar, “Fano interference governs wave transport in disordered systems,” Nat. Commun.3, 914 (2012).
[CrossRef] [PubMed]

A. E. Miroshnichenko and Y. S. Kivshar, “Fano resonances in all-dielectric oligomers,” Nano Lett.12, 6459–6463 (2012).
[CrossRef] [PubMed]

Y. Francescato, V. Giannini, and S. A. Maier, “Plasmonic systems unveiled by Fano resonances,” ACS Nano6, 1830–1838 (2012).
[CrossRef] [PubMed]

M. Tribelsky, A. Miroshnichenko, and Y. Kivshar, “Unconventional Fano resonances in light scattering by small particles,” Europhys. Lett.97, 44005 (2012).
[CrossRef]

2010 (5)

C. P. Burrows and W. L. Barnes, “Large spectral extinction due to overlap of dipolar and quadrupolar plasmonic modes of metallic nanoparticles in arrays,” Opt. Express18, 3187–3198 (2010).
[CrossRef] [PubMed]

M. V. Rybin, A. B. Khanikaev, M. Inoue, A. K. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Bragg scattering induces Fano resonance in photonic crystals,” Photonics Nanostruct. Fundam. Appl.8, 86–93 (2010).
[CrossRef]

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys.82, 2257–2298 (2010).
[CrossRef]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9, 707–715 (2010).
[CrossRef]

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328, 1135–1138 (2010).
[CrossRef] [PubMed]

2009 (2)

P. Garcia, M. Ibisate, R. Sapienza, D. Wiersma, and C. López, “Mie resonances to tailor random lasers,” Phys. Rev. A80, 013833 (2009).
[CrossRef]

M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg scattering in photonic crystals,” Phys. Rev. Lett.103, 023901 (2009).
[CrossRef] [PubMed]

2008 (2)

S. Gottardo, R. Sapienza, P. D. Garcia, A. Blanco, D. S. Wiersma, and C. López, “Resonance-driven random lasing,” Nat. Photonics2, 429–432 (2008).
[CrossRef]

M. I. Tribelsky, S. Flach, A. E. Miroshnichenko, A. V. Gorbach, and Y. S. Kivshar, “Light scattering by a finite obstacle and Fano resonances,” Phys. Rev. Lett.100, 043903 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

2005 (1)

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys. Condens. Matt.17, 3717–3734 (2005).
[CrossRef]

2003 (1)

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B67, 205402 (2003).
[CrossRef]

2002 (1)

M. Limonov, S. Lee, S. Tajima, and A. Yamanaka, “Superconductivity-induced resonant raman scattering in multilayer high-Tc superconductors,” Phys. Rev. B66, 054509 (2002).
[CrossRef]

1998 (2)

V. Madhavan, W. Chen, T. Jamneala, M. F. Crommie, and N. S. Wingreen, “Tunneling into a single magnetic atom: Spectroscopic evidence of the Kondo resonance,” Science280, 567–569 (1998).
[CrossRef] [PubMed]

M. F. Limonov, A. I. Rykov, S. Tajima, and A. Yamanaka, “Raman scattering study on fully oxygenated YBa2CuO7single crystals: x-y anisotropy in the superconductivity-induced effects,” Phys. Rev. Lett.80, 825–828 (1998).
[CrossRef]

1988 (1)

J.-P. Connerade and A. M. Lane, “Interacting resonances in atomic spectroscopy,” Rep. Prog. Phys.51, 1439–1478 (1988).
[CrossRef]

1961 (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev.124, 1866–1878 (1961).
[CrossRef]

Aizpurua, J.

Atwater, H. A.

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B67, 205402 (2003).
[CrossRef]

Bao, J.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328, 1135–1138 (2010).
[CrossRef] [PubMed]

Bao, K.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328, 1135–1138 (2010).
[CrossRef] [PubMed]

Bardhan, R.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328, 1135–1138 (2010).
[CrossRef] [PubMed]

Barnes, W. L.

Belov, P. A.

M. V. Rybin, P. V. Kapitanova, D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, Y. S. Kivshar, and M. F. Limonov, “Fano resonances in antennas: General control over radiation patterns,” Phys. Rev. B88, 205106 (2013).
[CrossRef]

Blanco, A.

S. Gottardo, R. Sapienza, P. D. Garcia, A. Blanco, D. S. Wiersma, and C. López, “Resonance-driven random lasing,” Nat. Photonics2, 429–432 (2008).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1998).
[CrossRef]

Bryant, G. W.

Burrows, C. P.

Capasso, F.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328, 1135–1138 (2010).
[CrossRef] [PubMed]

Chen, W.

V. Madhavan, W. Chen, T. Jamneala, M. F. Crommie, and N. S. Wingreen, “Tunneling into a single magnetic atom: Spectroscopic evidence of the Kondo resonance,” Science280, 567–569 (1998).
[CrossRef] [PubMed]

Chong, C. T.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9, 707–715 (2010).
[CrossRef]

Connerade, J.-P.

J.-P. Connerade and A. M. Lane, “Interacting resonances in atomic spectroscopy,” Rep. Prog. Phys.51, 1439–1478 (1988).
[CrossRef]

Crommie, M. F.

V. Madhavan, W. Chen, T. Jamneala, M. F. Crommie, and N. S. Wingreen, “Tunneling into a single magnetic atom: Spectroscopic evidence of the Kondo resonance,” Science280, 567–569 (1998).
[CrossRef] [PubMed]

Fan, J. A.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328, 1135–1138 (2010).
[CrossRef] [PubMed]

Fano, U.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev.124, 1866–1878 (1961).
[CrossRef]

Filonov, D. S.

M. V. Rybin, P. V. Kapitanova, D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, Y. S. Kivshar, and M. F. Limonov, “Fano resonances in antennas: General control over radiation patterns,” Phys. Rev. B88, 205106 (2013).
[CrossRef]

Flach, S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys.82, 2257–2298 (2010).
[CrossRef]

M. I. Tribelsky, S. Flach, A. E. Miroshnichenko, A. V. Gorbach, and Y. S. Kivshar, “Light scattering by a finite obstacle and Fano resonances,” Phys. Rev. Lett.100, 043903 (2008).
[CrossRef] [PubMed]

Foteinopoulou, S.

Francescato, Y.

Y. Francescato, V. Giannini, and S. A. Maier, “Plasmonic systems unveiled by Fano resonances,” ACS Nano6, 1830–1838 (2012).
[CrossRef] [PubMed]

Garcia, P.

P. Garcia, M. Ibisate, R. Sapienza, D. Wiersma, and C. López, “Mie resonances to tailor random lasers,” Phys. Rev. A80, 013833 (2009).
[CrossRef]

Garcia, P. D.

S. Gottardo, R. Sapienza, P. D. Garcia, A. Blanco, D. S. Wiersma, and C. López, “Resonance-driven random lasing,” Nat. Photonics2, 429–432 (2008).
[CrossRef]

García de Abajo, F. J.

Giannini, V.

Y. Francescato, V. Giannini, and S. A. Maier, “Plasmonic systems unveiled by Fano resonances,” ACS Nano6, 1830–1838 (2012).
[CrossRef] [PubMed]

Giessen, H.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9, 707–715 (2010).
[CrossRef]

Gorbach, A. V.

M. I. Tribelsky, S. Flach, A. E. Miroshnichenko, A. V. Gorbach, and Y. S. Kivshar, “Light scattering by a finite obstacle and Fano resonances,” Phys. Rev. Lett.100, 043903 (2008).
[CrossRef] [PubMed]

Gottardo, S.

S. Gottardo, R. Sapienza, P. D. Garcia, A. Blanco, D. S. Wiersma, and C. López, “Resonance-driven random lasing,” Nat. Photonics2, 429–432 (2008).
[CrossRef]

Halas, N. J.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9, 707–715 (2010).
[CrossRef]

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328, 1135–1138 (2010).
[CrossRef] [PubMed]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1998).
[CrossRef]

Ibisate, M.

P. Garcia, M. Ibisate, R. Sapienza, D. Wiersma, and C. López, “Mie resonances to tailor random lasers,” Phys. Rev. A80, 013833 (2009).
[CrossRef]

Inoue, M.

M. V. Rybin, A. B. Khanikaev, M. Inoue, A. K. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Bragg scattering induces Fano resonance in photonic crystals,” Photonics Nanostruct. Fundam. Appl.8, 86–93 (2010).
[CrossRef]

M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg scattering in photonic crystals,” Phys. Rev. Lett.103, 023901 (2009).
[CrossRef] [PubMed]

Jamneala, T.

V. Madhavan, W. Chen, T. Jamneala, M. F. Crommie, and N. S. Wingreen, “Tunneling into a single magnetic atom: Spectroscopic evidence of the Kondo resonance,” Science280, 567–569 (1998).
[CrossRef] [PubMed]

Kapitanova, P. V.

M. V. Rybin, P. V. Kapitanova, D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, Y. S. Kivshar, and M. F. Limonov, “Fano resonances in antennas: General control over radiation patterns,” Phys. Rev. B88, 205106 (2013).
[CrossRef]

Khanikaev, A. B.

M. V. Rybin, A. B. Khanikaev, M. Inoue, A. K. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Bragg scattering induces Fano resonance in photonic crystals,” Photonics Nanostruct. Fundam. Appl.8, 86–93 (2010).
[CrossRef]

M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg scattering in photonic crystals,” Phys. Rev. Lett.103, 023901 (2009).
[CrossRef] [PubMed]

Kik, P. G.

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B67, 205402 (2003).
[CrossRef]

Kivshar, Y.

M. Tribelsky, A. Miroshnichenko, and Y. Kivshar, “Unconventional Fano resonances in light scattering by small particles,” Europhys. Lett.97, 44005 (2012).
[CrossRef]

Kivshar, Y. S.

M. V. Rybin, P. V. Kapitanova, D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, Y. S. Kivshar, and M. F. Limonov, “Fano resonances in antennas: General control over radiation patterns,” Phys. Rev. B88, 205106 (2013).
[CrossRef]

A. N. Poddubny, M. V. Rybin, M. F. Limonov, and Y. S. Kivshar, “Fano interference governs wave transport in disordered systems,” Nat. Commun.3, 914 (2012).
[CrossRef] [PubMed]

A. E. Miroshnichenko and Y. S. Kivshar, “Fano resonances in all-dielectric oligomers,” Nano Lett.12, 6459–6463 (2012).
[CrossRef] [PubMed]

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys.82, 2257–2298 (2010).
[CrossRef]

M. I. Tribelsky, S. Flach, A. E. Miroshnichenko, A. V. Gorbach, and Y. S. Kivshar, “Light scattering by a finite obstacle and Fano resonances,” Phys. Rev. Lett.100, 043903 (2008).
[CrossRef] [PubMed]

Lane, A. M.

J.-P. Connerade and A. M. Lane, “Interacting resonances in atomic spectroscopy,” Rep. Prog. Phys.51, 1439–1478 (1988).
[CrossRef]

Lee, S.

M. Limonov, S. Lee, S. Tajima, and A. Yamanaka, “Superconductivity-induced resonant raman scattering in multilayer high-Tc superconductors,” Phys. Rev. B66, 054509 (2002).
[CrossRef]

Limonov, M.

M. Limonov, S. Lee, S. Tajima, and A. Yamanaka, “Superconductivity-induced resonant raman scattering in multilayer high-Tc superconductors,” Phys. Rev. B66, 054509 (2002).
[CrossRef]

Limonov, M. F.

M. V. Rybin, P. V. Kapitanova, D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, Y. S. Kivshar, and M. F. Limonov, “Fano resonances in antennas: General control over radiation patterns,” Phys. Rev. B88, 205106 (2013).
[CrossRef]

A. N. Poddubny, M. V. Rybin, M. F. Limonov, and Y. S. Kivshar, “Fano interference governs wave transport in disordered systems,” Nat. Commun.3, 914 (2012).
[CrossRef] [PubMed]

M. V. Rybin, A. B. Khanikaev, M. Inoue, A. K. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Bragg scattering induces Fano resonance in photonic crystals,” Photonics Nanostruct. Fundam. Appl.8, 86–93 (2010).
[CrossRef]

M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg scattering in photonic crystals,” Phys. Rev. Lett.103, 023901 (2009).
[CrossRef] [PubMed]

M. F. Limonov, A. I. Rykov, S. Tajima, and A. Yamanaka, “Raman scattering study on fully oxygenated YBa2CuO7single crystals: x-y anisotropy in the superconductivity-induced effects,” Phys. Rev. Lett.80, 825–828 (1998).
[CrossRef]

López, C.

P. Garcia, M. Ibisate, R. Sapienza, D. Wiersma, and C. López, “Mie resonances to tailor random lasers,” Phys. Rev. A80, 013833 (2009).
[CrossRef]

S. Gottardo, R. Sapienza, P. D. Garcia, A. Blanco, D. S. Wiersma, and C. López, “Resonance-driven random lasing,” Nat. Photonics2, 429–432 (2008).
[CrossRef]

Luk’yanchuk, B.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9, 707–715 (2010).
[CrossRef]

Madhavan, V.

V. Madhavan, W. Chen, T. Jamneala, M. F. Crommie, and N. S. Wingreen, “Tunneling into a single magnetic atom: Spectroscopic evidence of the Kondo resonance,” Science280, 567–569 (1998).
[CrossRef] [PubMed]

Maier, S. A.

Y. Francescato, V. Giannini, and S. A. Maier, “Plasmonic systems unveiled by Fano resonances,” ACS Nano6, 1830–1838 (2012).
[CrossRef] [PubMed]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9, 707–715 (2010).
[CrossRef]

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B67, 205402 (2003).
[CrossRef]

Manoharan, V. N.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328, 1135–1138 (2010).
[CrossRef] [PubMed]

Miroshnichenko, A.

M. Tribelsky, A. Miroshnichenko, and Y. Kivshar, “Unconventional Fano resonances in light scattering by small particles,” Europhys. Lett.97, 44005 (2012).
[CrossRef]

Miroshnichenko, A. E.

A. E. Miroshnichenko and Y. S. Kivshar, “Fano resonances in all-dielectric oligomers,” Nano Lett.12, 6459–6463 (2012).
[CrossRef] [PubMed]

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys.82, 2257–2298 (2010).
[CrossRef]

M. I. Tribelsky, S. Flach, A. E. Miroshnichenko, A. V. Gorbach, and Y. S. Kivshar, “Light scattering by a finite obstacle and Fano resonances,” Phys. Rev. Lett.100, 043903 (2008).
[CrossRef] [PubMed]

Moroz, A.

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys. Condens. Matt.17, 3717–3734 (2005).
[CrossRef]

Nordlander, P.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9, 707–715 (2010).
[CrossRef]

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328, 1135–1138 (2010).
[CrossRef] [PubMed]

Poddubny, A. N.

A. N. Poddubny, M. V. Rybin, M. F. Limonov, and Y. S. Kivshar, “Fano interference governs wave transport in disordered systems,” Nat. Commun.3, 914 (2012).
[CrossRef] [PubMed]

Romero, I.

Rybin, M. V.

M. V. Rybin, P. V. Kapitanova, D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, Y. S. Kivshar, and M. F. Limonov, “Fano resonances in antennas: General control over radiation patterns,” Phys. Rev. B88, 205106 (2013).
[CrossRef]

A. N. Poddubny, M. V. Rybin, M. F. Limonov, and Y. S. Kivshar, “Fano interference governs wave transport in disordered systems,” Nat. Commun.3, 914 (2012).
[CrossRef] [PubMed]

M. V. Rybin, A. B. Khanikaev, M. Inoue, A. K. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Bragg scattering induces Fano resonance in photonic crystals,” Photonics Nanostruct. Fundam. Appl.8, 86–93 (2010).
[CrossRef]

M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg scattering in photonic crystals,” Phys. Rev. Lett.103, 023901 (2009).
[CrossRef] [PubMed]

Rykov, A. I.

M. F. Limonov, A. I. Rykov, S. Tajima, and A. Yamanaka, “Raman scattering study on fully oxygenated YBa2CuO7single crystals: x-y anisotropy in the superconductivity-induced effects,” Phys. Rev. Lett.80, 825–828 (1998).
[CrossRef]

Samusev, A. K.

M. V. Rybin, A. B. Khanikaev, M. Inoue, A. K. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Bragg scattering induces Fano resonance in photonic crystals,” Photonics Nanostruct. Fundam. Appl.8, 86–93 (2010).
[CrossRef]

Samusev, K. B.

M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg scattering in photonic crystals,” Phys. Rev. Lett.103, 023901 (2009).
[CrossRef] [PubMed]

Sapienza, R.

P. Garcia, M. Ibisate, R. Sapienza, D. Wiersma, and C. López, “Mie resonances to tailor random lasers,” Phys. Rev. A80, 013833 (2009).
[CrossRef]

S. Gottardo, R. Sapienza, P. D. Garcia, A. Blanco, D. S. Wiersma, and C. López, “Resonance-driven random lasing,” Nat. Photonics2, 429–432 (2008).
[CrossRef]

Shvets, G.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328, 1135–1138 (2010).
[CrossRef] [PubMed]

Slobozhanyuk, A. P.

M. V. Rybin, P. V. Kapitanova, D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, Y. S. Kivshar, and M. F. Limonov, “Fano resonances in antennas: General control over radiation patterns,” Phys. Rev. B88, 205106 (2013).
[CrossRef]

Steel, M. J.

M. V. Rybin, A. B. Khanikaev, M. Inoue, A. K. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Bragg scattering induces Fano resonance in photonic crystals,” Photonics Nanostruct. Fundam. Appl.8, 86–93 (2010).
[CrossRef]

M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg scattering in photonic crystals,” Phys. Rev. Lett.103, 023901 (2009).
[CrossRef] [PubMed]

Tajima, S.

M. Limonov, S. Lee, S. Tajima, and A. Yamanaka, “Superconductivity-induced resonant raman scattering in multilayer high-Tc superconductors,” Phys. Rev. B66, 054509 (2002).
[CrossRef]

M. F. Limonov, A. I. Rykov, S. Tajima, and A. Yamanaka, “Raman scattering study on fully oxygenated YBa2CuO7single crystals: x-y anisotropy in the superconductivity-induced effects,” Phys. Rev. Lett.80, 825–828 (1998).
[CrossRef]

Tribelsky, M.

M. Tribelsky, A. Miroshnichenko, and Y. Kivshar, “Unconventional Fano resonances in light scattering by small particles,” Europhys. Lett.97, 44005 (2012).
[CrossRef]

Tribelsky, M. I.

M. I. Tribelsky, S. Flach, A. E. Miroshnichenko, A. V. Gorbach, and Y. S. Kivshar, “Light scattering by a finite obstacle and Fano resonances,” Phys. Rev. Lett.100, 043903 (2008).
[CrossRef] [PubMed]

Vandenbem, C.

Vigneron, J.

Wiersma, D.

P. Garcia, M. Ibisate, R. Sapienza, D. Wiersma, and C. López, “Mie resonances to tailor random lasers,” Phys. Rev. A80, 013833 (2009).
[CrossRef]

Wiersma, D. S.

S. Gottardo, R. Sapienza, P. D. Garcia, A. Blanco, D. S. Wiersma, and C. López, “Resonance-driven random lasing,” Nat. Photonics2, 429–432 (2008).
[CrossRef]

Wingreen, N. S.

V. Madhavan, W. Chen, T. Jamneala, M. F. Crommie, and N. S. Wingreen, “Tunneling into a single magnetic atom: Spectroscopic evidence of the Kondo resonance,” Science280, 567–569 (1998).
[CrossRef] [PubMed]

Wu, C.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328, 1135–1138 (2010).
[CrossRef] [PubMed]

Yamanaka, A.

M. Limonov, S. Lee, S. Tajima, and A. Yamanaka, “Superconductivity-induced resonant raman scattering in multilayer high-Tc superconductors,” Phys. Rev. B66, 054509 (2002).
[CrossRef]

M. F. Limonov, A. I. Rykov, S. Tajima, and A. Yamanaka, “Raman scattering study on fully oxygenated YBa2CuO7single crystals: x-y anisotropy in the superconductivity-induced effects,” Phys. Rev. Lett.80, 825–828 (1998).
[CrossRef]

Yannopapas, V.

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys. Condens. Matt.17, 3717–3734 (2005).
[CrossRef]

Yushin, G.

M. V. Rybin, A. B. Khanikaev, M. Inoue, A. K. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Bragg scattering induces Fano resonance in photonic crystals,” Photonics Nanostruct. Fundam. Appl.8, 86–93 (2010).
[CrossRef]

M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg scattering in photonic crystals,” Phys. Rev. Lett.103, 023901 (2009).
[CrossRef] [PubMed]

Zheludev, N. I.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9, 707–715 (2010).
[CrossRef]

ACS Nano (1)

Y. Francescato, V. Giannini, and S. A. Maier, “Plasmonic systems unveiled by Fano resonances,” ACS Nano6, 1830–1838 (2012).
[CrossRef] [PubMed]

Europhys. Lett. (1)

M. Tribelsky, A. Miroshnichenko, and Y. Kivshar, “Unconventional Fano resonances in light scattering by small particles,” Europhys. Lett.97, 44005 (2012).
[CrossRef]

J. Phys. Condens. Matt. (1)

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys. Condens. Matt.17, 3717–3734 (2005).
[CrossRef]

Nano Lett. (1)

A. E. Miroshnichenko and Y. S. Kivshar, “Fano resonances in all-dielectric oligomers,” Nano Lett.12, 6459–6463 (2012).
[CrossRef] [PubMed]

Nat. Commun. (1)

A. N. Poddubny, M. V. Rybin, M. F. Limonov, and Y. S. Kivshar, “Fano interference governs wave transport in disordered systems,” Nat. Commun.3, 914 (2012).
[CrossRef] [PubMed]

Nat. Mater. (1)

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9, 707–715 (2010).
[CrossRef]

Nat. Photonics (1)

S. Gottardo, R. Sapienza, P. D. Garcia, A. Blanco, D. S. Wiersma, and C. López, “Resonance-driven random lasing,” Nat. Photonics2, 429–432 (2008).
[CrossRef]

Opt. Express (3)

Photonics Nanostruct. Fundam. Appl. (1)

M. V. Rybin, A. B. Khanikaev, M. Inoue, A. K. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Bragg scattering induces Fano resonance in photonic crystals,” Photonics Nanostruct. Fundam. Appl.8, 86–93 (2010).
[CrossRef]

Phys. Rev. (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev.124, 1866–1878 (1961).
[CrossRef]

Phys. Rev. A (1)

P. Garcia, M. Ibisate, R. Sapienza, D. Wiersma, and C. López, “Mie resonances to tailor random lasers,” Phys. Rev. A80, 013833 (2009).
[CrossRef]

Phys. Rev. B (3)

M. V. Rybin, P. V. Kapitanova, D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, Y. S. Kivshar, and M. F. Limonov, “Fano resonances in antennas: General control over radiation patterns,” Phys. Rev. B88, 205106 (2013).
[CrossRef]

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B67, 205402 (2003).
[CrossRef]

M. Limonov, S. Lee, S. Tajima, and A. Yamanaka, “Superconductivity-induced resonant raman scattering in multilayer high-Tc superconductors,” Phys. Rev. B66, 054509 (2002).
[CrossRef]

Phys. Rev. Lett. (3)

M. I. Tribelsky, S. Flach, A. E. Miroshnichenko, A. V. Gorbach, and Y. S. Kivshar, “Light scattering by a finite obstacle and Fano resonances,” Phys. Rev. Lett.100, 043903 (2008).
[CrossRef] [PubMed]

M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg scattering in photonic crystals,” Phys. Rev. Lett.103, 023901 (2009).
[CrossRef] [PubMed]

M. F. Limonov, A. I. Rykov, S. Tajima, and A. Yamanaka, “Raman scattering study on fully oxygenated YBa2CuO7single crystals: x-y anisotropy in the superconductivity-induced effects,” Phys. Rev. Lett.80, 825–828 (1998).
[CrossRef]

Rep. Prog. Phys. (1)

J.-P. Connerade and A. M. Lane, “Interacting resonances in atomic spectroscopy,” Rep. Prog. Phys.51, 1439–1478 (1988).
[CrossRef]

Rev. Mod. Phys. (1)

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys.82, 2257–2298 (2010).
[CrossRef]

Science (2)

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328, 1135–1138 (2010).
[CrossRef] [PubMed]

V. Madhavan, W. Chen, T. Jamneala, M. F. Crommie, and N. S. Wingreen, “Tunneling into a single magnetic atom: Spectroscopic evidence of the Kondo resonance,” Science280, 567–569 (1998).
[CrossRef] [PubMed]

Other (3)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1998).
[CrossRef]

M. F. Limonov and R. M. De La Rue, eds., Optical Properties of Photonic Structures: Interplay of Order and Disorder (CRC Press, 2012).
[CrossRef]

C. M. Soukoulis, ed., Photonic Band Gap Materials, Vol. 315 of NATO ASI Series E (Springer, 1996).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Spectra of the squared modules of the coefficients (a,b) |d0|2 and (c,d) |a0|2 for a single infinite dielectric rod at various values of the rod dielectric permittivity: (a, c) ε1 = 4 and (b, d) 50. Permittivity of the surrounding medium ε2 = 1. Blue curves represent the background [ r J n ( x ε 2 ) ] / [ r H n ( 1 ) ( x ε 2 ) ]. The size parameter x = 2πr/λ.

Fig. 2
Fig. 2

Spectrum of the Mie scattering efficiency Qsca,0 for the dipole mode TE0k for a single dielectric circular rod and different values of real dielectric permittivity ε1. The rod is embedded in air, ε2 = 1. The corresponding values of the Fano parameter q are shown above the plot. Curves are shifted vertically by the values shown. Insert: Dependence of the Q factor for the TE0k resonance Mie modes (k = 1 to 9) on ε1.

Fig. 3
Fig. 3

(a) Red: squared Lorenz-Mie coefficient |a0|2 for a circular rod (ε1 = 50) embedded in air (ε2 = 1). Blue, black and green curves present the results for the Fano fitting of the TE02, TE05 and TE07 modes. The corresponding values of the Fano parameter q are shown on the top. (b) Bessel functions Jn(x) for n = 0, 1, 2. (c) Dependence of the Fano parameter q on the size parameter x = 2πr/λ for the dipole mode TE0k (red) and multipole modes TE1k (green) and TE2k (blue) for a circular rod (ε1 = 50) embedded in air (ε2 = 1). The Fano line shapes for selected values of q are shown on the right.

Equations (7)

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{ E n J n ( x ε 2 ) + A n H n ( 1 ) ( x ε 2 ) = D n J n ( x ε 1 ) , ε 1 E n r J n ( x ε 2 ) + ε 1 A n r H n ( 1 ) ( x ε 2 ) = ε 2 D n r J n ( x ε 1 ) ,
a n = ε 2 J n ( x ε 2 ) r J n ( x ε 1 ) ε 1 r J n ( x ε 2 ) J n ( x ε 1 ) ε 1 r H n ( 1 ) ( x ε 2 ) J n ( x ε 1 ) ε 2 H n ( 1 ) ( x ε 2 ) r J n ( x ε 1 ) ,
d n = J n ( x ε 2 ) r H n ( 1 ) ( x ε 2 ) H n ( 1 ) ( x ε 2 ) r J n ( x ε 2 ) J n ( x ε 1 ) r H n ( 1 ) ( x ε 2 ) ε 2 ε 1 H n ( 1 ) ( x ε 2 ) r J n ( x ε 1 ) .
I ( ω ) = ( q + Ω ) 2 1 + Ω 2 sin 2 Δ ,
ε 2 d n r J n ( x ε 1 ) + [ ε 1 E n r J n ( x ε 2 ) ] = ε 1 a n r H n ( 1 ) ( x ε 2 ) ,
Narrow resonance + Slow varying background = Fano profile ,
A ( ω ) exp [ i φ A ( ω ) ] 1 Ω + i + B ( ω ) exp [ i φ B ( ω ) ] = ( q + Ω ) 2 1 + Ω 2 sin 2 Δ ,

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