Abstract

We establish full-wave electromagnetic scattering theory to study the near-field and far-field spectra of radially anisotropic coated nanowires. For coated nanowires containing radially anisotropic core and plasmonic shell, unconventional Fano resonances are predicted due to the interference between dipole cloaking mode and dipole resonant mode. In contrast to Z-shaped Fano profile with small modulation depth for coated nanospheres in Argyropoulos et al, Phys. Rev. Lett. 108, 263905 (2012), we predict S-shaped Fano profile with high depth for coated nanowires. An off-resonance field enhancement in the radially anisotropic core is found at the Fano dip, and its’ magnitude is approximately the same as that the one at the low-energy resonant wavelength. Furthermore, with our adjustment of the inner size and the permittivity elements of the anisotropic core, tunable Fano-like profiles can be realized. These results may be useful for potential applications in different fields of nanotechnology.

© 2013 OSA

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  1. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev.124(6), 1866–1878(1961).
    [CrossRef]
  2. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys.82(3), 2257–2298(2010).
    [CrossRef]
  3. 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]
  4. F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988(2008).
    [CrossRef] [PubMed]
  5. F. Hao, P. Nordlander, Y. Sonnefraud, P. V. Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and Fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano3(3), 643–652(2009).
    [CrossRef] [PubMed]
  6. Z. Y. Fang, J. Y. Cai, Z. B. Yan, P. Nordlander, N. J. Halas, and X. Zhu, “Removing a wedge from a metallic nanodisk reveals a Fano resonance,” Nano Lett.11(10), 4475–4479(2011).
    [CrossRef] [PubMed]
  7. K. C. Woo, L. Shao, H. J. Chen, Y. Liang, J. F. Wang, and H. Q. Lin, “Universal scaling and Fano resonance in the plasmon coupling between gold nanorods,” ACS Nano5(7), 5976–5986(2011).
    [CrossRef] [PubMed]
  8. G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, N. Del Fatti, F. Vallee, and P. F. Brevet, “Fano profiles induced by near-field coupling in heterogeneous dimers of gold and silver nanoparticles,” Phys. Rev. Lett.101(19), 197401(2008).
    [CrossRef] [PubMed]
  9. Z. J. Yang, Z. S. Zhang, W. Zhang, Z. H. Hao, and Q. Q. Wang, “Twinned Fano interferences induced by hybridized plasmons in Au-Ag nanorod heterodimers,” Appl. Phys. Lett.96(13), 131113(2010).
    [CrossRef]
  10. S. Sheikholeslami, Y. W. Jun, P. K. Jain, and A. P. Alivisatos, “Coupling of optical resonances in a compositionally asymmetric plasmonic nanoparticle dimer,” Nano Lett.10(7), 2655–2660(2010).
    [CrossRef] [PubMed]
  11. O. Pena-Rodriguez, U. Pal, M. Campoy-Quiles, L. Rodriguez-Fernandez, M. Garriga, and M. I. Alonso, “Enhanced Fano resonance in asymmetrical Au:Ag heterodimers,” J. Phys. Chem. C115(14), 6410–6414(2011).
    [CrossRef]
  12. S. Mukherjee, H. Sobhani, J. B. Lassiter, R. Bardhan, P. Nordlander, and N. J. Halas, “Fanoshells: nanoparticles with built-in Fano resonances,” Nano Lett.10(7), 2694–2701(2010).
    [CrossRef] [PubMed]
  13. A. E. Miroshnichenko, “Off-resonance field enhancement by spherical nanoshells,” Phys. Rev. A81(5), 053818 (2010).
    [CrossRef]
  14. O. Pena-Rodriguez and U. Pal, “Au/Ag core-shell nanoparticles: efficient all-plasmonic Fano-resonance generators,” Nanoscale3(9), 3609–3612(2011).
    [CrossRef] [PubMed]
  15. H. J. Chen, L. Shao, Y. C. Man, C. M. Zhao, J. F. Wang, and B. C. Yang, “Fano resonance in (gold core)-(dielectric shell) nanostructures without symmetry breaking,” Small8(10), 1503–1509(2012).
    [CrossRef] [PubMed]
  16. D. J. Wu, S. M. Liang, and X. J. Liu, “A tunable Fano resonance in silver nanoshell with a spherically anisotropic core,” J. Chem. Phys.136(3), 034502(2012).
    [CrossRef] [PubMed]
  17. 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(4), 043903(2008).
    [CrossRef] [PubMed]
  18. B. S. Luk’yanchuk, A. E. Miroshnichenko, and Y. S. Kivshar, “Fano resonances and topological optics: an interplay of far- and near-field interference phenomena,” J. Opt.15(7), 073001 (2013).
    [CrossRef]
  19. M. I. Tribelksy, A. E. Miroshnichenko, and Y. S. Kivshar, “Unconventional Fano resonances in light scattering by small particles,” Europhys. Lett.97(4), 44005(2012).
    [CrossRef]
  20. T. J. Arruda, A. S. Martinez, and F. A. Pinheiro, “Unconventional Fano effect and off-resonance field enhancement in plasmonic coated spheres,” Phys. Rev. A87(4), 043841(2013).
    [CrossRef]
  21. M. Kociak, O. Stephan, L. Henrard, V. Charbois, A. Rothschild, R. Tenne, and C. Colliex, “Experimental evidence of surface-plasmon coupling in anisotropic hollow nanoparticles,” Phys. Rev. Lett.87(7), 075501(2001).
    [CrossRef] [PubMed]
  22. D. Taverna, M. Kociak, V. Charbois, and L. Henrard, “Electron energy-loss spectrum of an electron passing near a locally anisotropic nanotube,” Phys. Rev. B66(23), 235419(2002).
    [CrossRef]
  23. Q. Cheng, W. X. Jiang, and T. J. Cui, “Spatial power combination for omnidirectional radiation via anisotropic metamaterials,” Phys. Rev. Lett.108(21), 213903(2012).
    [CrossRef] [PubMed]
  24. Y. Yuan, N. Wang, and J. H. Lim, “On the omnidirectional radiation via radially anisotropic zero-index metamaterials,” EPL100(3), 34005(2012).
    [CrossRef]
  25. S. Xu, X. X. Cheng, R. R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. L. Huang, X. M. Zhang, F. X. Yu, B. L. Zhang, and H. S. Chen, “Experimental Demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett.109(22), 223903(2012).
    [CrossRef]
  26. X. Sheng, H.S. Chen, B. L. Zhang, B. I. Wu, and J. A. Kong, “Route to low-scattering cylindrical cloaks with finite permittivity and permeability,” Phys. Rev. A79(15), 155122(2009).
  27. Y. X. Ni, L. Gao, and C. W. Qiu, “Achieving invisibility of homogeneous cylindrically anisotropic cylinders,” Plasmonics5(3), 251–258(2010).
    [CrossRef]
  28. Y. W. Jin, D. L. Gao, and L. Gao, “Plasmonic resonant light scattering by a cylinder with radial anisotropy,” Prog. Electromag. Res.106, 335–347(2010).
    [CrossRef]
  29. H. L. Chen and L. Gao, “Anomalous electromagnetic scattering from radially anisotropic nanowires,” Phys. Rev. A86(3), 033825(2012).
    [CrossRef]
  30. C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alu, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett.108(26), 263905(2012).
    [CrossRef] [PubMed]
  31. X. P. Yu and L. Gao, “Nonlinear dielectric response in partially resonant composites with radial dielectric anisotropy,” Phys. Lett. A359(5), 516–522(2006).
    [CrossRef]
  32. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science302(5644), 419–422(2003).
    [CrossRef] [PubMed]
  33. J. J. Zhang and A. Zayats, “Multiple Fano resonances in single-layere nonconcentric core-shell nanostructures,” Opt. Express21(7), 8426–8436(2013).
    [CrossRef] [PubMed]
  34. M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics6, 737–748(2012).
    [CrossRef]
  35. J. Butet, G. Bachelier, I. Russier-Antoine, F. Bertorelle, A. Mosset, N. Lascoux, C. Jonin, E. Benichou, and P. F. Brevet, “Nonlinear Fano profiles in the optical second-harmonic generation from silver nanoparticles,” Phys. Rev. B86(7), 075430(2012).
    [CrossRef]
  36. T. J. Arruda, F. A. Pinheiro, and A. S. Martinez, “Electromagnetic energy within coated spheres containing dispersive metamaterials,” J. Opt.14(6), 065101(2012).
    [CrossRef]
  37. T. J. Arruda and A. S. Martinez, “Electromagnetic energy within a magnetic infinite cylinder and scattering properties for oblique incidence,” J. Opt. Soc. Am. A27(7), 1679–1686(2012).
    [CrossRef]

2013

B. S. Luk’yanchuk, A. E. Miroshnichenko, and Y. S. Kivshar, “Fano resonances and topological optics: an interplay of far- and near-field interference phenomena,” J. Opt.15(7), 073001 (2013).
[CrossRef]

T. J. Arruda, A. S. Martinez, and F. A. Pinheiro, “Unconventional Fano effect and off-resonance field enhancement in plasmonic coated spheres,” Phys. Rev. A87(4), 043841(2013).
[CrossRef]

J. J. Zhang and A. Zayats, “Multiple Fano resonances in single-layere nonconcentric core-shell nanostructures,” Opt. Express21(7), 8426–8436(2013).
[CrossRef] [PubMed]

2012

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics6, 737–748(2012).
[CrossRef]

J. Butet, G. Bachelier, I. Russier-Antoine, F. Bertorelle, A. Mosset, N. Lascoux, C. Jonin, E. Benichou, and P. F. Brevet, “Nonlinear Fano profiles in the optical second-harmonic generation from silver nanoparticles,” Phys. Rev. B86(7), 075430(2012).
[CrossRef]

T. J. Arruda, F. A. Pinheiro, and A. S. Martinez, “Electromagnetic energy within coated spheres containing dispersive metamaterials,” J. Opt.14(6), 065101(2012).
[CrossRef]

T. J. Arruda and A. S. Martinez, “Electromagnetic energy within a magnetic infinite cylinder and scattering properties for oblique incidence,” J. Opt. Soc. Am. A27(7), 1679–1686(2012).
[CrossRef]

H. L. Chen and L. Gao, “Anomalous electromagnetic scattering from radially anisotropic nanowires,” Phys. Rev. A86(3), 033825(2012).
[CrossRef]

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alu, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett.108(26), 263905(2012).
[CrossRef] [PubMed]

Q. Cheng, W. X. Jiang, and T. J. Cui, “Spatial power combination for omnidirectional radiation via anisotropic metamaterials,” Phys. Rev. Lett.108(21), 213903(2012).
[CrossRef] [PubMed]

Y. Yuan, N. Wang, and J. H. Lim, “On the omnidirectional radiation via radially anisotropic zero-index metamaterials,” EPL100(3), 34005(2012).
[CrossRef]

S. Xu, X. X. Cheng, R. R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. L. Huang, X. M. Zhang, F. X. Yu, B. L. Zhang, and H. S. Chen, “Experimental Demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett.109(22), 223903(2012).
[CrossRef]

M. I. Tribelksy, A. E. Miroshnichenko, and Y. S. Kivshar, “Unconventional Fano resonances in light scattering by small particles,” Europhys. Lett.97(4), 44005(2012).
[CrossRef]

H. J. Chen, L. Shao, Y. C. Man, C. M. Zhao, J. F. Wang, and B. C. Yang, “Fano resonance in (gold core)-(dielectric shell) nanostructures without symmetry breaking,” Small8(10), 1503–1509(2012).
[CrossRef] [PubMed]

D. J. Wu, S. M. Liang, and X. J. Liu, “A tunable Fano resonance in silver nanoshell with a spherically anisotropic core,” J. Chem. Phys.136(3), 034502(2012).
[CrossRef] [PubMed]

2011

O. Pena-Rodriguez, U. Pal, M. Campoy-Quiles, L. Rodriguez-Fernandez, M. Garriga, and M. I. Alonso, “Enhanced Fano resonance in asymmetrical Au:Ag heterodimers,” J. Phys. Chem. C115(14), 6410–6414(2011).
[CrossRef]

Z. Y. Fang, J. Y. Cai, Z. B. Yan, P. Nordlander, N. J. Halas, and X. Zhu, “Removing a wedge from a metallic nanodisk reveals a Fano resonance,” Nano Lett.11(10), 4475–4479(2011).
[CrossRef] [PubMed]

K. C. Woo, L. Shao, H. J. Chen, Y. Liang, J. F. Wang, and H. Q. Lin, “Universal scaling and Fano resonance in the plasmon coupling between gold nanorods,” ACS Nano5(7), 5976–5986(2011).
[CrossRef] [PubMed]

O. Pena-Rodriguez and U. Pal, “Au/Ag core-shell nanoparticles: efficient all-plasmonic Fano-resonance generators,” Nanoscale3(9), 3609–3612(2011).
[CrossRef] [PubMed]

2010

Y. X. Ni, L. Gao, and C. W. Qiu, “Achieving invisibility of homogeneous cylindrically anisotropic cylinders,” Plasmonics5(3), 251–258(2010).
[CrossRef]

Y. W. Jin, D. L. Gao, and L. Gao, “Plasmonic resonant light scattering by a cylinder with radial anisotropy,” Prog. Electromag. Res.106, 335–347(2010).
[CrossRef]

Z. J. Yang, Z. S. Zhang, W. Zhang, Z. H. Hao, and Q. Q. Wang, “Twinned Fano interferences induced by hybridized plasmons in Au-Ag nanorod heterodimers,” Appl. Phys. Lett.96(13), 131113(2010).
[CrossRef]

S. Sheikholeslami, Y. W. Jun, P. K. Jain, and A. P. Alivisatos, “Coupling of optical resonances in a compositionally asymmetric plasmonic nanoparticle dimer,” Nano Lett.10(7), 2655–2660(2010).
[CrossRef] [PubMed]

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys.82(3), 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]

S. Mukherjee, H. Sobhani, J. B. Lassiter, R. Bardhan, P. Nordlander, and N. J. Halas, “Fanoshells: nanoparticles with built-in Fano resonances,” Nano Lett.10(7), 2694–2701(2010).
[CrossRef] [PubMed]

A. E. Miroshnichenko, “Off-resonance field enhancement by spherical nanoshells,” Phys. Rev. A81(5), 053818 (2010).
[CrossRef]

2009

F. Hao, P. Nordlander, Y. Sonnefraud, P. V. Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and Fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano3(3), 643–652(2009).
[CrossRef] [PubMed]

X. Sheng, H.S. Chen, B. L. Zhang, B. I. Wu, and J. A. Kong, “Route to low-scattering cylindrical cloaks with finite permittivity and permeability,” Phys. Rev. A79(15), 155122(2009).

2008

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988(2008).
[CrossRef] [PubMed]

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, N. Del Fatti, F. Vallee, and P. F. Brevet, “Fano profiles induced by near-field coupling in heterogeneous dimers of gold and silver nanoparticles,” Phys. Rev. Lett.101(19), 197401(2008).
[CrossRef] [PubMed]

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(4), 043903(2008).
[CrossRef] [PubMed]

2006

X. P. Yu and L. Gao, “Nonlinear dielectric response in partially resonant composites with radial dielectric anisotropy,” Phys. Lett. A359(5), 516–522(2006).
[CrossRef]

2003

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science302(5644), 419–422(2003).
[CrossRef] [PubMed]

2002

D. Taverna, M. Kociak, V. Charbois, and L. Henrard, “Electron energy-loss spectrum of an electron passing near a locally anisotropic nanotube,” Phys. Rev. B66(23), 235419(2002).
[CrossRef]

2001

M. Kociak, O. Stephan, L. Henrard, V. Charbois, A. Rothschild, R. Tenne, and C. Colliex, “Experimental evidence of surface-plasmon coupling in anisotropic hollow nanoparticles,” Phys. Rev. Lett.87(7), 075501(2001).
[CrossRef] [PubMed]

1961

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev.124(6), 1866–1878(1961).
[CrossRef]

Alivisatos, A. P.

S. Sheikholeslami, Y. W. Jun, P. K. Jain, and A. P. Alivisatos, “Coupling of optical resonances in a compositionally asymmetric plasmonic nanoparticle dimer,” Nano Lett.10(7), 2655–2660(2010).
[CrossRef] [PubMed]

Alonso, M. I.

O. Pena-Rodriguez, U. Pal, M. Campoy-Quiles, L. Rodriguez-Fernandez, M. Garriga, and M. I. Alonso, “Enhanced Fano resonance in asymmetrical Au:Ag heterodimers,” J. Phys. Chem. C115(14), 6410–6414(2011).
[CrossRef]

Alu, A.

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alu, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett.108(26), 263905(2012).
[CrossRef] [PubMed]

Argyropoulos, C.

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alu, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett.108(26), 263905(2012).
[CrossRef] [PubMed]

Arruda, T. J.

T. J. Arruda, A. S. Martinez, and F. A. Pinheiro, “Unconventional Fano effect and off-resonance field enhancement in plasmonic coated spheres,” Phys. Rev. A87(4), 043841(2013).
[CrossRef]

T. J. Arruda, F. A. Pinheiro, and A. S. Martinez, “Electromagnetic energy within coated spheres containing dispersive metamaterials,” J. Opt.14(6), 065101(2012).
[CrossRef]

T. J. Arruda and A. S. Martinez, “Electromagnetic energy within a magnetic infinite cylinder and scattering properties for oblique incidence,” J. Opt. Soc. Am. A27(7), 1679–1686(2012).
[CrossRef]

Bachelier, G.

J. Butet, G. Bachelier, I. Russier-Antoine, F. Bertorelle, A. Mosset, N. Lascoux, C. Jonin, E. Benichou, and P. F. Brevet, “Nonlinear Fano profiles in the optical second-harmonic generation from silver nanoparticles,” Phys. Rev. B86(7), 075430(2012).
[CrossRef]

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, N. Del Fatti, F. Vallee, and P. F. Brevet, “Fano profiles induced by near-field coupling in heterogeneous dimers of gold and silver nanoparticles,” Phys. Rev. Lett.101(19), 197401(2008).
[CrossRef] [PubMed]

Bardhan, R.

S. Mukherjee, H. Sobhani, J. B. Lassiter, R. Bardhan, P. Nordlander, and N. J. Halas, “Fanoshells: nanoparticles with built-in Fano resonances,” Nano Lett.10(7), 2694–2701(2010).
[CrossRef] [PubMed]

Benichou, E.

J. Butet, G. Bachelier, I. Russier-Antoine, F. Bertorelle, A. Mosset, N. Lascoux, C. Jonin, E. Benichou, and P. F. Brevet, “Nonlinear Fano profiles in the optical second-harmonic generation from silver nanoparticles,” Phys. Rev. B86(7), 075430(2012).
[CrossRef]

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, N. Del Fatti, F. Vallee, and P. F. Brevet, “Fano profiles induced by near-field coupling in heterogeneous dimers of gold and silver nanoparticles,” Phys. Rev. Lett.101(19), 197401(2008).
[CrossRef] [PubMed]

Bertorelle, F.

J. Butet, G. Bachelier, I. Russier-Antoine, F. Bertorelle, A. Mosset, N. Lascoux, C. Jonin, E. Benichou, and P. F. Brevet, “Nonlinear Fano profiles in the optical second-harmonic generation from silver nanoparticles,” Phys. Rev. B86(7), 075430(2012).
[CrossRef]

Brevet, P. F.

J. Butet, G. Bachelier, I. Russier-Antoine, F. Bertorelle, A. Mosset, N. Lascoux, C. Jonin, E. Benichou, and P. F. Brevet, “Nonlinear Fano profiles in the optical second-harmonic generation from silver nanoparticles,” Phys. Rev. B86(7), 075430(2012).
[CrossRef]

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, N. Del Fatti, F. Vallee, and P. F. Brevet, “Fano profiles induced by near-field coupling in heterogeneous dimers of gold and silver nanoparticles,” Phys. Rev. Lett.101(19), 197401(2008).
[CrossRef] [PubMed]

Butet, J.

J. Butet, G. Bachelier, I. Russier-Antoine, F. Bertorelle, A. Mosset, N. Lascoux, C. Jonin, E. Benichou, and P. F. Brevet, “Nonlinear Fano profiles in the optical second-harmonic generation from silver nanoparticles,” Phys. Rev. B86(7), 075430(2012).
[CrossRef]

Cai, J. Y.

Z. Y. Fang, J. Y. Cai, Z. B. Yan, P. Nordlander, N. J. Halas, and X. Zhu, “Removing a wedge from a metallic nanodisk reveals a Fano resonance,” Nano Lett.11(10), 4475–4479(2011).
[CrossRef] [PubMed]

Campoy-Quiles, M.

O. Pena-Rodriguez, U. Pal, M. Campoy-Quiles, L. Rodriguez-Fernandez, M. Garriga, and M. I. Alonso, “Enhanced Fano resonance in asymmetrical Au:Ag heterodimers,” J. Phys. Chem. C115(14), 6410–6414(2011).
[CrossRef]

Charbois, V.

D. Taverna, M. Kociak, V. Charbois, and L. Henrard, “Electron energy-loss spectrum of an electron passing near a locally anisotropic nanotube,” Phys. Rev. B66(23), 235419(2002).
[CrossRef]

M. Kociak, O. Stephan, L. Henrard, V. Charbois, A. Rothschild, R. Tenne, and C. Colliex, “Experimental evidence of surface-plasmon coupling in anisotropic hollow nanoparticles,” Phys. Rev. Lett.87(7), 075501(2001).
[CrossRef] [PubMed]

Chen, H. J.

H. J. Chen, L. Shao, Y. C. Man, C. M. Zhao, J. F. Wang, and B. C. Yang, “Fano resonance in (gold core)-(dielectric shell) nanostructures without symmetry breaking,” Small8(10), 1503–1509(2012).
[CrossRef] [PubMed]

K. C. Woo, L. Shao, H. J. Chen, Y. Liang, J. F. Wang, and H. Q. Lin, “Universal scaling and Fano resonance in the plasmon coupling between gold nanorods,” ACS Nano5(7), 5976–5986(2011).
[CrossRef] [PubMed]

Chen, H. L.

H. L. Chen and L. Gao, “Anomalous electromagnetic scattering from radially anisotropic nanowires,” Phys. Rev. A86(3), 033825(2012).
[CrossRef]

Chen, H. S.

S. Xu, X. X. Cheng, R. R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. L. Huang, X. M. Zhang, F. X. Yu, B. L. Zhang, and H. S. Chen, “Experimental Demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett.109(22), 223903(2012).
[CrossRef]

Chen, H.S.

X. Sheng, H.S. Chen, B. L. Zhang, B. I. Wu, and J. A. Kong, “Route to low-scattering cylindrical cloaks with finite permittivity and permeability,” Phys. Rev. A79(15), 155122(2009).

Chen, P. Y.

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alu, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett.108(26), 263905(2012).
[CrossRef] [PubMed]

Cheng, Q.

Q. Cheng, W. X. Jiang, and T. J. Cui, “Spatial power combination for omnidirectional radiation via anisotropic metamaterials,” Phys. Rev. Lett.108(21), 213903(2012).
[CrossRef] [PubMed]

Cheng, X. X.

S. Xu, X. X. Cheng, R. R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. L. Huang, X. M. Zhang, F. X. Yu, B. L. Zhang, and H. S. Chen, “Experimental Demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett.109(22), 223903(2012).
[CrossRef]

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]

Colliex, C.

M. Kociak, O. Stephan, L. Henrard, V. Charbois, A. Rothschild, R. Tenne, and C. Colliex, “Experimental evidence of surface-plasmon coupling in anisotropic hollow nanoparticles,” Phys. Rev. Lett.87(7), 075501(2001).
[CrossRef] [PubMed]

Cui, T. J.

Q. Cheng, W. X. Jiang, and T. J. Cui, “Spatial power combination for omnidirectional radiation via anisotropic metamaterials,” Phys. Rev. Lett.108(21), 213903(2012).
[CrossRef] [PubMed]

D’Aguanno, G.

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alu, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett.108(26), 263905(2012).
[CrossRef] [PubMed]

Del Fatti, N.

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, N. Del Fatti, F. Vallee, and P. F. Brevet, “Fano profiles induced by near-field coupling in heterogeneous dimers of gold and silver nanoparticles,” Phys. Rev. Lett.101(19), 197401(2008).
[CrossRef] [PubMed]

Dorpe, P. V.

F. Hao, P. Nordlander, Y. Sonnefraud, P. V. Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and Fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano3(3), 643–652(2009).
[CrossRef] [PubMed]

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988(2008).
[CrossRef] [PubMed]

Fang, Z. Y.

Z. Y. Fang, J. Y. Cai, Z. B. Yan, P. Nordlander, N. J. Halas, and X. Zhu, “Removing a wedge from a metallic nanodisk reveals a Fano resonance,” Nano Lett.11(10), 4475–4479(2011).
[CrossRef] [PubMed]

Fano, U.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev.124(6), 1866–1878(1961).
[CrossRef]

Flach, S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys.82(3), 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(4), 043903(2008).
[CrossRef] [PubMed]

Gao, D. L.

Y. W. Jin, D. L. Gao, and L. Gao, “Plasmonic resonant light scattering by a cylinder with radial anisotropy,” Prog. Electromag. Res.106, 335–347(2010).
[CrossRef]

Gao, L.

H. L. Chen and L. Gao, “Anomalous electromagnetic scattering from radially anisotropic nanowires,” Phys. Rev. A86(3), 033825(2012).
[CrossRef]

Y. W. Jin, D. L. Gao, and L. Gao, “Plasmonic resonant light scattering by a cylinder with radial anisotropy,” Prog. Electromag. Res.106, 335–347(2010).
[CrossRef]

Y. X. Ni, L. Gao, and C. W. Qiu, “Achieving invisibility of homogeneous cylindrically anisotropic cylinders,” Plasmonics5(3), 251–258(2010).
[CrossRef]

X. P. Yu and L. Gao, “Nonlinear dielectric response in partially resonant composites with radial dielectric anisotropy,” Phys. Lett. A359(5), 516–522(2006).
[CrossRef]

Garriga, M.

O. Pena-Rodriguez, U. Pal, M. Campoy-Quiles, L. Rodriguez-Fernandez, M. Garriga, and M. I. Alonso, “Enhanced Fano resonance in asymmetrical Au:Ag heterodimers,” J. Phys. Chem. C115(14), 6410–6414(2011).
[CrossRef]

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(4), 043903(2008).
[CrossRef] [PubMed]

Halas, N. J.

Z. Y. Fang, J. Y. Cai, Z. B. Yan, P. Nordlander, N. J. Halas, and X. Zhu, “Removing a wedge from a metallic nanodisk reveals a Fano resonance,” Nano Lett.11(10), 4475–4479(2011).
[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. Mukherjee, H. Sobhani, J. B. Lassiter, R. Bardhan, P. Nordlander, and N. J. Halas, “Fanoshells: nanoparticles with built-in Fano resonances,” Nano Lett.10(7), 2694–2701(2010).
[CrossRef] [PubMed]

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988(2008).
[CrossRef] [PubMed]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science302(5644), 419–422(2003).
[CrossRef] [PubMed]

Hao, F.

F. Hao, P. Nordlander, Y. Sonnefraud, P. V. Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and Fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano3(3), 643–652(2009).
[CrossRef] [PubMed]

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988(2008).
[CrossRef] [PubMed]

Hao, Z. H.

Z. J. Yang, Z. S. Zhang, W. Zhang, Z. H. Hao, and Q. Q. Wang, “Twinned Fano interferences induced by hybridized plasmons in Au-Ag nanorod heterodimers,” Appl. Phys. Lett.96(13), 131113(2010).
[CrossRef]

Henrard, L.

D. Taverna, M. Kociak, V. Charbois, and L. Henrard, “Electron energy-loss spectrum of an electron passing near a locally anisotropic nanotube,” Phys. Rev. B66(23), 235419(2002).
[CrossRef]

M. Kociak, O. Stephan, L. Henrard, V. Charbois, A. Rothschild, R. Tenne, and C. Colliex, “Experimental evidence of surface-plasmon coupling in anisotropic hollow nanoparticles,” Phys. Rev. Lett.87(7), 075501(2001).
[CrossRef] [PubMed]

Huang, Z. L.

S. Xu, X. X. Cheng, R. R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. L. Huang, X. M. Zhang, F. X. Yu, B. L. Zhang, and H. S. Chen, “Experimental Demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett.109(22), 223903(2012).
[CrossRef]

Jain, P. K.

S. Sheikholeslami, Y. W. Jun, P. K. Jain, and A. P. Alivisatos, “Coupling of optical resonances in a compositionally asymmetric plasmonic nanoparticle dimer,” Nano Lett.10(7), 2655–2660(2010).
[CrossRef] [PubMed]

Jiang, W. X.

Q. Cheng, W. X. Jiang, and T. J. Cui, “Spatial power combination for omnidirectional radiation via anisotropic metamaterials,” Phys. Rev. Lett.108(21), 213903(2012).
[CrossRef] [PubMed]

Jin, Y. W.

Y. W. Jin, D. L. Gao, and L. Gao, “Plasmonic resonant light scattering by a cylinder with radial anisotropy,” Prog. Electromag. Res.106, 335–347(2010).
[CrossRef]

Jonin, C.

J. Butet, G. Bachelier, I. Russier-Antoine, F. Bertorelle, A. Mosset, N. Lascoux, C. Jonin, E. Benichou, and P. F. Brevet, “Nonlinear Fano profiles in the optical second-harmonic generation from silver nanoparticles,” Phys. Rev. B86(7), 075430(2012).
[CrossRef]

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, N. Del Fatti, F. Vallee, and P. F. Brevet, “Fano profiles induced by near-field coupling in heterogeneous dimers of gold and silver nanoparticles,” Phys. Rev. Lett.101(19), 197401(2008).
[CrossRef] [PubMed]

Jun, Y. W.

S. Sheikholeslami, Y. W. Jun, P. K. Jain, and A. P. Alivisatos, “Coupling of optical resonances in a compositionally asymmetric plasmonic nanoparticle dimer,” Nano Lett.10(7), 2655–2660(2010).
[CrossRef] [PubMed]

Kauranen, M.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics6, 737–748(2012).
[CrossRef]

Kivshar, Y. S.

B. S. Luk’yanchuk, A. E. Miroshnichenko, and Y. S. Kivshar, “Fano resonances and topological optics: an interplay of far- and near-field interference phenomena,” J. Opt.15(7), 073001 (2013).
[CrossRef]

M. I. Tribelksy, A. E. Miroshnichenko, and Y. S. Kivshar, “Unconventional Fano resonances in light scattering by small particles,” Europhys. Lett.97(4), 44005(2012).
[CrossRef]

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys.82(3), 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(4), 043903(2008).
[CrossRef] [PubMed]

Kociak, M.

D. Taverna, M. Kociak, V. Charbois, and L. Henrard, “Electron energy-loss spectrum of an electron passing near a locally anisotropic nanotube,” Phys. Rev. B66(23), 235419(2002).
[CrossRef]

M. Kociak, O. Stephan, L. Henrard, V. Charbois, A. Rothschild, R. Tenne, and C. Colliex, “Experimental evidence of surface-plasmon coupling in anisotropic hollow nanoparticles,” Phys. Rev. Lett.87(7), 075501(2001).
[CrossRef] [PubMed]

Kong, J. A.

X. Sheng, H.S. Chen, B. L. Zhang, B. I. Wu, and J. A. Kong, “Route to low-scattering cylindrical cloaks with finite permittivity and permeability,” Phys. Rev. A79(15), 155122(2009).

Lascoux, N.

J. Butet, G. Bachelier, I. Russier-Antoine, F. Bertorelle, A. Mosset, N. Lascoux, C. Jonin, E. Benichou, and P. F. Brevet, “Nonlinear Fano profiles in the optical second-harmonic generation from silver nanoparticles,” Phys. Rev. B86(7), 075430(2012).
[CrossRef]

Lassiter, J. B.

S. Mukherjee, H. Sobhani, J. B. Lassiter, R. Bardhan, P. Nordlander, and N. J. Halas, “Fanoshells: nanoparticles with built-in Fano resonances,” Nano Lett.10(7), 2694–2701(2010).
[CrossRef] [PubMed]

Liang, S. M.

D. J. Wu, S. M. Liang, and X. J. Liu, “A tunable Fano resonance in silver nanoshell with a spherically anisotropic core,” J. Chem. Phys.136(3), 034502(2012).
[CrossRef] [PubMed]

Liang, Y.

K. C. Woo, L. Shao, H. J. Chen, Y. Liang, J. F. Wang, and H. Q. Lin, “Universal scaling and Fano resonance in the plasmon coupling between gold nanorods,” ACS Nano5(7), 5976–5986(2011).
[CrossRef] [PubMed]

Lim, J. H.

Y. Yuan, N. Wang, and J. H. Lim, “On the omnidirectional radiation via radially anisotropic zero-index metamaterials,” EPL100(3), 34005(2012).
[CrossRef]

Lin, H. Q.

K. C. Woo, L. Shao, H. J. Chen, Y. Liang, J. F. Wang, and H. Q. Lin, “Universal scaling and Fano resonance in the plasmon coupling between gold nanorods,” ACS Nano5(7), 5976–5986(2011).
[CrossRef] [PubMed]

Liu, X. J.

D. J. Wu, S. M. Liang, and X. J. Liu, “A tunable Fano resonance in silver nanoshell with a spherically anisotropic core,” J. Chem. Phys.136(3), 034502(2012).
[CrossRef] [PubMed]

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]

Luk’yanchuk, B. S.

B. S. Luk’yanchuk, A. E. Miroshnichenko, and Y. S. Kivshar, “Fano resonances and topological optics: an interplay of far- and near-field interference phenomena,” J. Opt.15(7), 073001 (2013).
[CrossRef]

Maier, S. A.

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]

F. Hao, P. Nordlander, Y. Sonnefraud, P. V. Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and Fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano3(3), 643–652(2009).
[CrossRef] [PubMed]

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988(2008).
[CrossRef] [PubMed]

Man, Y. C.

H. J. Chen, L. Shao, Y. C. Man, C. M. Zhao, J. F. Wang, and B. C. Yang, “Fano resonance in (gold core)-(dielectric shell) nanostructures without symmetry breaking,” Small8(10), 1503–1509(2012).
[CrossRef] [PubMed]

Martinez, A. S.

T. J. Arruda, A. S. Martinez, and F. A. Pinheiro, “Unconventional Fano effect and off-resonance field enhancement in plasmonic coated spheres,” Phys. Rev. A87(4), 043841(2013).
[CrossRef]

T. J. Arruda and A. S. Martinez, “Electromagnetic energy within a magnetic infinite cylinder and scattering properties for oblique incidence,” J. Opt. Soc. Am. A27(7), 1679–1686(2012).
[CrossRef]

T. J. Arruda, F. A. Pinheiro, and A. S. Martinez, “Electromagnetic energy within coated spheres containing dispersive metamaterials,” J. Opt.14(6), 065101(2012).
[CrossRef]

Miroshnichenko, A. E.

B. S. Luk’yanchuk, A. E. Miroshnichenko, and Y. S. Kivshar, “Fano resonances and topological optics: an interplay of far- and near-field interference phenomena,” J. Opt.15(7), 073001 (2013).
[CrossRef]

M. I. Tribelksy, A. E. Miroshnichenko, and Y. S. Kivshar, “Unconventional Fano resonances in light scattering by small particles,” Europhys. Lett.97(4), 44005(2012).
[CrossRef]

A. E. Miroshnichenko, “Off-resonance field enhancement by spherical nanoshells,” Phys. Rev. A81(5), 053818 (2010).
[CrossRef]

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys.82(3), 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(4), 043903(2008).
[CrossRef] [PubMed]

Monticone, F.

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alu, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett.108(26), 263905(2012).
[CrossRef] [PubMed]

Moser, H. O.

S. Xu, X. X. Cheng, R. R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. L. Huang, X. M. Zhang, F. X. Yu, B. L. Zhang, and H. S. Chen, “Experimental Demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett.109(22), 223903(2012).
[CrossRef]

Mosset, A.

J. Butet, G. Bachelier, I. Russier-Antoine, F. Bertorelle, A. Mosset, N. Lascoux, C. Jonin, E. Benichou, and P. F. Brevet, “Nonlinear Fano profiles in the optical second-harmonic generation from silver nanoparticles,” Phys. Rev. B86(7), 075430(2012).
[CrossRef]

Mukherjee, S.

S. Mukherjee, H. Sobhani, J. B. Lassiter, R. Bardhan, P. Nordlander, and N. J. Halas, “Fanoshells: nanoparticles with built-in Fano resonances,” Nano Lett.10(7), 2694–2701(2010).
[CrossRef] [PubMed]

Ni, Y. X.

Y. X. Ni, L. Gao, and C. W. Qiu, “Achieving invisibility of homogeneous cylindrically anisotropic cylinders,” Plasmonics5(3), 251–258(2010).
[CrossRef]

Nordlander, P.

Z. Y. Fang, J. Y. Cai, Z. B. Yan, P. Nordlander, N. J. Halas, and X. Zhu, “Removing a wedge from a metallic nanodisk reveals a Fano resonance,” Nano Lett.11(10), 4475–4479(2011).
[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. Mukherjee, H. Sobhani, J. B. Lassiter, R. Bardhan, P. Nordlander, and N. J. Halas, “Fanoshells: nanoparticles with built-in Fano resonances,” Nano Lett.10(7), 2694–2701(2010).
[CrossRef] [PubMed]

F. Hao, P. Nordlander, Y. Sonnefraud, P. V. Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and Fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano3(3), 643–652(2009).
[CrossRef] [PubMed]

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988(2008).
[CrossRef] [PubMed]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science302(5644), 419–422(2003).
[CrossRef] [PubMed]

Pal, U.

O. Pena-Rodriguez and U. Pal, “Au/Ag core-shell nanoparticles: efficient all-plasmonic Fano-resonance generators,” Nanoscale3(9), 3609–3612(2011).
[CrossRef] [PubMed]

O. Pena-Rodriguez, U. Pal, M. Campoy-Quiles, L. Rodriguez-Fernandez, M. Garriga, and M. I. Alonso, “Enhanced Fano resonance in asymmetrical Au:Ag heterodimers,” J. Phys. Chem. C115(14), 6410–6414(2011).
[CrossRef]

Pena-Rodriguez, O.

O. Pena-Rodriguez, U. Pal, M. Campoy-Quiles, L. Rodriguez-Fernandez, M. Garriga, and M. I. Alonso, “Enhanced Fano resonance in asymmetrical Au:Ag heterodimers,” J. Phys. Chem. C115(14), 6410–6414(2011).
[CrossRef]

O. Pena-Rodriguez and U. Pal, “Au/Ag core-shell nanoparticles: efficient all-plasmonic Fano-resonance generators,” Nanoscale3(9), 3609–3612(2011).
[CrossRef] [PubMed]

Pinheiro, F. A.

T. J. Arruda, A. S. Martinez, and F. A. Pinheiro, “Unconventional Fano effect and off-resonance field enhancement in plasmonic coated spheres,” Phys. Rev. A87(4), 043841(2013).
[CrossRef]

T. J. Arruda, F. A. Pinheiro, and A. S. Martinez, “Electromagnetic energy within coated spheres containing dispersive metamaterials,” J. Opt.14(6), 065101(2012).
[CrossRef]

Prodan, E.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science302(5644), 419–422(2003).
[CrossRef] [PubMed]

Qiu, C. W.

Y. X. Ni, L. Gao, and C. W. Qiu, “Achieving invisibility of homogeneous cylindrically anisotropic cylinders,” Plasmonics5(3), 251–258(2010).
[CrossRef]

Radloff, C.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science302(5644), 419–422(2003).
[CrossRef] [PubMed]

Rodriguez-Fernandez, L.

O. Pena-Rodriguez, U. Pal, M. Campoy-Quiles, L. Rodriguez-Fernandez, M. Garriga, and M. I. Alonso, “Enhanced Fano resonance in asymmetrical Au:Ag heterodimers,” J. Phys. Chem. C115(14), 6410–6414(2011).
[CrossRef]

Rothschild, A.

M. Kociak, O. Stephan, L. Henrard, V. Charbois, A. Rothschild, R. Tenne, and C. Colliex, “Experimental evidence of surface-plasmon coupling in anisotropic hollow nanoparticles,” Phys. Rev. Lett.87(7), 075501(2001).
[CrossRef] [PubMed]

Russier-Antoine, I.

J. Butet, G. Bachelier, I. Russier-Antoine, F. Bertorelle, A. Mosset, N. Lascoux, C. Jonin, E. Benichou, and P. F. Brevet, “Nonlinear Fano profiles in the optical second-harmonic generation from silver nanoparticles,” Phys. Rev. B86(7), 075430(2012).
[CrossRef]

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, N. Del Fatti, F. Vallee, and P. F. Brevet, “Fano profiles induced by near-field coupling in heterogeneous dimers of gold and silver nanoparticles,” Phys. Rev. Lett.101(19), 197401(2008).
[CrossRef] [PubMed]

Shao, L.

H. J. Chen, L. Shao, Y. C. Man, C. M. Zhao, J. F. Wang, and B. C. Yang, “Fano resonance in (gold core)-(dielectric shell) nanostructures without symmetry breaking,” Small8(10), 1503–1509(2012).
[CrossRef] [PubMed]

K. C. Woo, L. Shao, H. J. Chen, Y. Liang, J. F. Wang, and H. Q. Lin, “Universal scaling and Fano resonance in the plasmon coupling between gold nanorods,” ACS Nano5(7), 5976–5986(2011).
[CrossRef] [PubMed]

Sheikholeslami, S.

S. Sheikholeslami, Y. W. Jun, P. K. Jain, and A. P. Alivisatos, “Coupling of optical resonances in a compositionally asymmetric plasmonic nanoparticle dimer,” Nano Lett.10(7), 2655–2660(2010).
[CrossRef] [PubMed]

Shen, Z.

S. Xu, X. X. Cheng, R. R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. L. Huang, X. M. Zhang, F. X. Yu, B. L. Zhang, and H. S. Chen, “Experimental Demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett.109(22), 223903(2012).
[CrossRef]

Sheng, X.

X. Sheng, H.S. Chen, B. L. Zhang, B. I. Wu, and J. A. Kong, “Route to low-scattering cylindrical cloaks with finite permittivity and permeability,” Phys. Rev. A79(15), 155122(2009).

Sobhani, H.

S. Mukherjee, H. Sobhani, J. B. Lassiter, R. Bardhan, P. Nordlander, and N. J. Halas, “Fanoshells: nanoparticles with built-in Fano resonances,” Nano Lett.10(7), 2694–2701(2010).
[CrossRef] [PubMed]

Sonnefraud, Y.

F. Hao, P. Nordlander, Y. Sonnefraud, P. V. Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and Fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano3(3), 643–652(2009).
[CrossRef] [PubMed]

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988(2008).
[CrossRef] [PubMed]

Stephan, O.

M. Kociak, O. Stephan, L. Henrard, V. Charbois, A. Rothschild, R. Tenne, and C. Colliex, “Experimental evidence of surface-plasmon coupling in anisotropic hollow nanoparticles,” Phys. Rev. Lett.87(7), 075501(2001).
[CrossRef] [PubMed]

Taverna, D.

D. Taverna, M. Kociak, V. Charbois, and L. Henrard, “Electron energy-loss spectrum of an electron passing near a locally anisotropic nanotube,” Phys. Rev. B66(23), 235419(2002).
[CrossRef]

Tenne, R.

M. Kociak, O. Stephan, L. Henrard, V. Charbois, A. Rothschild, R. Tenne, and C. Colliex, “Experimental evidence of surface-plasmon coupling in anisotropic hollow nanoparticles,” Phys. Rev. Lett.87(7), 075501(2001).
[CrossRef] [PubMed]

Tribelksy, M. I.

M. I. Tribelksy, A. E. Miroshnichenko, and Y. S. Kivshar, “Unconventional Fano resonances in light scattering by small particles,” Europhys. Lett.97(4), 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(4), 043903(2008).
[CrossRef] [PubMed]

Vallee, F.

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, N. Del Fatti, F. Vallee, and P. F. Brevet, “Fano profiles induced by near-field coupling in heterogeneous dimers of gold and silver nanoparticles,” Phys. Rev. Lett.101(19), 197401(2008).
[CrossRef] [PubMed]

Wang, J. F.

H. J. Chen, L. Shao, Y. C. Man, C. M. Zhao, J. F. Wang, and B. C. Yang, “Fano resonance in (gold core)-(dielectric shell) nanostructures without symmetry breaking,” Small8(10), 1503–1509(2012).
[CrossRef] [PubMed]

K. C. Woo, L. Shao, H. J. Chen, Y. Liang, J. F. Wang, and H. Q. Lin, “Universal scaling and Fano resonance in the plasmon coupling between gold nanorods,” ACS Nano5(7), 5976–5986(2011).
[CrossRef] [PubMed]

Wang, N.

Y. Yuan, N. Wang, and J. H. Lim, “On the omnidirectional radiation via radially anisotropic zero-index metamaterials,” EPL100(3), 34005(2012).
[CrossRef]

Wang, Q. Q.

Z. J. Yang, Z. S. Zhang, W. Zhang, Z. H. Hao, and Q. Q. Wang, “Twinned Fano interferences induced by hybridized plasmons in Au-Ag nanorod heterodimers,” Appl. Phys. Lett.96(13), 131113(2010).
[CrossRef]

Woo, K. C.

K. C. Woo, L. Shao, H. J. Chen, Y. Liang, J. F. Wang, and H. Q. Lin, “Universal scaling and Fano resonance in the plasmon coupling between gold nanorods,” ACS Nano5(7), 5976–5986(2011).
[CrossRef] [PubMed]

Wu, B. I.

X. Sheng, H.S. Chen, B. L. Zhang, B. I. Wu, and J. A. Kong, “Route to low-scattering cylindrical cloaks with finite permittivity and permeability,” Phys. Rev. A79(15), 155122(2009).

Wu, D. J.

D. J. Wu, S. M. Liang, and X. J. Liu, “A tunable Fano resonance in silver nanoshell with a spherically anisotropic core,” J. Chem. Phys.136(3), 034502(2012).
[CrossRef] [PubMed]

Xu, S.

S. Xu, X. X. Cheng, R. R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. L. Huang, X. M. Zhang, F. X. Yu, B. L. Zhang, and H. S. Chen, “Experimental Demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett.109(22), 223903(2012).
[CrossRef]

Xu, Y.

S. Xu, X. X. Cheng, R. R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. L. Huang, X. M. Zhang, F. X. Yu, B. L. Zhang, and H. S. Chen, “Experimental Demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett.109(22), 223903(2012).
[CrossRef]

Yan, Z. B.

Z. Y. Fang, J. Y. Cai, Z. B. Yan, P. Nordlander, N. J. Halas, and X. Zhu, “Removing a wedge from a metallic nanodisk reveals a Fano resonance,” Nano Lett.11(10), 4475–4479(2011).
[CrossRef] [PubMed]

Yang, B. C.

H. J. Chen, L. Shao, Y. C. Man, C. M. Zhao, J. F. Wang, and B. C. Yang, “Fano resonance in (gold core)-(dielectric shell) nanostructures without symmetry breaking,” Small8(10), 1503–1509(2012).
[CrossRef] [PubMed]

Yang, Z. J.

Z. J. Yang, Z. S. Zhang, W. Zhang, Z. H. Hao, and Q. Q. Wang, “Twinned Fano interferences induced by hybridized plasmons in Au-Ag nanorod heterodimers,” Appl. Phys. Lett.96(13), 131113(2010).
[CrossRef]

Yu, F. X.

S. Xu, X. X. Cheng, R. R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. L. Huang, X. M. Zhang, F. X. Yu, B. L. Zhang, and H. S. Chen, “Experimental Demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett.109(22), 223903(2012).
[CrossRef]

Yu, X. P.

X. P. Yu and L. Gao, “Nonlinear dielectric response in partially resonant composites with radial dielectric anisotropy,” Phys. Lett. A359(5), 516–522(2006).
[CrossRef]

Yuan, Y.

Y. Yuan, N. Wang, and J. H. Lim, “On the omnidirectional radiation via radially anisotropic zero-index metamaterials,” EPL100(3), 34005(2012).
[CrossRef]

Zayats, A.

Zayats, A. V.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics6, 737–748(2012).
[CrossRef]

Zhang, B. L.

S. Xu, X. X. Cheng, R. R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. L. Huang, X. M. Zhang, F. X. Yu, B. L. Zhang, and H. S. Chen, “Experimental Demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett.109(22), 223903(2012).
[CrossRef]

X. Sheng, H.S. Chen, B. L. Zhang, B. I. Wu, and J. A. Kong, “Route to low-scattering cylindrical cloaks with finite permittivity and permeability,” Phys. Rev. A79(15), 155122(2009).

Zhang, J. J.

Zhang, R. R.

S. Xu, X. X. Cheng, R. R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. L. Huang, X. M. Zhang, F. X. Yu, B. L. Zhang, and H. S. Chen, “Experimental Demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett.109(22), 223903(2012).
[CrossRef]

Zhang, W.

Z. J. Yang, Z. S. Zhang, W. Zhang, Z. H. Hao, and Q. Q. Wang, “Twinned Fano interferences induced by hybridized plasmons in Au-Ag nanorod heterodimers,” Appl. Phys. Lett.96(13), 131113(2010).
[CrossRef]

Zhang, X. M.

S. Xu, X. X. Cheng, R. R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. L. Huang, X. M. Zhang, F. X. Yu, B. L. Zhang, and H. S. Chen, “Experimental Demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett.109(22), 223903(2012).
[CrossRef]

Zhang, Z. S.

Z. J. Yang, Z. S. Zhang, W. Zhang, Z. H. Hao, and Q. Q. Wang, “Twinned Fano interferences induced by hybridized plasmons in Au-Ag nanorod heterodimers,” Appl. Phys. Lett.96(13), 131113(2010).
[CrossRef]

Zhao, C. M.

H. J. Chen, L. Shao, Y. C. Man, C. M. Zhao, J. F. Wang, and B. C. Yang, “Fano resonance in (gold core)-(dielectric shell) nanostructures without symmetry breaking,” Small8(10), 1503–1509(2012).
[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]

Zhu, X.

Z. Y. Fang, J. Y. Cai, Z. B. Yan, P. Nordlander, N. J. Halas, and X. Zhu, “Removing a wedge from a metallic nanodisk reveals a Fano resonance,” Nano Lett.11(10), 4475–4479(2011).
[CrossRef] [PubMed]

ACS Nano

F. Hao, P. Nordlander, Y. Sonnefraud, P. V. Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and Fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano3(3), 643–652(2009).
[CrossRef] [PubMed]

K. C. Woo, L. Shao, H. J. Chen, Y. Liang, J. F. Wang, and H. Q. Lin, “Universal scaling and Fano resonance in the plasmon coupling between gold nanorods,” ACS Nano5(7), 5976–5986(2011).
[CrossRef] [PubMed]

Appl. Phys. Lett.

Z. J. Yang, Z. S. Zhang, W. Zhang, Z. H. Hao, and Q. Q. Wang, “Twinned Fano interferences induced by hybridized plasmons in Au-Ag nanorod heterodimers,” Appl. Phys. Lett.96(13), 131113(2010).
[CrossRef]

EPL

Y. Yuan, N. Wang, and J. H. Lim, “On the omnidirectional radiation via radially anisotropic zero-index metamaterials,” EPL100(3), 34005(2012).
[CrossRef]

Europhys. Lett.

M. I. Tribelksy, A. E. Miroshnichenko, and Y. S. Kivshar, “Unconventional Fano resonances in light scattering by small particles,” Europhys. Lett.97(4), 44005(2012).
[CrossRef]

J. Chem. Phys.

D. J. Wu, S. M. Liang, and X. J. Liu, “A tunable Fano resonance in silver nanoshell with a spherically anisotropic core,” J. Chem. Phys.136(3), 034502(2012).
[CrossRef] [PubMed]

J. Opt.

B. S. Luk’yanchuk, A. E. Miroshnichenko, and Y. S. Kivshar, “Fano resonances and topological optics: an interplay of far- and near-field interference phenomena,” J. Opt.15(7), 073001 (2013).
[CrossRef]

T. J. Arruda, F. A. Pinheiro, and A. S. Martinez, “Electromagnetic energy within coated spheres containing dispersive metamaterials,” J. Opt.14(6), 065101(2012).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. Chem. C

O. Pena-Rodriguez, U. Pal, M. Campoy-Quiles, L. Rodriguez-Fernandez, M. Garriga, and M. I. Alonso, “Enhanced Fano resonance in asymmetrical Au:Ag heterodimers,” J. Phys. Chem. C115(14), 6410–6414(2011).
[CrossRef]

Nano Lett.

S. Mukherjee, H. Sobhani, J. B. Lassiter, R. Bardhan, P. Nordlander, and N. J. Halas, “Fanoshells: nanoparticles with built-in Fano resonances,” Nano Lett.10(7), 2694–2701(2010).
[CrossRef] [PubMed]

S. Sheikholeslami, Y. W. Jun, P. K. Jain, and A. P. Alivisatos, “Coupling of optical resonances in a compositionally asymmetric plasmonic nanoparticle dimer,” Nano Lett.10(7), 2655–2660(2010).
[CrossRef] [PubMed]

Z. Y. Fang, J. Y. Cai, Z. B. Yan, P. Nordlander, N. J. Halas, and X. Zhu, “Removing a wedge from a metallic nanodisk reveals a Fano resonance,” Nano Lett.11(10), 4475–4479(2011).
[CrossRef] [PubMed]

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988(2008).
[CrossRef] [PubMed]

Nanoscale

O. Pena-Rodriguez and U. Pal, “Au/Ag core-shell nanoparticles: efficient all-plasmonic Fano-resonance generators,” Nanoscale3(9), 3609–3612(2011).
[CrossRef] [PubMed]

Nat. Mater.

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

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics6, 737–748(2012).
[CrossRef]

Opt. Express

Phys. Lett. A

X. P. Yu and L. Gao, “Nonlinear dielectric response in partially resonant composites with radial dielectric anisotropy,” Phys. Lett. A359(5), 516–522(2006).
[CrossRef]

Phys. Rev.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev.124(6), 1866–1878(1961).
[CrossRef]

Phys. Rev. A

A. E. Miroshnichenko, “Off-resonance field enhancement by spherical nanoshells,” Phys. Rev. A81(5), 053818 (2010).
[CrossRef]

H. L. Chen and L. Gao, “Anomalous electromagnetic scattering from radially anisotropic nanowires,” Phys. Rev. A86(3), 033825(2012).
[CrossRef]

T. J. Arruda, A. S. Martinez, and F. A. Pinheiro, “Unconventional Fano effect and off-resonance field enhancement in plasmonic coated spheres,” Phys. Rev. A87(4), 043841(2013).
[CrossRef]

X. Sheng, H.S. Chen, B. L. Zhang, B. I. Wu, and J. A. Kong, “Route to low-scattering cylindrical cloaks with finite permittivity and permeability,” Phys. Rev. A79(15), 155122(2009).

Phys. Rev. B

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Phys. Rev. Lett.

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alu, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett.108(26), 263905(2012).
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S. Xu, X. X. Cheng, R. R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. L. Huang, X. M. Zhang, F. X. Yu, B. L. Zhang, and H. S. Chen, “Experimental Demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett.109(22), 223903(2012).
[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(4), 043903(2008).
[CrossRef] [PubMed]

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, N. Del Fatti, F. Vallee, and P. F. Brevet, “Fano profiles induced by near-field coupling in heterogeneous dimers of gold and silver nanoparticles,” Phys. Rev. Lett.101(19), 197401(2008).
[CrossRef] [PubMed]

Plasmonics

Y. X. Ni, L. Gao, and C. W. Qiu, “Achieving invisibility of homogeneous cylindrically anisotropic cylinders,” Plasmonics5(3), 251–258(2010).
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Prog. Electromag. Res.

Y. W. Jin, D. L. Gao, and L. Gao, “Plasmonic resonant light scattering by a cylinder with radial anisotropy,” Prog. Electromag. Res.106, 335–347(2010).
[CrossRef]

Rev. Mod. Phys.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys.82(3), 2257–2298(2010).
[CrossRef]

Science

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science302(5644), 419–422(2003).
[CrossRef] [PubMed]

Small

H. J. Chen, L. Shao, Y. C. Man, C. M. Zhao, J. F. Wang, and B. C. Yang, “Fano resonance in (gold core)-(dielectric shell) nanostructures without symmetry breaking,” Small8(10), 1503–1509(2012).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Geometry of the infinitely-long coated nanowire. The incident wave propagates in the direction of x.

Fig. 2
Fig. 2

(a) Extinction efficiency Qext as a function of the incident wavelength λ and the aspect ratio η for εcr = εcθ = 2 and b = 30nm. (b) The resonant efficiency and (c) the cloaking efficiency where the small efficiency and the large efficiency are, respectively, marked in gray. Resonant scattering (red solid line) and cloaking (blue solid line) conditions are also shown.

Fig. 3
Fig. 3

Extinction efficiency (Qext) versus the incident wavelength from the coated nanocylinders [Fig. 3(a)] and coated nanospheres [Fig. 3(c)] for a = 1nm and b = 30nm. To understand the Fano-like profiles, the cloaking (blue solid line) and resonant scattering (red dash line) are shown for the cylindrical (spherical) case in Fig. 3(b) [Fig. 3(d)].

Fig. 4
Fig. 4

Distributions of the magnetic fields for (a) high-energy asymmetrical dipolar resonant scattering wavelength [point I with λ = 345.671nm in Fig. 3(a)], (b) dipolar cloaking wavelength [point II with λ = 364.961nm in Fig. 3(a)], and (c) low-energy symmetric dipolar resonant scattering wavelength [point III with λ = 365.379nm in Fig. 3(a)].

Fig. 5
Fig. 5

Extinction efficiency of dipole modes versus the incident wavelength for various core radii. Other parameters are εcr = εcθ = 2 and b = 100nm.

Fig. 6
Fig. 6

Extinction efficiency versus wavelength for a = 10nm and b = 100nm. In comparison, we keep εce = 2, with various εcr (or εcθ) such as εcr = 1/32 (navy dash dot line), εcr = 1/8 (magenta dash line), εcr = 1/2 (blue dot line), εcr = 2 (black solid line), εcr = 8 (red dot line), εcr = 32 (olive dash line), and εcr = 128 (violet dash dot line).

Equations (22)

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ε i = ( ε i r 0 0 0 ε i θ 0 0 0 ε i z ) , μ i = ( μ i r 0 0 0 μ i θ 0 0 0 μ i z ) , i = c , s
× H = i ω ε 0 ε i E and × E = i ω μ 0 μ i H .
1 r [ r ( r ε i θ H z r ) ] + 1 r 2 θ ( 1 ε i r H z θ ) + ω 2 ε 0 μ 0 μ i z H z = 0.
r 2 d 2 Φ ( r ) d r 2 + r d Φ ( r ) d r + ( ω 2 ε 0 μ 0 ε i θ μ i z r 2 m 2 ε i θ ε i r ) Φ ( r ) = 0.
H z = m = i m A m J c m ( k c r ) e i m θ , r < a ,
H z = m = i m [ B m J s m ( k s r ) + C m N s m ( k s r ) ] e i m θ , a < r < b ,
H z = m = i m [ J m ( k 0 r ) + D m H m ( k 0 r ) ] e i m θ , r > b ,
A m = | 0 J s m ( k s a ) N s m ( k s a ) 0 0 k s J s m ( k s a ) k s N s m ( k s a ) 0 J m ( k 0 b ) J s m ( k s b ) N s m ( k s b ) H m ( k 0 b ) k 0 J m ( k 0 b ) 1 ε s θ k s J s m ( k s b ) 1 ε s θ k s N s m ( k s b ) k 0 H m ( k 0 b ) | | J c m ( k c a ) J s m ( k s a ) N s m ( k s a ) 0 ε s θ ε c θ k c J c m ( k c a ) k s J s m ( k s a ) k s N s m ( k s a ) 0 0 J s m ( k s b ) N s m ( k s b ) H m ( k 0 b ) 0 1 ε s θ k s J s m ( k s b ) 1 ε s θ k s N s m ( k s b ) k 0 H m ( k 0 b ) | ,
B m = | J c m ( k c a ) 0 N s m ( k s a ) 0 ε s θ ε c θ k c J c m ( k c a ) 0 k s N s m ( k s a ) 0 0 J m ( k 0 b ) N s m ( k s b ) H m ( k 0 b ) 0 k 0 J m ( k 0 b ) 1 ε s θ k s N s m ( k s b ) k 0 H m ( k 0 b ) | | J c m ( k c a ) J s m ( k s a ) N s m ( k s a ) 0 ε s θ ε c θ k c J c m ( k c a ) k s J s m ( k s a ) k s N s m ( k s a ) 0 0 J s m ( k s b ) N s m ( k s b ) H m ( k 0 b ) 0 1 ε s θ k s J s m ( k s b ) 1 ε s θ k s N s m ( k s b ) k 0 H m ( k 0 b ) | ,
C m = | J c m ( k c a ) J s m ( k s a ) 0 0 ε s θ ε c θ k c J c m ( k c a ) k s J s m ( k s a ) 0 0 0 J s m ( k s b ) J m ( k 0 b ) H m ( k 0 b ) 0 1 ε s θ k s J s m ( k s b ) k 0 J m ( k 0 b ) k 0 H m ( k 0 b ) | | J c m ( k c a ) J s m ( k s a ) N s m ( k s a ) 0 ε s θ ε c θ k c J c m ( k c a ) k s J s m ( k s a ) k s N s m ( k s a ) 0 0 J s m ( k s b ) N s m ( k s b ) H m ( k 0 b ) 0 1 ε s θ k s J s m ( k s b ) 1 ε s θ k s N s m ( k s b ) k 0 H m ( k 0 b ) | ,
D m = | J c m ( k c a ) J s m ( k s a ) N s m ( k s a ) 0 ε s θ ε c θ k c J c m ( k c a ) k s J s m ( k s a ) k s N s m ( k s a ) 0 0 J s m ( k s b ) N s m ( k s b ) J m ( k 0 b ) 0 1 ε s θ k s J s m ( k s b ) 1 ε s θ k s N s m ( k s b ) k 0 J m ( k 0 b ) | | J c m ( k c a ) J s m ( k s a ) N s m ( k s a ) 0 ε s θ ε c θ k c J c m ( k c a ) k s J s m ( k s a ) k s N s m ( k s a ) 0 0 J s m ( k s b ) N s m ( k s b ) H m ( k 0 b ) 0 1 ε s θ k s J s m ( k s b ) 1 ε s θ k s N s m ( k s b ) k 0 H m ( k 0 b ) | .
H z = N M + P c Q ( r a ) ε c θ / ε c r , r < a , H z = N M + P s Q , a < r < b , H z = P o Q , r > b ,
N = i π 2 [ 2 b + b k 0 2 ln ( k 0 b 2 ) ] [ 2 a + a k s 2 ln ( k s a 2 ) ] ,
M = ( 1 + 2 i ln ( k 0 b / 2 ) π ) [ b k s 2 π ( 1 a ε s + a k 0 2 ln ( k s a / 2 ) 2 ) ] + ( 2 i b π b k 0 2 2 ) [ 2 π a + k s 2 π ln ( k s b / 2 ) + a k 0 2 ε s π ln ( a / b ) ] ,
P c = 8 a b 2 k 0 ε s ε c r ε c θ ,
P s = 4 b 2 k 0 ε s r [ a 2 ( ε c r ε c θ ε s ) + r 2 ( ε c r ε c θ + ε s ) ] ,
P o = i b 2 k 0 2 r ( k 0 2 r 2 π 4 i ) [ a 2 ( ε c r ε c θ ε s ) ( 1 + ε s ) + b 2 ( ε c r ε c θ + ε s ) ( 1 ε s ) ] ,
Q = b 2 ( ε c r ε c θ + ε s ) [ 4 i b 2 k 0 2 π + ε s ( 4 i + b 2 k 0 2 π ) ] + a 2 ( ε c r ε c θ ε s ) [ b 2 k 0 2 π 4 i + ε s ( 4 i + b 2 k 0 2 π ) ] .
η ( ε c r ε c θ ε s ) ( ε s 1 ) + ( ε c r ε c θ + ε s ) ( ε s + 1 ) = 0 ,
η ( ε c r ε c θ ε s ) ( ε s + 1 ) + ( ε c r ε c θ + ε s ) ( ε s 1 ) = 0
ε c r ε c θ = ε s .
F ( ε ) = σ 0 ( ε + q ) 2 1 + ε 2

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