Abstract

We address electromagnetic (EM) wave scattering by an infinite coated cylinder at an arbitrary incidence angle. The time-averaged EM energy stored inside the core-shell cylinder is analytically calculated for TM- and TE-polarized incident plane waves. An analytical expression relating the internal energy to the absorption cross section is derived. As an application, the EM energy inside dielectric cylinders coated with isotropic graphene layers epitaxially grown on silicon carbide (SiC) is studied. We find that off-resonance field enhancement occurs in graphene SiC microshells for TM-polarized terahertz waves, a phenomenon that can be explained in terms of Fano resonances.

© 2014 Optical Society of America

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    [CrossRef]
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  4. B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. 103, 153901 (2009).
    [CrossRef]
  5. A. Alù, D. Rainwater, and A. Kerkhoff, “Plasmonic cloaking of cylinders: finite length, oblique illumination and cross-polarization coupling,” New J. Phys. 12, 103028 (2010).
    [CrossRef]
  6. W. J. M. Kort-Kamp, F. S. S. Rosa, F. A. Pinheiro, and C. Farina, “Tuning plasmonic cloaks with an external magnetic field,” Phys. Rev. Lett. 111, 215504 (2013).
    [CrossRef]
  7. J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
    [CrossRef]
  8. A. C. Lind and J. M. Greenberg, “Electromagnetic scattering by obliquely oriented cylinders,” J. Appl. Phys. 37, 3195–3203 (1966).
    [CrossRef]
  9. M. Kerker and E. Matijevic, “Scattering of electromagnetic waves from concentric infinite cylinders,” J. Opt. Soc. Am. 51, 506–508 (1961).
    [CrossRef]
  10. G. A. Shah, “Scattering of plane electromagnetic waves by infinite concentric circular cylinders at oblique incidence,” Mon. Not. R. Astron. Soc. 148, 93–102 (1970).
  11. R. Ruppin, “Electromagnetic energy inside an irradiated cylinder,” J. Opt. Soc. Am. A 15, 1891–1895 (1998).
    [CrossRef]
  12. T. J. Arruda and A. S. Martinez, “Electromagnetic energy within a magnetic infinite cylinder and scattering properties for oblique incidence,” J. Opt. Soc. Am. A 27, 1679–1687 (2010).
    [CrossRef]
  13. A. Bott and W. Zdunkowski, “Electromagnetic energy within dielectric spheres,” J. Opt. Soc. Am. A 4, 1361–1365 (1987).
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    [CrossRef]
  16. B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, and A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
    [CrossRef]
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    [CrossRef]
  18. T. J. Arruda, F. A. Pinheiro, and A. S. Martinez, “Electromagnetic energy within coated spheres containing dispersive metamaterials,” J. Opt. 14, 065101 (2012).
    [CrossRef]
  19. T. J. Arruda, F. A. Pinheiro, and A. S. Martinez, “Electromagnetic energy within single-resonance chiral metamaterial spheres,” J. Opt. Soc. Am. A 30, 1205–1212 (2013).
    [CrossRef]
  20. A. E. Miroshnichenko, “Off-resonance field enhancement by spherical nanoshells,” Phys. Rev. A 81, 053818 (2010).
    [CrossRef]
  21. 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, 073001 (2013).
    [CrossRef]
  22. M. I. Tribelsky, A. E. Miroshnichenko, and Y. S. Kivshar, “Unconventional Fano resonances in light scattering by small particles,” Europhys. Lett. 97, 44005 (2012).
    [CrossRef]
  23. T. J. Arruda, A. S. Martinez, and F. A. Pinheiro, “Unconventional Fano effect and off-resonance field enhancement in plasmonic coated spheres,” Phys. Rev. A 87, 043841 (2013).
    [CrossRef]
  24. H. L. Chen and L. Gao, “Tunablity of the unconventional Fano resonances in coated nanowires with radial anisotropy,” Opt. Express 21, 23619–23630 (2013).
    [CrossRef]
  25. U. Schroter and A. Dereux, “Surface plasmon polaritons on metal cylinders with dielectric core,” Phys. Rev. B 64, 125420 (2001).
    [CrossRef]
  26. Y. Jin, P. Zhang, and S. He, “Abnormal enhancement of electric field inside a thin permittivity-near-zero object in free space,” Phys. Rev. B 82, 075118 (2010).
    [CrossRef]
  27. I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, Th. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).
    [CrossRef]
  28. S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108, 047401 (2012).
    [CrossRef]
  29. F. A. Pinheiro, A. S. Martinez, and L. C. Sampaio, “New effects in light scattering in disordered media and coherent backscattering cone: system of magnetic particles,” Phys. Rev. Lett. 84, 1435–1438 (2000).
    [CrossRef]
  30. F. A. Pinheiro, A. S. Martinez, and L. C. Sampaio, “Vanishing of energy transport velocity and diffusion constant of electromagnetic waves in disordered magnetic media,” Phys. Rev. Lett. 85, 5563–5566 (2000).
    [CrossRef]
  31. L. D. Landau and E. M. Lifshits, Electrodynamics of Continuous Media (Pergamon, 1984).
  32. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University, 1958).
  33. P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990).
  34. R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” J. Phys. A 3, 233–245 (1970).
    [CrossRef]
  35. R. Ruppin, “Electromagnetic energy density in a dispersive and absorptive material,” Phys. Lett. A 299, 309–312 (2002).
    [CrossRef]
  36. L. Gao and Y. Huang, “Extinction properties of a coated sphere containing a left-handed material,” Opt. Commun. 239, 25–31 (2004).
    [CrossRef]
  37. 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]

2013 (5)

W. J. M. Kort-Kamp, F. S. S. Rosa, F. A. Pinheiro, and C. Farina, “Tuning plasmonic cloaks with an external magnetic field,” Phys. Rev. Lett. 111, 215504 (2013).
[CrossRef]

T. J. Arruda, F. A. Pinheiro, and A. S. Martinez, “Electromagnetic energy within single-resonance chiral metamaterial spheres,” J. Opt. Soc. Am. A 30, 1205–1212 (2013).
[CrossRef]

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, 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. A 87, 043841 (2013).
[CrossRef]

H. L. Chen and L. Gao, “Tunablity of the unconventional Fano resonances in coated nanowires with radial anisotropy,” Opt. Express 21, 23619–23630 (2013).
[CrossRef]

2012 (4)

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

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, Th. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).
[CrossRef]

S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108, 047401 (2012).
[CrossRef]

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

2011 (1)

R. Ruppin, “Electric and magnetic energies within dispersive metamaterial spheres,” J. Opt. 13, 095101 (2011).
[CrossRef]

2010 (6)

T. J. Arruda and A. S. Martinez, “Electromagnetic energy within a magnetic sphere,” J. Opt. Soc. Am. A 27, 992–1001 (2010).
[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. A 27, 1679–1687 (2010).
[CrossRef]

A. Alù, D. Rainwater, and A. Kerkhoff, “Plasmonic cloaking of cylinders: finite length, oblique illumination and cross-polarization coupling,” New J. Phys. 12, 103028 (2010).
[CrossRef]

A. E. Miroshnichenko, “Off-resonance field enhancement by spherical nanoshells,” Phys. Rev. A 81, 053818 (2010).
[CrossRef]

Y. Jin, P. Zhang, and S. He, “Abnormal enhancement of electric field inside a thin permittivity-near-zero object in free space,” Phys. Rev. B 82, 075118 (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]

2009 (1)

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. 103, 153901 (2009).
[CrossRef]

2004 (1)

L. Gao and Y. Huang, “Extinction properties of a coated sphere containing a left-handed material,” Opt. Commun. 239, 25–31 (2004).
[CrossRef]

2002 (1)

R. Ruppin, “Electromagnetic energy density in a dispersive and absorptive material,” Phys. Lett. A 299, 309–312 (2002).
[CrossRef]

2001 (1)

U. Schroter and A. Dereux, “Surface plasmon polaritons on metal cylinders with dielectric core,” Phys. Rev. B 64, 125420 (2001).
[CrossRef]

2000 (2)

F. A. Pinheiro, A. S. Martinez, and L. C. Sampaio, “New effects in light scattering in disordered media and coherent backscattering cone: system of magnetic particles,” Phys. Rev. Lett. 84, 1435–1438 (2000).
[CrossRef]

F. A. Pinheiro, A. S. Martinez, and L. C. Sampaio, “Vanishing of energy transport velocity and diffusion constant of electromagnetic waves in disordered magnetic media,” Phys. Rev. Lett. 85, 5563–5566 (2000).
[CrossRef]

1998 (2)

1992 (1)

B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, and A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
[CrossRef]

1987 (1)

1970 (2)

G. A. Shah, “Scattering of plane electromagnetic waves by infinite concentric circular cylinders at oblique incidence,” Mon. Not. R. Astron. Soc. 148, 93–102 (1970).

R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” J. Phys. A 3, 233–245 (1970).
[CrossRef]

1966 (1)

A. C. Lind and J. M. Greenberg, “Electromagnetic scattering by obliquely oriented cylinders,” J. Appl. Phys. 37, 3195–3203 (1966).
[CrossRef]

1961 (1)

1955 (1)

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
[CrossRef]

1918 (1)

L. Rayleigh, “The dispersal of light by a dielectric cylinder,” Philos. Mag. 36(215), 365–376 (1918).
[CrossRef]

Alù, A.

A. Alù, D. Rainwater, and A. Kerkhoff, “Plasmonic cloaking of cylinders: finite length, oblique illumination and cross-polarization coupling,” New J. Phys. 12, 103028 (2010).
[CrossRef]

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. 103, 153901 (2009).
[CrossRef]

Arruda, T. J.

Barber, P. W.

P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990).

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Bott, A.

Chen, H. L.

Chen, J.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, Th. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (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]

Crassee, I.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, Th. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).
[CrossRef]

de Abajo, F. J. G.

S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108, 047401 (2012).
[CrossRef]

Dereux, A.

U. Schroter and A. Dereux, “Surface plasmon polaritons on metal cylinders with dielectric core,” Phys. Rev. B 64, 125420 (2001).
[CrossRef]

Edwards, B.

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. 103, 153901 (2009).
[CrossRef]

Engheta, N.

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. 103, 153901 (2009).
[CrossRef]

Farina, C.

W. J. M. Kort-Kamp, F. S. S. Rosa, F. A. Pinheiro, and C. Farina, “Tuning plasmonic cloaks with an external magnetic field,” Phys. Rev. Lett. 111, 215504 (2013).
[CrossRef]

Gao, L.

H. L. Chen and L. Gao, “Tunablity of the unconventional Fano resonances in coated nanowires with radial anisotropy,” Opt. Express 21, 23619–23630 (2013).
[CrossRef]

L. Gao and Y. Huang, “Extinction properties of a coated sphere containing a left-handed material,” Opt. Commun. 239, 25–31 (2004).
[CrossRef]

Gaponenko, I.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, Th. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).
[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]

Greenberg, J. M.

A. C. Lind and J. M. Greenberg, “Electromagnetic scattering by obliquely oriented cylinders,” J. Appl. Phys. 37, 3195–3203 (1966).
[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]

He, S.

Y. Jin, P. Zhang, and S. He, “Abnormal enhancement of electric field inside a thin permittivity-near-zero object in free space,” Phys. Rev. B 82, 075118 (2010).
[CrossRef]

Hill, S. C.

P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990).

Huang, Y.

L. Gao and Y. Huang, “Extinction properties of a coated sphere containing a left-handed material,” Opt. Commun. 239, 25–31 (2004).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Jin, Y.

Y. Jin, P. Zhang, and S. He, “Abnormal enhancement of electric field inside a thin permittivity-near-zero object in free space,” Phys. Rev. B 82, 075118 (2010).
[CrossRef]

Kerker, M.

Kerkhoff, A.

A. Alù, D. Rainwater, and A. Kerkhoff, “Plasmonic cloaking of cylinders: finite length, oblique illumination and cross-polarization coupling,” New J. Phys. 12, 103028 (2010).
[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, 073001 (2013).
[CrossRef]

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

Koppens, F. H. L.

S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108, 047401 (2012).
[CrossRef]

Kort-Kamp, W. J. M.

W. J. M. Kort-Kamp, F. S. S. Rosa, F. A. Pinheiro, and C. Farina, “Tuning plasmonic cloaks with an external magnetic field,” Phys. Rev. Lett. 111, 215504 (2013).
[CrossRef]

Kuzmenko, A. B.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, Th. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).
[CrossRef]

Lagendijk, A.

B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, and A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
[CrossRef]

Landau, L. D.

L. D. Landau and E. M. Lifshits, Electrodynamics of Continuous Media (Pergamon, 1984).

Lifshits, E. M.

L. D. Landau and E. M. Lifshits, Electrodynamics of Continuous Media (Pergamon, 1984).

Lind, A. C.

A. C. Lind and J. M. Greenberg, “Electromagnetic scattering by obliquely oriented cylinders,” J. Appl. Phys. 37, 3195–3203 (1966).
[CrossRef]

Loudon, R.

R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” J. Phys. A 3, 233–245 (1970).
[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]

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, 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]

Martinez, A. S.

T. J. Arruda, F. A. Pinheiro, and A. S. Martinez, “Electromagnetic energy within single-resonance chiral metamaterial spheres,” J. Opt. Soc. Am. A 30, 1205–1212 (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. A 87, 043841 (2013).
[CrossRef]

T. J. Arruda, F. A. Pinheiro, and A. S. Martinez, “Electromagnetic energy within coated spheres containing dispersive metamaterials,” J. Opt. 14, 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. A 27, 1679–1687 (2010).
[CrossRef]

T. J. Arruda and A. S. Martinez, “Electromagnetic energy within a magnetic sphere,” J. Opt. Soc. Am. A 27, 992–1001 (2010).
[CrossRef]

F. A. Pinheiro, A. S. Martinez, and L. C. Sampaio, “Vanishing of energy transport velocity and diffusion constant of electromagnetic waves in disordered magnetic media,” Phys. Rev. Lett. 85, 5563–5566 (2000).
[CrossRef]

F. A. Pinheiro, A. S. Martinez, and L. C. Sampaio, “New effects in light scattering in disordered media and coherent backscattering cone: system of magnetic particles,” Phys. Rev. Lett. 84, 1435–1438 (2000).
[CrossRef]

Matijevic, E.

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, 073001 (2013).
[CrossRef]

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

A. E. Miroshnichenko, “Off-resonance field enhancement by spherical nanoshells,” Phys. Rev. A 81, 053818 (2010).
[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]

Orlita, M.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, Th. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).
[CrossRef]

Ostler, M.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, Th. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).
[CrossRef]

Pinheiro, F. A.

W. J. M. Kort-Kamp, F. S. S. Rosa, F. A. Pinheiro, and C. Farina, “Tuning plasmonic cloaks with an external magnetic field,” Phys. Rev. Lett. 111, 215504 (2013).
[CrossRef]

T. J. Arruda, F. A. Pinheiro, and A. S. Martinez, “Electromagnetic energy within single-resonance chiral metamaterial spheres,” J. Opt. Soc. Am. A 30, 1205–1212 (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. A 87, 043841 (2013).
[CrossRef]

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

F. A. Pinheiro, A. S. Martinez, and L. C. Sampaio, “New effects in light scattering in disordered media and coherent backscattering cone: system of magnetic particles,” Phys. Rev. Lett. 84, 1435–1438 (2000).
[CrossRef]

F. A. Pinheiro, A. S. Martinez, and L. C. Sampaio, “Vanishing of energy transport velocity and diffusion constant of electromagnetic waves in disordered magnetic media,” Phys. Rev. Lett. 85, 5563–5566 (2000).
[CrossRef]

Potemski, M.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, Th. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).
[CrossRef]

Rainwater, D.

A. Alù, D. Rainwater, and A. Kerkhoff, “Plasmonic cloaking of cylinders: finite length, oblique illumination and cross-polarization coupling,” New J. Phys. 12, 103028 (2010).
[CrossRef]

Rayleigh, L.

L. Rayleigh, “The dispersal of light by a dielectric cylinder,” Philos. Mag. 36(215), 365–376 (1918).
[CrossRef]

Rosa, F. S. S.

W. J. M. Kort-Kamp, F. S. S. Rosa, F. A. Pinheiro, and C. Farina, “Tuning plasmonic cloaks with an external magnetic field,” Phys. Rev. Lett. 111, 215504 (2013).
[CrossRef]

Ruppin, R.

R. Ruppin, “Electric and magnetic energies within dispersive metamaterial spheres,” J. Opt. 13, 095101 (2011).
[CrossRef]

R. Ruppin, “Electromagnetic energy density in a dispersive and absorptive material,” Phys. Lett. A 299, 309–312 (2002).
[CrossRef]

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[CrossRef]

F. A. Pinheiro, A. S. Martinez, and L. C. Sampaio, “New effects in light scattering in disordered media and coherent backscattering cone: system of magnetic particles,” Phys. Rev. Lett. 84, 1435–1438 (2000).
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[CrossRef]

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[CrossRef]

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[CrossRef]

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

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).
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A. E. Miroshnichenko, “Off-resonance field enhancement by spherical nanoshells,” Phys. Rev. A 81, 053818 (2010).
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T. J. Arruda, A. S. Martinez, and F. A. Pinheiro, “Unconventional Fano effect and off-resonance field enhancement in plasmonic coated spheres,” Phys. Rev. A 87, 043841 (2013).
[CrossRef]

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[CrossRef]

U. Schroter and A. Dereux, “Surface plasmon polaritons on metal cylinders with dielectric core,” Phys. Rev. B 64, 125420 (2001).
[CrossRef]

Y. Jin, P. Zhang, and S. He, “Abnormal enhancement of electric field inside a thin permittivity-near-zero object in free space,” Phys. Rev. B 82, 075118 (2010).
[CrossRef]

Phys. Rev. Lett. (5)

S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108, 047401 (2012).
[CrossRef]

F. A. Pinheiro, A. S. Martinez, and L. C. Sampaio, “New effects in light scattering in disordered media and coherent backscattering cone: system of magnetic particles,” Phys. Rev. Lett. 84, 1435–1438 (2000).
[CrossRef]

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[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Scatterer geometry: a cylinder (ϵ1,μ1) with radius a coated with a cylindrical shell (ϵ2,μ2) with thickness d=ba. (a) A plane wave propagating in the xz plane is incident on the cylinder and makes an angle ζ with z axis. (b) A transverse section of the coated circular cylinder in the xy plane.

Fig. 2.
Fig. 2.

Electric permittivity ϵ2=ϵgra(ω) for the graphene grown on SiC [Eq. (39)] as a function of the frequency f=ω/(2π). Note that one has ϵ2<0 for 16THz<f<9.4THz and 0<ϵ2/ϵ0<1 for 9.4THz<f<15THz.

Fig. 3.
Fig. 3.

EM scattering by a dielectric cylinder (ϵ1/ϵ0=11.7+0.01i; μ1=μ0), with radius a=5μm, coated with a graphene SiC shell [ϵ2=ϵgra(ω); μ2=μ0] [Eq. (39)], with thickness d=1μm, under TM polarization. (a) Extinction efficiency Qext(I), (b) absorption efficiency Qabs(I), and (c) internal energy W1,2(I)/W0, as functions of the frequency f=ω/(2π) for some angles ζ between the incident wave and the cylinder axis. The plasmon resonance (f1.2THz) in the scattering quantities does not coincide with the resonance in the internal energy (f1.0THz).

Fig. 4.
Fig. 4.

EM scattering by a dielectric cylinder (ϵ1/ϵ0=11.7+0.01i; μ1=μ0), with radius a=5μm, with (solid line) and without (dashed line) a graphene coating [ϵ2=ϵgra(ω); μ2=μ0] [Eq. (39)], with thickness d=1μm, under TM polarization. (a) Scattering and absorption efficiencies for the normal incidence (ζ=90°), showing large absorption in the graphene SiC plasmon resonance. The peaks for the (bare) Si cylinder correspond to monopole (n=0), dipole (n=1), quadrupole (n=2), and octupole (n=3) Mie resonances. (b) Internal energy for the normal incidence. There is off-resonance field enhancement due to the graphene SiC coating at f1.0THz.

Fig. 5.
Fig. 5.

EM scattering by a dielectric cylinder (ϵ1/ϵ0=11.7+0.01i; μ1=μ0), with radius a=5μm, with (solid line) and without (dashed line) a graphene SiC layer (ϵ2=ϵgra(ω); μ2=μ0) [Eq. (39)], with thickness d=1μm, under TM polarization. (a) Backscattering efficiency Qback(I). (b) Electric [WE1(I)] and magnetic [WH1(I)] energies within the dielectric cylinder core. (c) Electric [WE2(I)] and magnetic [WH2(I)] energies within the graphene SiC layer. The Fano resonances are due to dipole–quadrupole (f10.2THz) and quadrupole–octupole (f14.0THz) interferences and correspond to large amounts of energy inside the cylindrical core.

Equations (48)

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E1r(I)=in=[dn(I)nJn(ρ1)ρ1cn(I)cosζm1Jn(ρ1)]φn(ϕ,z),
E1ϕ(I)=n=[cn(I)cosζm1nJn(ρ1)ρ1dn(I)Jn(ρ1)]φn(ϕ,z),
E1z(I)=n=cn(I)ρ1m1krJn(ρ1)φn(ϕ,z),
E2r(I)=in=[gn(I)nJn(ρ2)ρ2fn(I)cosζm2Jn(ρ2)+wn(I)nYn(ρ2)ρ2vn(I)cosζm2Yn(ρ2)]φn(ϕ,z),
E2ϕ(I)=n=[fn(I)cosζm2nJn(ρ2)ρ2gn(I)Jn(ρ2)+vn(I)cosζm2nYn(ρ2)ρ2wn(I)Yn(ρ2)]φn(ϕ,z),
E2z(I)=n=ρ2m2kr[fn(I)Jn(ρ2)+vn(I)Yn(ρ2)]φn(ϕ,z),
cn(I)=m1m2η2Jn(η2x)η1Jn(η1x)[AnPn(I)+Qn(I)]VnRn(I),
dn(I)=μ1μ2η2Jn(η2x)η1Jn(η1x)[VnPn(I)+CnQn(I)]γnVnRn(I),
fn(I)=(Anγn2CnWn)Pn(I)+(1γn2CnDn)Qn(I)Rn(I)(VnBnCn),
gn(I)=γnPn(I)Rn(I),
vn(I)=(AnBnγn2VnWn)Pn(I)+(Bnγn2VnDn)Qn(I)Rn(I)(VnBnCn),
wn(I)=γnQn(I)Rn(I),
cn(II)=m1m2η2Jn(η2x)η1Jn(η1x)[WnPn(II)+DnQn(II)]γnWnRn(II),
dn(II)=μ1μ2η2Jn(η2x)η1Jn(η1x)[BnPn(II)+Qn(II)]WnRn(II),
fn(II)=γnPn(II)Rn(II),
gn(II)=(Bnγn2VnDn)Pn(II)+(1γn2CnDn)Qn(II)Rn(II)(WnAnDn),
vn(II)=γnQn(II)Rn(II),
wn(II)=(AnBnγn2VnWn)Pn(II)+(Anγn2CnWn)Qn(II)Rn(II)(WnAnDn).
uqt=14[ϵq(eff)|Eq|2+μq(eff)|Hq|2],
Wq(l1,l2)=L/2L/2dz02πdϕl1l2drruqt.
W0(l1,l2)=ϵ02|E0|2π(l22l12)L.
2|AnJn(ρ)ρBJn(ρ)+CnYn(ρ)ρDYn(ρ)|2+2|AJn(ρ)BnJn(ρ)ρ+CYn(ρ)DnYn(ρ)ρ|2=|(AB)Jn1(ρ)+(CD)Yn1(ρ)|2+|(A+B)Jn+1(ρ)+(C+D)Yn+1(ρ)|2.
Iq,n(ZZ¯)(l1,l2)=1(l22l12)l1l2drrZn(ρq)Z¯n(ρq*)=r2[ρq*Zn(ρq)Z¯n(ρq*)ρqZn(ρq)Z¯n(ρq*)](l22l12)(ρq2ρq*2)|r=l1r=l2,
Iq,n(ZZ¯)(l1,l2)=ϱ±,n(ZZ¯)r24(l22l12)[2Zn(ρq)Z¯n(ρq)Zn1(ρq)Z¯n+1(ρq)Zn+1(ρq)Z¯n1(ρq)]|r=l1r=l2,
WE1rϕ(a)W0(0,a)=ϵ1(eff)2ϵ0n=[|cncosζm1dn|2I1,n1(JJ)(0,a)+|cncosζm1+dn|2I1,n+1(JJ)(0,a)],
WE1z(a)W0(0,a)=ϵ1(eff)ϵ0|η1m1|2n=|cn|2I1,n(JJ)(0,a),
WE2rϕ(a,b)W0(a,b)=ϵ2(eff)2ϵ0n={|fncosζm2gn|2I2,n1(JJ)(a,b)+|fncosζm2+gn|2I2,n+1(JJ)(a,b)+|vncosζm2wn|2I2,n1(YY)(a,b)+|vncosζm2+wn|2I2,n+1(YY)(a,b)+2Re[(fncosζm2gn)×(vn*cosζm2*wn*)I2,n1(JY)(a,b)]+2Re[(fncosζm2+gn)×(vn*cosζm2*+wn*)I2,n+1(JY)(a,b)]},
WE2z(a,b)W0(a,b)=ϵ2(eff)ϵ0|η2m2|2n={|fn|2I2,n(JJ)(a,b)+|vn|2I2,n(YY)(a,b)+2Re[fnvn*I2,n(JY)(a,b)]},
W1,2(a,b)W0(0,b)=S2W1(0,a)W0(0,a)+(1S2)W2(a,b)W0(a,b),
Qsca(I)=2yn=[|an(I)|2+|bn(I)|2],
Qext(I)=2yn=Re[bn(I)],
Qabs(I)=Qext(I)Qsca(I),
an(I)=iμ2η2Jn(η2y)η0Hn(1)(η0y)[V¯nPn(I)+C¯nQn(I)]γnV¯nRn(I),
bn(I)=1m2η2Jn(η2y)η0Hn(1)(η0y)[A¯nPn(I)+Qn(I)]V¯nRn(I)+Jn(η0y)Hn(1)(η0y),
an(II)=1μ2η2Jn(η2y)η0Hn(1)(η0y)[B¯nPn(II)+Qn(II)]W¯nRn(II)+Jn(η0y)Hn(1)(η0y),
bn(II)=im2η2Jn(η2y)η0Hn(1)(η0y)[W¯nPn(II)+D¯nQn(II)]γnW¯nRn(II),
Qabs=πy{[ϵ1ϵ1(eff)W1E(0,a)W0(0,a)+μ1μ1(eff)W1H(0,a)W0(0,a)]S2+[ϵ2ϵ2(eff)W2E(a,b)W0(a,b)+μ2μ2(eff)W2H(a,b)W0(a,b)](1S2)},
σ(ω)=2Dπ(iω+iγω02/ω)+σb,
ϵgra(ω)ϵ0=1+iσ(ω)ωϵ0d.
ϵ2(eff)(ω)=ϵ2(ω)+2ωγϵ2(ω),
An=Jn(η2x)Yn(η2x)[μ1Ln(J)(η1x)μ2Ln(J)(η2x)μ1Ln(J)(η1x)μ2Ln(Y)(η2x)],Bn=Jn(η2x)Yn(η2x)[ϵ1Ln(J)(η1x)ϵ2Ln(J)(η2x)ϵ1Ln(J)(η1x)ϵ2Ln(Y)(η2x)],Cn=μ2(1η22/η12)m2η22x2[μ1Ln(J)(η1x)μ2Ln(Y)(η2x)],Dn=ϵ2(1η22/η12)m2η22x2[ϵ1Ln(J)(η1x)ϵ2Ln(Y)(η2x)],Vn=Jn(η2x)Yn(η2x)Cn,Wn=Jn(η2x)Yn(η2x)Dn,
A¯n=Jn(η2y)Yn(η2y)[μ2Ln(J)(η2y)μ0Ln(H)(η0y)μ2Ln(Y)(η2y)μ0Ln(H)(η0y)],B¯n=Jn(η2y)Yn(η2y)[ε2Ln(J)(η2y)ε0Ln(H)(η0y)ε2Ln(Y)(η2y)ε0Ln(H)(η0y)],C¯n=μ2(1η02/η22)m2η02y2[μ2Ln(Y)(η2y)μ0Ln(H)(η0y)],D¯n=ε2(1η02/η22)m2η02y2[ε2Ln(Y)(η2y)ε0Ln(H)(η0y)],V¯n=Jn(η2y)Yn(η2y)C¯n,W¯n=Jn(η2y)Yn(η2y)D¯n,
Fn(I)=2iε2[πYn(η2y)Hn(1)(η0y)]1m˜2η2η0y2[ε0Ln(H)(η0y)ε2Ln(Y)(η2y)],Pn(I)Fn(I)=V¯n(1γn2CnDn)Vn(1γn2C¯nDn),+Bn(CnC¯n),Qn(I)Fn(I)=A¯n(VnBnCn)An(V¯nBnC¯n),+γn2Wn(CnV¯nC¯nVn),
Fn(II)=2iμ2[πYn(η2y)Hn(1)(η0y)]1η2η0y2[μ0Ln(H)(η0y)μ2Ln(Y)(η2y)],Pn(II)Fn(II)=W¯n(1γn2CnDn)Wn(1γn2CnD¯n),+An(DnD¯n),Qn(II)Fn(II)=B¯n(WnAnDn)Bn(W¯nAnD¯n),+γn2Vn(DnW¯nD¯nWn),
Rn(I)=(Anγn2CnWn)[γn2V¯n(DnD¯n),+B¯n(1γn2C¯nDn)Bn(1γn2C¯nD¯n)],+(1γn2CnDn)[A¯n(BnB¯n),+γn2W¯n(V¯nBnC¯n)γn2Wn(V¯nB¯nC¯n)],+γn2(VnBnCn)[(WnW¯n),+D¯n(A¯nγn2C¯nWn)Dn(A¯nγn2C¯nW¯n)],
Rn(II)=(Bnγn2DnVn)[γn2W¯n(CnC¯n),+A¯n(1γn2CnD¯n)An(1γn2C¯nD¯n)],+(1γn2CnDn)[B¯n(AnA¯n),+γn2V¯n(W¯nAnD¯n)γn2Vn(W¯nA¯nD¯n)],+γn2(WnAnDn)[(VnV¯n),+C¯n(B¯nγn2D¯nVn)Cn(B¯nγn2D¯nV¯n)],
an=an(II)=m˜2Jn(y)αnJn(y)α˜nm˜2Hn(1)(y)αnHn(1)(y)α˜n,bn=bn(I)=Jn(y)βnm˜2Jn(y)β˜nHn(1)(y)βnm˜2Hn(1)(y)β˜n,cn=cn(I)=fn(I)[Jn(m2x)BnYn(m2x)]Jn(m1x),dn=dn(II)=m˜2gn(II)[Jn(m2x)AnYn(m2x)]m˜1Jn(m1x),fn=fn(I)=2i/πyHn(1)(y)βnm˜2Hn(1)(y)β˜n,gn=gn(II)=2i/πym˜2Hn(1)(y)αnHn(1)(y)α˜n,vn=vn(I)=Bnfn(I),wn=wn(II)=Angn(II),
An=m˜1Jn(m1x)Jn(m2x)m˜2Jn(m1x)Jn(m2x)m˜1Jn(m1x)Yn(m2x)m˜2Jn(m1x)Yn(m2x),Bn=m˜2Jn(m1x)Jn(m2x)m˜1Jn(m1x)Jn(m2x)m˜2Jn(m1x)Yn(m2x)m˜1Jn(m1x)Yn(m2x),αn=Jn(m2y)AnYn(m2y),βn=Jn(m2y)BnYn(m2y),α˜n=Jn(m2y)AnYn(m2y),β˜n=Jn(m2y)BnYn(m2y),

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