Abstract

Electromagnetic wave scattering from a metallic multiwalled carbon nanotube is investigated by using the boundary-value approach and modal series expansion of the scattered and transmitted fields. Electronic excitations of each wall of the system are modeled as an infinitesimally thin cylindrical layer of the free electrons, whose dynamics are described by means of the fluid theory. The system is illuminated by a cylindrical wave from a line source that is placed in a direction parallel to the nanotube axis. The problem is two-dimensional, and the solution to both types of polarization (electric and magnetic line source) is presented.

© 2011 Optical Society of America

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  1. G. Ya. Slepyan, S. A. Maksimenko, A. Lakhtakia, O. M. Yevtushenko, and A. V. Gusakov, “Electronic and electromagnetic properties of nanotubes,” Phys. Rev. B 57, 9485–9497(1998).
    [CrossRef]
  2. G. Ya. Slepyan, S. A. Maksimenko, A. Lakhtakia, O. M. Yevtushenko, and A. V. Gusakov, “Electrodynamics of carbon nanotubes: dynamic conductivity, impedance boundary conditions, and surface wave propagation,” Phys. Rev. B 60, 17136–17149 (1999).
    [CrossRef]
  3. M. V. Shuba, S. A. Maksimenko, and A. Lakhtakia, “Electromagnetic wave propagation in an almost circular bundle of closely packed metallic carbon nanotubes,” Phys. Rev. B 76, 155407(2007).
    [CrossRef]
  4. L. Wei and Y. N. Wang, “Electromagnetic wave propagation in single-wall carbon nanotubes,” Phys. Lett. A 333, 303–309(2004).
    [CrossRef]
  5. H. Khosravi and A. Moradi, “Comment on: ‘Electromagnetic wave propagation in single-wall carbon nanotubes’,” Phys. Lett. A 364, 515–516 (2007).
    [CrossRef]
  6. G. W. Hanson, “Fundamental transmitting properties of carbon nanotube antennas,” IEEE Trans. Antennas Propag. 53, 3426–3435 (2005).
    [CrossRef]
  7. A. Moradi, “Plasma wave propagation in a pair of carbon nanotubes,” JETP Lett. 88, 795–798 (2008).
    [CrossRef]
  8. A. Moradi, “Guided dispersion characteristics of metallic single-walled carbon nanotubes in the presence of dielectric media,” Opt. Commun. 283, 160–163 (2010).
    [CrossRef]
  9. L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13, 6645–6650 (2005).
    [CrossRef] [PubMed]
  10. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
    [CrossRef] [PubMed]
  11. Z. Ye, W. D. Deering, A. Krokhin, and J. A. Roberts, “Microwave absorption by an array of carbon nanotubes: a phenomenological model,” Phys. Rev. B 74, 075425 (2006).
    [CrossRef]
  12. Z. Peng, J. Peng, and Y. Ou, “Microwave absorbing properties of hydrogen plasma in single wall carbon nanotubes,” Phys. Lett. A 359, 56–60 (2006).
    [CrossRef]
  13. A. Moradi, “Microwave absorption of magnetized hydrogen plasma in carbon nanotubes,” Phys. Plasmas 16, 113501 (2009).
    [CrossRef]
  14. A. Moradi, “Microwave response of magnetized hydrogen plasma in carbon nanotubes: multiple reflection effects,” Appl. Opt. 49, 1728–1733 (2010).
    [CrossRef] [PubMed]
  15. G. Miano and F. Villone, “An integral formulation for the electrodynamics of metallic carbon nanotubes based on a fluid model,” IEEE Trans. Antennas Propag. 54, 2713–2724(2006).
    [CrossRef]
  16. G. Ya. Slepyan, M. V. Shuba, S. A. Maksimenko, and A. Lakhtakia, “Theory of optical scattering by achiral carbon nanotubes and their potential as optical nanoantennas,” Phys. Rev. B 73, 195416 (2006).
    [CrossRef]
  17. J. Hao and G. W. Hanson, “Electromagnetic scattering from finite-length metallic carbon nanotubes in the lower IR bands,” Phys. Rev. B 74, 035119 (2006).
    [CrossRef]
  18. S. M. Mikki and A. Kishk, “Theory of optical scattering by carbon nanotube,” Microw. Opt. Technol. Lett. 49, 2360–2364(2007).
    [CrossRef]
  19. S. M. Mikki and A. Kishk, “Electromagnetic scattering by multi-walled carbon nanotubes,” PIER 17, 49–67 (2009).
    [CrossRef]
  20. E. Malic, M. Hirtschulz, F. Milde, Y. Wu, J. Maultzsch, T. F. Heinz, A. Knorr, and S. Reich, Phys. Rev. B 77, 045432 (2008).
    [CrossRef]
  21. G. Nasis, I.-G. Plegas, D. S. Sofronis, and H. T. Anastassiu, “Transmission and scattering properties of carbon nanotube arrays,” in EMC Europe Workshop 2009—Materials in EMC Applications(National Technical University of Athens, 2009), pp. 13–16.
  22. A. Moradi, “Oblique incidence scattering from single-walled carbon nanotubes,” Phys. Plasmas 17, 033504 (2010).
    [CrossRef]
  23. H. Khosravi and A. Moradi, “Scattering cross section of metallic two-walled carbon nanotubes,” Opt. Commun. 284, 2629–2632(2011).
    [CrossRef]
  24. H. Khosravi and A. Moradi, “Scattering properties of metallic carbon nanotubes in the presence of dielectric media,” J. Mod. Opt. (to be published).
  25. A. Moradi, “Optical scattering by a spherical two-dimensional electron gas: application to the C60 molecule,” Optik (to be published), doi:10.1016/j.ijleo.2011.01.016.
    [CrossRef]
  26. S. A. Schelkunoff, “Some equivalence theorems of electromagnetic and their application to radiation problems,” Bell Syst. Tech. J. 15, 92–112 (1936).
  27. R. F. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, 1961).
  28. C. A. Balanis, Antenna Theory: Analysis and Design (Wiley, 1982).
  29. C. A. Balanis, Advanced Engineering Electromagnetics(Wiley, 1989).
  30. R. P. Parrikar, A. A. Kishk, and A. Z. Elsherbeni, “Scattering from an impedance cylinder embedded in a nonconcentric dielectric cylinder,” in Proceedings of the IEEE SoutheastCon 1990 (IEEE, 1991), Vol.  3, pp. 1002–1007.
    [CrossRef]

2011

H. Khosravi and A. Moradi, “Scattering cross section of metallic two-walled carbon nanotubes,” Opt. Commun. 284, 2629–2632(2011).
[CrossRef]

2010

A. Moradi, “Oblique incidence scattering from single-walled carbon nanotubes,” Phys. Plasmas 17, 033504 (2010).
[CrossRef]

A. Moradi, “Guided dispersion characteristics of metallic single-walled carbon nanotubes in the presence of dielectric media,” Opt. Commun. 283, 160–163 (2010).
[CrossRef]

A. Moradi, “Microwave response of magnetized hydrogen plasma in carbon nanotubes: multiple reflection effects,” Appl. Opt. 49, 1728–1733 (2010).
[CrossRef] [PubMed]

2009

A. Moradi, “Microwave absorption of magnetized hydrogen plasma in carbon nanotubes,” Phys. Plasmas 16, 113501 (2009).
[CrossRef]

S. M. Mikki and A. Kishk, “Electromagnetic scattering by multi-walled carbon nanotubes,” PIER 17, 49–67 (2009).
[CrossRef]

2008

E. Malic, M. Hirtschulz, F. Milde, Y. Wu, J. Maultzsch, T. F. Heinz, A. Knorr, and S. Reich, Phys. Rev. B 77, 045432 (2008).
[CrossRef]

A. Moradi, “Plasma wave propagation in a pair of carbon nanotubes,” JETP Lett. 88, 795–798 (2008).
[CrossRef]

2007

H. Khosravi and A. Moradi, “Comment on: ‘Electromagnetic wave propagation in single-wall carbon nanotubes’,” Phys. Lett. A 364, 515–516 (2007).
[CrossRef]

M. V. Shuba, S. A. Maksimenko, and A. Lakhtakia, “Electromagnetic wave propagation in an almost circular bundle of closely packed metallic carbon nanotubes,” Phys. Rev. B 76, 155407(2007).
[CrossRef]

S. M. Mikki and A. Kishk, “Theory of optical scattering by carbon nanotube,” Microw. Opt. Technol. Lett. 49, 2360–2364(2007).
[CrossRef]

2006

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef] [PubMed]

Z. Ye, W. D. Deering, A. Krokhin, and J. A. Roberts, “Microwave absorption by an array of carbon nanotubes: a phenomenological model,” Phys. Rev. B 74, 075425 (2006).
[CrossRef]

Z. Peng, J. Peng, and Y. Ou, “Microwave absorbing properties of hydrogen plasma in single wall carbon nanotubes,” Phys. Lett. A 359, 56–60 (2006).
[CrossRef]

G. Miano and F. Villone, “An integral formulation for the electrodynamics of metallic carbon nanotubes based on a fluid model,” IEEE Trans. Antennas Propag. 54, 2713–2724(2006).
[CrossRef]

G. Ya. Slepyan, M. V. Shuba, S. A. Maksimenko, and A. Lakhtakia, “Theory of optical scattering by achiral carbon nanotubes and their potential as optical nanoantennas,” Phys. Rev. B 73, 195416 (2006).
[CrossRef]

J. Hao and G. W. Hanson, “Electromagnetic scattering from finite-length metallic carbon nanotubes in the lower IR bands,” Phys. Rev. B 74, 035119 (2006).
[CrossRef]

2005

G. W. Hanson, “Fundamental transmitting properties of carbon nanotube antennas,” IEEE Trans. Antennas Propag. 53, 3426–3435 (2005).
[CrossRef]

L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13, 6645–6650 (2005).
[CrossRef] [PubMed]

2004

L. Wei and Y. N. Wang, “Electromagnetic wave propagation in single-wall carbon nanotubes,” Phys. Lett. A 333, 303–309(2004).
[CrossRef]

1999

G. Ya. Slepyan, S. A. Maksimenko, A. Lakhtakia, O. M. Yevtushenko, and A. V. Gusakov, “Electrodynamics of carbon nanotubes: dynamic conductivity, impedance boundary conditions, and surface wave propagation,” Phys. Rev. B 60, 17136–17149 (1999).
[CrossRef]

1998

G. Ya. Slepyan, S. A. Maksimenko, A. Lakhtakia, O. M. Yevtushenko, and A. V. Gusakov, “Electronic and electromagnetic properties of nanotubes,” Phys. Rev. B 57, 9485–9497(1998).
[CrossRef]

1936

S. A. Schelkunoff, “Some equivalence theorems of electromagnetic and their application to radiation problems,” Bell Syst. Tech. J. 15, 92–112 (1936).

Anastassiu, H. T.

G. Nasis, I.-G. Plegas, D. S. Sofronis, and H. T. Anastassiu, “Transmission and scattering properties of carbon nanotube arrays,” in EMC Europe Workshop 2009—Materials in EMC Applications(National Technical University of Athens, 2009), pp. 13–16.

Balanis, C. A.

C. A. Balanis, Antenna Theory: Analysis and Design (Wiley, 1982).

C. A. Balanis, Advanced Engineering Electromagnetics(Wiley, 1989).

Deering, W. D.

Z. Ye, W. D. Deering, A. Krokhin, and J. A. Roberts, “Microwave absorption by an array of carbon nanotubes: a phenomenological model,” Phys. Rev. B 74, 075425 (2006).
[CrossRef]

Elsherbeni, A. Z.

R. P. Parrikar, A. A. Kishk, and A. Z. Elsherbeni, “Scattering from an impedance cylinder embedded in a nonconcentric dielectric cylinder,” in Proceedings of the IEEE SoutheastCon 1990 (IEEE, 1991), Vol.  3, pp. 1002–1007.
[CrossRef]

Gusakov, A. V.

G. Ya. Slepyan, S. A. Maksimenko, A. Lakhtakia, O. M. Yevtushenko, and A. V. Gusakov, “Electrodynamics of carbon nanotubes: dynamic conductivity, impedance boundary conditions, and surface wave propagation,” Phys. Rev. B 60, 17136–17149 (1999).
[CrossRef]

G. Ya. Slepyan, S. A. Maksimenko, A. Lakhtakia, O. M. Yevtushenko, and A. V. Gusakov, “Electronic and electromagnetic properties of nanotubes,” Phys. Rev. B 57, 9485–9497(1998).
[CrossRef]

Han, Z.

Hanson, G. W.

J. Hao and G. W. Hanson, “Electromagnetic scattering from finite-length metallic carbon nanotubes in the lower IR bands,” Phys. Rev. B 74, 035119 (2006).
[CrossRef]

G. W. Hanson, “Fundamental transmitting properties of carbon nanotube antennas,” IEEE Trans. Antennas Propag. 53, 3426–3435 (2005).
[CrossRef]

Hao, J.

J. Hao and G. W. Hanson, “Electromagnetic scattering from finite-length metallic carbon nanotubes in the lower IR bands,” Phys. Rev. B 74, 035119 (2006).
[CrossRef]

Harrington, R. F.

R. F. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, 1961).

He, S.

Heinz, T. F.

E. Malic, M. Hirtschulz, F. Milde, Y. Wu, J. Maultzsch, T. F. Heinz, A. Knorr, and S. Reich, Phys. Rev. B 77, 045432 (2008).
[CrossRef]

Hirtschulz, M.

E. Malic, M. Hirtschulz, F. Milde, Y. Wu, J. Maultzsch, T. F. Heinz, A. Knorr, and S. Reich, Phys. Rev. B 77, 045432 (2008).
[CrossRef]

Khosravi, H.

H. Khosravi and A. Moradi, “Scattering cross section of metallic two-walled carbon nanotubes,” Opt. Commun. 284, 2629–2632(2011).
[CrossRef]

H. Khosravi and A. Moradi, “Comment on: ‘Electromagnetic wave propagation in single-wall carbon nanotubes’,” Phys. Lett. A 364, 515–516 (2007).
[CrossRef]

H. Khosravi and A. Moradi, “Scattering properties of metallic carbon nanotubes in the presence of dielectric media,” J. Mod. Opt. (to be published).

Kishk, A.

S. M. Mikki and A. Kishk, “Electromagnetic scattering by multi-walled carbon nanotubes,” PIER 17, 49–67 (2009).
[CrossRef]

S. M. Mikki and A. Kishk, “Theory of optical scattering by carbon nanotube,” Microw. Opt. Technol. Lett. 49, 2360–2364(2007).
[CrossRef]

Kishk, A. A.

R. P. Parrikar, A. A. Kishk, and A. Z. Elsherbeni, “Scattering from an impedance cylinder embedded in a nonconcentric dielectric cylinder,” in Proceedings of the IEEE SoutheastCon 1990 (IEEE, 1991), Vol.  3, pp. 1002–1007.
[CrossRef]

Knorr, A.

E. Malic, M. Hirtschulz, F. Milde, Y. Wu, J. Maultzsch, T. F. Heinz, A. Knorr, and S. Reich, Phys. Rev. B 77, 045432 (2008).
[CrossRef]

Krokhin, A.

Z. Ye, W. D. Deering, A. Krokhin, and J. A. Roberts, “Microwave absorption by an array of carbon nanotubes: a phenomenological model,” Phys. Rev. B 74, 075425 (2006).
[CrossRef]

Lakhtakia, A.

M. V. Shuba, S. A. Maksimenko, and A. Lakhtakia, “Electromagnetic wave propagation in an almost circular bundle of closely packed metallic carbon nanotubes,” Phys. Rev. B 76, 155407(2007).
[CrossRef]

G. Ya. Slepyan, M. V. Shuba, S. A. Maksimenko, and A. Lakhtakia, “Theory of optical scattering by achiral carbon nanotubes and their potential as optical nanoantennas,” Phys. Rev. B 73, 195416 (2006).
[CrossRef]

G. Ya. Slepyan, S. A. Maksimenko, A. Lakhtakia, O. M. Yevtushenko, and A. V. Gusakov, “Electrodynamics of carbon nanotubes: dynamic conductivity, impedance boundary conditions, and surface wave propagation,” Phys. Rev. B 60, 17136–17149 (1999).
[CrossRef]

G. Ya. Slepyan, S. A. Maksimenko, A. Lakhtakia, O. M. Yevtushenko, and A. V. Gusakov, “Electronic and electromagnetic properties of nanotubes,” Phys. Rev. B 57, 9485–9497(1998).
[CrossRef]

Liu, L.

Maksimenko, S. A.

M. V. Shuba, S. A. Maksimenko, and A. Lakhtakia, “Electromagnetic wave propagation in an almost circular bundle of closely packed metallic carbon nanotubes,” Phys. Rev. B 76, 155407(2007).
[CrossRef]

G. Ya. Slepyan, M. V. Shuba, S. A. Maksimenko, and A. Lakhtakia, “Theory of optical scattering by achiral carbon nanotubes and their potential as optical nanoantennas,” Phys. Rev. B 73, 195416 (2006).
[CrossRef]

G. Ya. Slepyan, S. A. Maksimenko, A. Lakhtakia, O. M. Yevtushenko, and A. V. Gusakov, “Electrodynamics of carbon nanotubes: dynamic conductivity, impedance boundary conditions, and surface wave propagation,” Phys. Rev. B 60, 17136–17149 (1999).
[CrossRef]

G. Ya. Slepyan, S. A. Maksimenko, A. Lakhtakia, O. M. Yevtushenko, and A. V. Gusakov, “Electronic and electromagnetic properties of nanotubes,” Phys. Rev. B 57, 9485–9497(1998).
[CrossRef]

Malic, E.

E. Malic, M. Hirtschulz, F. Milde, Y. Wu, J. Maultzsch, T. F. Heinz, A. Knorr, and S. Reich, Phys. Rev. B 77, 045432 (2008).
[CrossRef]

Maultzsch, J.

E. Malic, M. Hirtschulz, F. Milde, Y. Wu, J. Maultzsch, T. F. Heinz, A. Knorr, and S. Reich, Phys. Rev. B 77, 045432 (2008).
[CrossRef]

Miano, G.

G. Miano and F. Villone, “An integral formulation for the electrodynamics of metallic carbon nanotubes based on a fluid model,” IEEE Trans. Antennas Propag. 54, 2713–2724(2006).
[CrossRef]

Mikki, S. M.

S. M. Mikki and A. Kishk, “Electromagnetic scattering by multi-walled carbon nanotubes,” PIER 17, 49–67 (2009).
[CrossRef]

S. M. Mikki and A. Kishk, “Theory of optical scattering by carbon nanotube,” Microw. Opt. Technol. Lett. 49, 2360–2364(2007).
[CrossRef]

Milde, F.

E. Malic, M. Hirtschulz, F. Milde, Y. Wu, J. Maultzsch, T. F. Heinz, A. Knorr, and S. Reich, Phys. Rev. B 77, 045432 (2008).
[CrossRef]

Moradi, A.

H. Khosravi and A. Moradi, “Scattering cross section of metallic two-walled carbon nanotubes,” Opt. Commun. 284, 2629–2632(2011).
[CrossRef]

A. Moradi, “Oblique incidence scattering from single-walled carbon nanotubes,” Phys. Plasmas 17, 033504 (2010).
[CrossRef]

A. Moradi, “Microwave response of magnetized hydrogen plasma in carbon nanotubes: multiple reflection effects,” Appl. Opt. 49, 1728–1733 (2010).
[CrossRef] [PubMed]

A. Moradi, “Guided dispersion characteristics of metallic single-walled carbon nanotubes in the presence of dielectric media,” Opt. Commun. 283, 160–163 (2010).
[CrossRef]

A. Moradi, “Microwave absorption of magnetized hydrogen plasma in carbon nanotubes,” Phys. Plasmas 16, 113501 (2009).
[CrossRef]

A. Moradi, “Plasma wave propagation in a pair of carbon nanotubes,” JETP Lett. 88, 795–798 (2008).
[CrossRef]

H. Khosravi and A. Moradi, “Comment on: ‘Electromagnetic wave propagation in single-wall carbon nanotubes’,” Phys. Lett. A 364, 515–516 (2007).
[CrossRef]

H. Khosravi and A. Moradi, “Scattering properties of metallic carbon nanotubes in the presence of dielectric media,” J. Mod. Opt. (to be published).

A. Moradi, “Optical scattering by a spherical two-dimensional electron gas: application to the C60 molecule,” Optik (to be published), doi:10.1016/j.ijleo.2011.01.016.
[CrossRef]

Nasis, G.

G. Nasis, I.-G. Plegas, D. S. Sofronis, and H. T. Anastassiu, “Transmission and scattering properties of carbon nanotube arrays,” in EMC Europe Workshop 2009—Materials in EMC Applications(National Technical University of Athens, 2009), pp. 13–16.

Ou, Y.

Z. Peng, J. Peng, and Y. Ou, “Microwave absorbing properties of hydrogen plasma in single wall carbon nanotubes,” Phys. Lett. A 359, 56–60 (2006).
[CrossRef]

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef] [PubMed]

Parrikar, R. P.

R. P. Parrikar, A. A. Kishk, and A. Z. Elsherbeni, “Scattering from an impedance cylinder embedded in a nonconcentric dielectric cylinder,” in Proceedings of the IEEE SoutheastCon 1990 (IEEE, 1991), Vol.  3, pp. 1002–1007.
[CrossRef]

Peng, J.

Z. Peng, J. Peng, and Y. Ou, “Microwave absorbing properties of hydrogen plasma in single wall carbon nanotubes,” Phys. Lett. A 359, 56–60 (2006).
[CrossRef]

Peng, Z.

Z. Peng, J. Peng, and Y. Ou, “Microwave absorbing properties of hydrogen plasma in single wall carbon nanotubes,” Phys. Lett. A 359, 56–60 (2006).
[CrossRef]

Plegas, I.-G.

G. Nasis, I.-G. Plegas, D. S. Sofronis, and H. T. Anastassiu, “Transmission and scattering properties of carbon nanotube arrays,” in EMC Europe Workshop 2009—Materials in EMC Applications(National Technical University of Athens, 2009), pp. 13–16.

Reich, S.

E. Malic, M. Hirtschulz, F. Milde, Y. Wu, J. Maultzsch, T. F. Heinz, A. Knorr, and S. Reich, Phys. Rev. B 77, 045432 (2008).
[CrossRef]

Roberts, J. A.

Z. Ye, W. D. Deering, A. Krokhin, and J. A. Roberts, “Microwave absorption by an array of carbon nanotubes: a phenomenological model,” Phys. Rev. B 74, 075425 (2006).
[CrossRef]

Schelkunoff, S. A.

S. A. Schelkunoff, “Some equivalence theorems of electromagnetic and their application to radiation problems,” Bell Syst. Tech. J. 15, 92–112 (1936).

Shuba, M. V.

M. V. Shuba, S. A. Maksimenko, and A. Lakhtakia, “Electromagnetic wave propagation in an almost circular bundle of closely packed metallic carbon nanotubes,” Phys. Rev. B 76, 155407(2007).
[CrossRef]

G. Ya. Slepyan, M. V. Shuba, S. A. Maksimenko, and A. Lakhtakia, “Theory of optical scattering by achiral carbon nanotubes and their potential as optical nanoantennas,” Phys. Rev. B 73, 195416 (2006).
[CrossRef]

Slepyan, G. Ya.

G. Ya. Slepyan, M. V. Shuba, S. A. Maksimenko, and A. Lakhtakia, “Theory of optical scattering by achiral carbon nanotubes and their potential as optical nanoantennas,” Phys. Rev. B 73, 195416 (2006).
[CrossRef]

G. Ya. Slepyan, S. A. Maksimenko, A. Lakhtakia, O. M. Yevtushenko, and A. V. Gusakov, “Electrodynamics of carbon nanotubes: dynamic conductivity, impedance boundary conditions, and surface wave propagation,” Phys. Rev. B 60, 17136–17149 (1999).
[CrossRef]

G. Ya. Slepyan, S. A. Maksimenko, A. Lakhtakia, O. M. Yevtushenko, and A. V. Gusakov, “Electronic and electromagnetic properties of nanotubes,” Phys. Rev. B 57, 9485–9497(1998).
[CrossRef]

Sofronis, D. S.

G. Nasis, I.-G. Plegas, D. S. Sofronis, and H. T. Anastassiu, “Transmission and scattering properties of carbon nanotube arrays,” in EMC Europe Workshop 2009—Materials in EMC Applications(National Technical University of Athens, 2009), pp. 13–16.

Villone, F.

G. Miano and F. Villone, “An integral formulation for the electrodynamics of metallic carbon nanotubes based on a fluid model,” IEEE Trans. Antennas Propag. 54, 2713–2724(2006).
[CrossRef]

Wang, Y. N.

L. Wei and Y. N. Wang, “Electromagnetic wave propagation in single-wall carbon nanotubes,” Phys. Lett. A 333, 303–309(2004).
[CrossRef]

Wei, L.

L. Wei and Y. N. Wang, “Electromagnetic wave propagation in single-wall carbon nanotubes,” Phys. Lett. A 333, 303–309(2004).
[CrossRef]

Wu, Y.

E. Malic, M. Hirtschulz, F. Milde, Y. Wu, J. Maultzsch, T. F. Heinz, A. Knorr, and S. Reich, Phys. Rev. B 77, 045432 (2008).
[CrossRef]

Ye, Z.

Z. Ye, W. D. Deering, A. Krokhin, and J. A. Roberts, “Microwave absorption by an array of carbon nanotubes: a phenomenological model,” Phys. Rev. B 74, 075425 (2006).
[CrossRef]

Yevtushenko, O. M.

G. Ya. Slepyan, S. A. Maksimenko, A. Lakhtakia, O. M. Yevtushenko, and A. V. Gusakov, “Electrodynamics of carbon nanotubes: dynamic conductivity, impedance boundary conditions, and surface wave propagation,” Phys. Rev. B 60, 17136–17149 (1999).
[CrossRef]

G. Ya. Slepyan, S. A. Maksimenko, A. Lakhtakia, O. M. Yevtushenko, and A. V. Gusakov, “Electronic and electromagnetic properties of nanotubes,” Phys. Rev. B 57, 9485–9497(1998).
[CrossRef]

Appl. Opt.

Bell Syst. Tech. J.

S. A. Schelkunoff, “Some equivalence theorems of electromagnetic and their application to radiation problems,” Bell Syst. Tech. J. 15, 92–112 (1936).

IEEE Trans. Antennas Propag.

G. Miano and F. Villone, “An integral formulation for the electrodynamics of metallic carbon nanotubes based on a fluid model,” IEEE Trans. Antennas Propag. 54, 2713–2724(2006).
[CrossRef]

G. W. Hanson, “Fundamental transmitting properties of carbon nanotube antennas,” IEEE Trans. Antennas Propag. 53, 3426–3435 (2005).
[CrossRef]

JETP Lett.

A. Moradi, “Plasma wave propagation in a pair of carbon nanotubes,” JETP Lett. 88, 795–798 (2008).
[CrossRef]

Microw. Opt. Technol. Lett.

S. M. Mikki and A. Kishk, “Theory of optical scattering by carbon nanotube,” Microw. Opt. Technol. Lett. 49, 2360–2364(2007).
[CrossRef]

Opt. Commun.

A. Moradi, “Guided dispersion characteristics of metallic single-walled carbon nanotubes in the presence of dielectric media,” Opt. Commun. 283, 160–163 (2010).
[CrossRef]

H. Khosravi and A. Moradi, “Scattering cross section of metallic two-walled carbon nanotubes,” Opt. Commun. 284, 2629–2632(2011).
[CrossRef]

Opt. Express

Phys. Lett. A

L. Wei and Y. N. Wang, “Electromagnetic wave propagation in single-wall carbon nanotubes,” Phys. Lett. A 333, 303–309(2004).
[CrossRef]

H. Khosravi and A. Moradi, “Comment on: ‘Electromagnetic wave propagation in single-wall carbon nanotubes’,” Phys. Lett. A 364, 515–516 (2007).
[CrossRef]

Z. Peng, J. Peng, and Y. Ou, “Microwave absorbing properties of hydrogen plasma in single wall carbon nanotubes,” Phys. Lett. A 359, 56–60 (2006).
[CrossRef]

Phys. Plasmas

A. Moradi, “Microwave absorption of magnetized hydrogen plasma in carbon nanotubes,” Phys. Plasmas 16, 113501 (2009).
[CrossRef]

A. Moradi, “Oblique incidence scattering from single-walled carbon nanotubes,” Phys. Plasmas 17, 033504 (2010).
[CrossRef]

Phys. Rev. B

Z. Ye, W. D. Deering, A. Krokhin, and J. A. Roberts, “Microwave absorption by an array of carbon nanotubes: a phenomenological model,” Phys. Rev. B 74, 075425 (2006).
[CrossRef]

E. Malic, M. Hirtschulz, F. Milde, Y. Wu, J. Maultzsch, T. F. Heinz, A. Knorr, and S. Reich, Phys. Rev. B 77, 045432 (2008).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Electric line source parallel to a MWCNT (top view).

Fig. 2
Fig. 2

Dependence of normalized SCS on wave energy of the electric line source for a three-walled CNT with radii a 1 = 1.02 nm , a 2 = 1.36 nm , a 3 = 1.7 nm (solid red curve), a two-walled CNT with radii a 1 = 1.36 nm , a 2 = 1.7 nm (dashed blue curve), and a SWCNT with radii a = 1.7 nm (dotted black curve), when the increments of the radii of the subsequent walls to be Δ a = 0.34 nm , γ = 2 × 10 14 Hz and ρ 0 = 100 nm .

Fig. 3
Fig. 3

Dependence of normalized SCS on wave energy of the electric line source for a three-walled CNT with radii a 1 = 1.02 nm , a 2 = 1.36 nm , a 3 = 1.7 nm , with a different value of ρ 0 when γ = 2 × 10 14 Hz .

Equations (30)

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E z i ( ρ , ϕ ) = E 0 H 0 ( 2 ) ( β | ρ ρ 0 | ) , E 0 = β 2 I e 4 ω ε 0 ,
E z i ( ρ , ϕ ) = E 0 m = + e j m ( ϕ ϕ 0 ) { J m ( β ρ ) H m ( 2 ) ( β ρ 0 ) , ρ ρ 0 , J m ( β ρ 0 ) H m ( 2 ) ( β ρ ) , ρ ρ 0 ,
E z s ( ρ , ϕ ) = E 0 m = + A m H m ( 2 ) ( β ρ 0 ) H m ( 2 ) ( β ρ ) e j m ( ϕ ϕ 0 ) , a N ρ ρ 0 , ρ ρ 0 .
E z t = E 0 m = + H m ( 2 ) ( β ρ 0 ) e j m ( ϕ ϕ 0 ) { B m i J m ( β ρ ) + C m i H m ( 2 ) ( β ρ ) , a i < ρ < a i + 1 , D m J m ( β ρ ) ρ < a 1 ,
E z ( ρ = a i , 0 ϕ , ϕ 0 2 π , z ) | ρ > a i = E z ( ρ = a i , 0 ϕ , ϕ 0 2 π , z ) | ρ < a i ,
H ϕ ( ρ = a i , 0 ϕ , ϕ 0 2 π , z ) | ρ > a i H ϕ ( ρ = a i , 0 ϕ , ϕ 0 2 π , z ) | ρ < a i = σ ( ω ) E z ( ρ = a i , 0 ϕ , ϕ 0 2 π , z ) ,
J m ( β a N ) + A m H m ( 2 ) ( β a N ) = B m N 1 J m ( β a N ) + C m N 1 H m ( 2 ) ( β a N ) ,
B m i + 1 J m ( β a i + 1 ) + C m i + 1 H m ( 2 ) ( β a i + 1 ) = B m i J m ( β a i + 1 ) + C m i H m ( 2 ) ( β a i + 1 ) , i = 1 , 2 , , N 2 ,
B m 1 J m ( β a 1 ) + C m 1 H m ( 2 ) ( β a 1 ) = D m J m ( β a 1 ) ,
j η [ J m ( β a N ) + A m H m ( 2 ) ( β a N ) B m N 1 J m ( β a N ) C m N 1 H m ( 2 ) ( β a N ) ] = σ ( ω ) [ J m ( β a N ) + A m H m ( 2 ) ( β a N ) ] ,
j η [ B m i + 1 J m ( β a i + 1 ) + C m i + 1 H m ( 2 ) ( β a i + 1 ) B m i J m ( β a i + 1 ) C m i H m ( 2 ) ( β a i + 1 ) ] = σ ( ω ) [ B m i J m ( β a i + 1 ) + C m i H m ( 2 ) ( β a i + 1 ) ] , i = 1 , 2 , , N 2 ,
j η [ B m 1 J m ( β a 1 ) + C m 1 H m ( 2 ) ( β a 1 ) D m J m ( β a 1 ) ] = σ ( ω ) D m J m ( β a 1 ) ,
E z ( ρ , ϕ ) = E 0 m = + e j m ( ϕ ϕ 0 ) { H m ( 2 ) ( β ρ 0 ) [ J m ( β ρ ) + A m H m ( 2 ) ( β ρ ) ] , a N ρ ρ 0 , H m ( 2 ) ( β ρ ) [ J m ( β ρ 0 ) + A m H m ( 2 ) ( β ρ 0 ) ] , ρ ρ 0 .
E z ( ρ , ϕ ) = E 0 2 j π β ρ e j β ρ m = + j m [ J m ( β ρ 0 ) + A m H m ( 2 ) ( β ρ 0 ) ] e j m ( ϕ ϕ 0 ) ,
F z s ( ω , ϕ , ϕ 0 ) = m = + j m A m H m ( 2 ) ( β ρ 0 ) e j m ( ϕ ϕ 0 ) ,
W ( ω , ϕ ) = 4 β F z s ( ω , ϕ , ϕ 0 ) 2 .
H z i ( ρ , ϕ ) = H 0 m = + e j m ( ϕ ϕ 0 ) { J m ( β ρ ) H m ( 2 ) ( β ρ 0 ) , ρ ρ 0 , J m ( β ρ 0 ) H m ( 2 ) ( β ρ ) , ρ ρ 0 ,
H z s ( ρ , ϕ ) = H 0 m = + a m H m ( 2 ) ( β ρ 0 ) H m ( 2 ) ( β ρ ) e j m ( ϕ ϕ 0 ) , a N ρ ρ 0 , ρ ρ 0 ,
H z t = H 0 m = + H m ( 2 ) ( β ρ 0 ) e j m ( ϕ ϕ 0 ) { b m i J m ( β ρ ) + c m i H m ( 2 ) ( β ρ ) , a i < ρ < a i + 1 , d m J m ( β ρ ) ρ < a 1 ,
E ϕ ( ρ = a i , 0 ϕ , ϕ 0 2 π , z ) | ρ > a i = E ϕ ( ρ = a i , 0 ϕ , ϕ 0 2 π , z ) | ρ < a i ,
H z ( ρ = a i , 0 ϕ , ϕ 0 2 π , z ) | ρ > a i H z ( ρ = a i , 0 ϕ , ϕ 0 2 π , z ) | ρ < a i = σ ( ω ) E ϕ ( ρ = a i , 0 ϕ , ϕ 0 2 π , z ) ,
J m ( β a N ) + a m H m ( 2 ) ( β a N ) = b m N 1 J m ( β a N ) + b m N 1 H m ( 2 ) ( β a N ) ,
b m i + 1 J m ( β a i + 1 ) + c m i + 1 H m ( 2 ) ( β a i + 1 ) = b m i J m ( β a i + 1 ) + c m i H m ( 2 ) ( β a i + 1 ) , i = 1 , 2 , , N 2 ,
b m 1 J m ( β a 1 ) + c m 1 H m ( 2 ) ( β a 1 ) = d m J m ( β a 1 ) ,
j η [ J m ( β a N ) + a m H m ( 2 ) ( β a N ) b m N 1 J m ( β a N ) c m N 1 H m ( 2 ) ( β a N ) ] = σ ( ω ) [ J m ( β a N ) + a m H m ( 2 ) ( β a N ) ] ,
j η [ b m i + 1 J m ( β a i + 1 ) + c m i + 1 H m ( 2 ) ( β a i + 1 ) b m i J m ( β a i + 1 ) c m i H m ( 2 ) ( β a i + 1 ) ] = σ ( ω ) [ b m i J m ( β a i + 1 ) + c m i H m ( 2 ) ( β a i + 1 ) ] , i = 1 , 2 , , N 2 ,
j η [ b m 1 J m ( β a 1 ) + c m 1 H m ( 2 ) ( β a 1 ) d m J m ( β a 1 ) ] = σ ( ω ) d m J m ( β a 1 ) .
H z ( ρ , ϕ ) = H 0 m = + e j m ( ϕ ϕ 0 ) { H m ( 2 ) ( β ρ 0 ) [ J m ( β ρ ) + a m H m ( 2 ) ( β ρ ) ] , a N ρ ρ 0 , H m ( 2 ) ( β ρ ) [ J m ( β ρ 0 ) + a m H m ( 2 ) ( β ρ 0 ) ] , ρ ρ 0 ,
H z ( ρ , ϕ ) = H 0 2 j π β ρ e j β ρ m = + j m [ J m ( β ρ 0 ) + a m H m ( 2 ) ( β ρ 0 ) ] e j m ( ϕ ϕ 0 ) ,
F z s ( ω , ϕ , ϕ 0 ) = m = + j m a m H m ( 2 ) ( β ρ 0 ) e j m ( ϕ ϕ 0 ) ,

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