Scattering of plane electromagnetic waves on carbon nanotube

Authors

  • Василь Іванович Канєвський Chuiko Institute of Surface Chemistry of National Academy of Sciences of Ukraine 17 General Naumov Str., Kyiv, Ukraine, 03164, Ukraine
  • Віктор Михайлович Розенбаум Chuiko Institute of Surface Chemistry of National Academy of Sciences of Ukraine 17 General Naumov Str., Kyiv, Ukraine, 03164, Ukraine
  • Наталія Григорівна Шкода Chuiko Institute of Surface Chemistry of National Academy of Sciences of Ukraine 17 General Naumov Str., Kyiv, Ukraine, 03164, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2013.14506

Keywords:

Cross section, carbon nanotubes, dielectric tensor, optical range

Abstract

The article presents an overview of the methods of production the tensor of dielectric permeability of multi-walled carbon nanotube (MWCNT) and the use of finite-element approach for calculating the scattering of a plane electromagnetic wave on the MWCNT in the optical range. The approach used was tested by calculation of the differential cross-sections of scattering of a metal rod in the far field and the distribution of electrical, magnetic fields, Poynting vector and conduction currents on the surface of the rod in the near field. The article presents the results of calculations of the scattering of plane electromagnetic waves on a MWCNT for parallel and normal polarized electric field vectors of the incident wave with respect to its axis. It was shown that in the far field the increase in length of MWCNT leads to the formation of the anisotropic angular distribution of the differential scattering cross sections, and the presence of anisotropic dielectric loss causes both quantitative and qualitative changes in the nature of the angular distribution of the differential cross sections: the losses not only scale the scattering cross-section, but also change their shape. Changing the direction of the electric component of the incident field from parallel to perpendicular (relative to the axis of the MWCNT) change the distribution of the differential cross sections: "petals" of the radiation pattern form in the direction perpendicular to the direction of incidence. The study of the distribution of electromagnetic fields within a solid dielectric cylinder showed that the dielectric losses do not prevent the permeability of the fields inside the cylinder, and this means that to describe the scattering on MWCNT it is necessary to consider the thickness of its wall

Author Biographies

Василь Іванович Канєвський, Chuiko Institute of Surface Chemistry of National Academy of Sciences of Ukraine 17 General Naumov Str., Kyiv, Ukraine, 03164

Ph. D.

Віктор Михайлович Розенбаум, Chuiko Institute of Surface Chemistry of National Academy of Sciences of Ukraine 17 General Naumov Str., Kyiv, Ukraine, 03164

Doctor of Science

Наталія Григорівна Шкода, Chuiko Institute of Surface Chemistry of National Academy of Sciences of Ukraine 17 General Naumov Str., Kyiv, Ukraine, 03164

Ph. D.

References

  1. Iijima, S. Helical microtubules of graphitic carbon [Текст] // Nature. – 1991. – V. 354. – P. 56-58.
  2. Treacy, M. Experimentally high Young’s modulus observed for individual carbon nanotubes [Текст] / M. Treacy, T.W. Ebbesen, J.M. Gibson // Nature. – 1996. – V. 381. – P. 678-680.
  3. Zhang, J. Stationary scanning X-ray source based on carbon nanotube field emitters [Текст] / J. Zhang, G. Yang, Y. Cheng // Appl. Phys. Lett. – 2005. – V. 86. – P. 376-379.
  4. LeMieux, M. C. Self-Sorted, Aligned Nanotube Networks for Thin-Film Transistors [Текст] / M.C. LeMieux, M. Roberts, S. Barman, Y.W. Jin, J.M. Kim, Z. Bao // Science. – 2008. – V. 321. – P. 101-104.
  5. Nikolic, B.K. First-principles quantum transport modeling of thermoelectricity in single-molecule nanojunctions with graphene nanoribbon electrodes [Текст] / B.K. Nikolic, K.K. Saha, T. Markussen // J. Comput. Electron. – 2012. – V. 11. – P. 78 92.
  6. Ying, L. Properties of carbon nanotube optical antennae [Текст] / L. Ying, Z. Baoqing // International Journal of Infrared and millimeter Waves. – 2008. – V. 29. – P. 990-996.
  7. Murmu, T. Vibration response of double-walled carbon nanotubes subjected to an externally applied longitudinal magnetic field: A nonlocal elasticity approach [Текст] / T. Murmu, M.A. McCarth, S. Adhikari // J. Sound and Vibration. – 2012. – V. 331. – P. 5069-5086.
  8. Sun, Z., L Band Ultrafast Fiber Laser Mode Locked by Carbon Nanotubes [Текст] / Z. Sun, A.G. Rozhin, F. Wang, A.C. Ferrari // Appl. Phys. Lett. 2008. – V. 93. P. 061114-061115.
  9. Itkis, M.E. Bolometric Infrared Photo-response of Suspended Single-Wall Carbon Nanotube Films [Текст] / M.E. Itkis, F. Borondics, A. Yu, R.C. Haddon // Science. – 2006. – V. 312. – P. 413-416.
  10. Lopez, C. Materials Aspects of Photonic Crystals [Текст] / C. Lopez // Adv. Mater. – 2003. – V. 15. – P. 1679-1704.
  11. John, S. Strong Localization of Photons in Certain Disordered Di-electric Superlattices [Текст] / S. John // Phys. Rev. Lett. – 1987. – V. 58. – P. 2486-2489.
  12. Johnsosn, G.S. Modeling the Flow of Light [Текст] / G.S. Johnsosn, A. Mekis, S.H. Fan, J.D. Joannopoulos // Comput. Sci. Eng. – 2001. – V. 3. – P. 38-47.
  13. Luo, C., All-angle Negative Refraction without Negative Effective Index [Текст] / C. Luo, S.G. Johnson, J.D. Joannopoulos, J.B. Pendry // Phys. Rev. B. – 2002. – V. 65. – P. 201104-201114.
  14. Soukoulis, C.M. Negative Refractive Index at Optical Wavelengths [Текст] / C.M. Soukoulis, S. Linden, M. Wegener // Science. – 2007. – V. 315. – P. 47-49.
  15. Ishau, A. Tuning the optical properties of multiwall carbon nanotube thin films by ion beams irradiation [Текст] / A. Ishau, L. Yan, G. Husnain, Lu Bo, A. Khalid // ACS Nano. – 2011. – V. 6. – P. 357-365.
  16. Vang, Zu-Po. Experimental Observation of an Extremely Dark Material Made By a Low-Density Nanotube Array [Текст] / Vang Zu-Po, L. Ci, J. Bur, Lin Shawn-Yu , P.M. Ajaean // Nano Lett. – 2008. – V. 8. – P. 446-451.
  17. Guo, G. Linear and Nonlinear Optical Properties of Carbon Nanotubes from First-Principals Calculations [Текст] / G. Guo, K. Chu, D.S. Wang, S.G. Duan // Phys. Rev. B. – 2004. – V. 69. – P. 205416-205429.
  18. Partoens, B. From Graphene to Graphite: Electronic Structure around the K Point [Текст] / B. Partoens, F.M. Peeters // Phys. Rev. B. –2004. – V. 74. – P. 205416-205429.
  19. Wooten, F. Optical properties of solids [Текст] / F. Wooten. – New York: Academic Press:, 1972. – 260 p.
  20. Markovic, M.I. Determination of the reflections of laser light of wave-lengths from the surface of aluminum using the Drude-Lorentz model [Текст] / M.I. Markovic, D. Rackis // Appl. Opt. – 1990. – V.29. – P. 3479-3483.
  21. Markovic, M.I. Determination of optical properties of aluminum in-cluding electron reradiation in the Lorentz-Drude Model [Текст] / M.I. Markovic, D. Rackis // Opt. Laser Technol. – 1990. – V.22. – P. 394-398.
  22. Kim, C.C. Modeling the optical dielectric function of semiconductors: Extension of the critical-point parabolic-band approximation [Текст] / C.C. Kim, J.W. Garland, H. Abad, P.M. Raccah // Phys Rev. B. – 1992. – V.45. – P.11749-11767.
  23. Lidorakis, E. Photonics with multiwall carbon nanotube arrays [Текст] / E. Lidorakis, A.C. Ferrari // ACS Nano. – 2009. – V. 3. – P. 1238-1248.
  24. Djurisic, A.B. Optical properties of graphite [Текст] / A.B. Djurisic, E.H. Li // J. Appl. Phys. – 1999. – V.85. – P. 7404-7410.
  25. Djurisic, A.B. Modeling the optical constants of solids using accep-tance-probability-controlled simulated annealing with an adaptive move generation procedure [Текст] / A.B. Djurisic, A.D. Rakic, J.M. Elazar // Phys. Rev. E. – 1997. – V. 55. – P. 4797-4803.
  26. Johnson, L.G. Optical properties of Graphite [Текст] / L.G. Johnson, G. Dresselhaus // Phys. Rev. B. – 1973. – V. 7. – P. 2275-2285.
  27. Ahuja, R. Optical properties of graphite from first-principles calcu-lations [Текст] / R. Ahuja, S. Auluck, J.M. Wills, M. Alouani, B. Johansson // Phys. Rev. B. – 1997 .– V. 55. – P. 4999-5005
  28. Painter, G.S. Electronic band Structure and optical properties of graphite from a variational approach [Текст] / G.S. Painter, D.E. Ellis // Phys. Rev. B. – 1970. – V. 1. – P. 4747-4752.
  29. Greenaway, D.L. Anisotropy of optical constants and the band structure graphite [Текст] / D.L. Greenaway, G. Harbeke // Phys. Rev. – 1969. – V. 178. – P. 1340-1348.
  30. Willis, R.F. Secondary-electron emission spectroscopy and obser-vation of high-energy excited states in graphite: theory and experiment [Текст] / R.F. Willis, B. Fitton // Phys. Rev. B. – 1999. – V. 9. – P. 1926-1937.
  31. Ellis, D.E. Discrete variational method for the energy-band problem with general crystal potentials [Текст] / D.E. Ellis G.S. Painter // Phys. Rev. B. – 1970. – V. 2. – P. 2887-2898.
  32. Stephan, O. Discretic response of isolated carbon nanotubes investigated by spatially resolved electron energy-loss spectroscopy: From multi-walled to single-walled nanotubes [Текст] / O. Stephan, D. Taverna, M. Kociak, K. Suenaga, L. Henrard, C. Colliex // Phys. Rev. B. – 2002. – V. 66. – P. 155422-155433.
  33. Garcia-Vidal, F.J. Effective medium theory of the optical properties of aligned carbon nanotubes [Текст] / F.J. Garcia-Vidal, J.M. Pitarke, J.B. Pendry // Phys. Rev. Lett. – 1997. – V. 78. – P. 4289-4292.
  34. Lu, W. Optical properties of aligned carbon nanotube systems stud-ied by effective-medium approximation method [Текст] / W. Lu, J. Dong., Li Zhen-Ya // Phys. Rev. B. – 2000. – V. 63. – P.033401-033404.
  35. Tanaka, K. The Science and Technology of Carbon Nanotubes [Текст] / K. Tanaka, T. Yamabe, K. Fukui. – New York: Elsevier, 1999. – 199 p.
  36. Baylis, A. Boundary Conditions for the Numerical Solutions of Elliptic Equations in Exterior regions [Текст] / A. Baylis, M. Gunzburger, M. Turkel // SIAM J. Appl. Math. – 1980. – V. 1. – P. 371-385.
  37. Матвеев, А.Н. Оптика [Текст] / А.Н. Матвеев.. – Москва: Высш. шк., 1985. – 342 с.
  38. Volakis, J.L. Finite Element Method for Electromagnetics [Текст] / J.L Volakis, A. Cbatterjee, L.C. Kempel. – IEEE Press, 1998. – 344 p.
  39. Jin, J. The Finite Element Method in Electromagnetics. Second Edition [Текст] / J. Jin. – New York: Willey, 2002. – 753 p.
  40. Chew, W.C. A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates [Текст] / W.C. Chew, W.C. Weedon // Microwave Opt. Tech. Lett. – 1994. – V. 7. – P. 599-604.
  41. Sacks, Z.S. A perfectly matched anisotropic absorber for use as an absorbing boundary condition [Текст] / Z.S. Sacks, D.M. Kingsland, R. Lee, J.F. Lee // IEEE Trans. Antennas Propagat. – 1995. – V. 43. – P. 1460-1463.
  42. Iijima, S. (1991). Helical microtubules of graphitic carbon. Nature, 354, 56-58.
  43. Treacy, M., Ebbesen, T.W., Gibson, J.M. (1996). Experimentally high Young’s modulus observed for individual carbon nanotubes. Nature, 381, 678 680.
  44. Zhang, J., Yang, G., Cheng, Y. (2005). Stationary scanning X-ray source based on carbon nanotube field emitters. Appl. Phys. Lett., 86, 376-379.
  45. LeMieux, M. C., Roberts, M., Barman, S., Jin, Y.W., Kim, J.M., Bao, Z. (2008). Self-Sorted, Aligned Nanotube Networks for Thin-Film Transistors. Science, 321, 101-104.
  46. Nikolic, B.K., Saha, K.K., Markussen, T. (2012). First-principles quantum transport modeling of thermoelectricity in single-molecule nanojunctions with graphene nanoribbon electrodes. J. Comput. Electron, 11, 78-92.
  47. Ying, L., Baoqing, Z. (2008). Properties of carbon nanotube optical antennae. International Journal of Infrared and millimeter Waves,. 29, 990-996.
  48. Murmu, T., McCarth, M.A., Adhikari, S. (2012). Vibration response of double-walled carbon nanotubes subjected to an externally applied longitudinal magnetic field: A nonlocal elasticity approach. J. Sound and Vibration, 331, 5069-5086.
  49. Sun, Z., Rozhin, A.G., Wang, F., Ferrari, A.C. (2008). L Band Ultrafast Fiber Laser Mode Locked by Carbon Nanotubes. Appl. Phys. Lett., 93, 061114-061115.
  50. Itkis, M.E., Borondics, F., Yu, A., Haddon, R.C. (2006). Bolometric Infrared Photo-response of Suspended Single-Wall Carbon Nanotube Films. Science, 312, 413-416.
  51. Lopez, C. (2003). Materials Aspects of Photonic Crystals. Adv. Mater., 15, 1679-1704.
  52. John, S. (1987). Strong Localization of Photons in Certain Disordered Dielectric Superlattices. Phys. Rev. Lett., 58, 2486-2489.
  53. Johnsosn, G.S., Mekis, A., Fan, S.H. Joannopoulos, J.D. (2001). Modeling the Flow of Light. Comput. Sci. Eng., 3, 38-47.
  54. Luo, C., Johnson, S.G., Joannopoulos, J.D., Pendry, J.B. (2002). All-angle Negative Refraction without Negative Effective Index. Phys. Rev. B., 65, 201104-201114.
  55. Soukoulis, C.M., Linden, S., Wegener, M. (2007). Negative Refractive Index at Optical Wavelengths. Science, 315, 47-49.
  56. Ishau, A., Yan, L., Husnain, G., Lu Bo, Khalid, A. (2011). Tuning the optical properties of multiwall carbon nanotube thin films by ion beams ir-radiation. ACS Nano, 6, 357-365.
  57. Vang, Zu-Po, Ci, L., Bur, J.A., Lin, S.Y., Ajaean, P.M. (2008). Experimental Observation of an Extremely Dark Material Made By a Low-Density Nanotube Array. Nano Lett., 8, 446-451.
  58. Guo, G., Chu, K., Wang, D.S., Duan ,S.G. (2004). Linear and Nonlinear Optical Properties of Carbon Nanotubes from First-Principals Calcula-tions. Phys. Rev. B., 69, 205416-205429.
  59. Partoens, B., Peeters, F.M. (2004). From Graphene to Graphite: Electronic Structure around the K Point. Phys. Rev. B., 74, 205416-205429.
  60. Wooten, F. (1972). Optical properties of solids. New York: Academic Press, 260.
  61. Markovic, M.I., Rackis, D. (1990). Determination of the reflections of laser light of wavelengths from the surface of aluminum using the Drude-Lorentz model. Appl. Opt.,29, 3479-3483.
  62. Markovic, M.I., Rackis, D. (1990). Determination of optical proper-ties of aluminum including electron reradiation in the Lorentz-Drude Model. Opt. Laser Technol., 22, 394-398.
  63. Kim, C.C., Garland, J.W, Abad, H., Raccah, P.M. (1992). Modeling the optical dielectric function of semiconductors: Extension of the critical-point parabolic-band approximation. Phys Rev. B., 45, 11749-11767.
  64. Lidorakis, E., Ferrari, A.C. (2009). Photonics with multiwall carbon nanotube arrays. ACS Nano, 3, 1238-1248.
  65. Djurisic, A.B., Li, E.H. (1999). Optical properties of graphite. J. Appl. Phys., 85, 7404-7410.
  66. Djurisic, A.B., Rakic, A.D., Elazar, J.M. (1997). Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with an adaptive move generation procedure. Phys. Rev. E., 55, 4797-4803.
  67. Johnson, L.G., Dresselhaus, G. (1973). Optical properties of Graphite. Phys. Rev. B., 7, 2275-2285.
  68. Ahuja, R., Auluck, S., Wills, J.M., Alouani, M., Johansson, B., Eriksson, O. (1997). Optical properties of graphite from first-principles calculations. Phys. Rev. B., 55, 4999-5005.
  69. Painter,G.S., Ellis, D.E. (1970). Electronic band Structure and optical properties of graphite from a variational approach. Phys. Rev. B., 1, 4747-4752.
  70. Greenaway, D.L, Harbeke, G. (1969). Anisotropy of optical con-stants and the band structure graphite. Phys. Rev., 178, 1340-1348.
  71. Willis, R.F., Fitton, B. (1999). Secondary-electron emission spec-troscopy and observation of high-energy excited states in graphite: theory and experiment. Phys. Rev. B., 9, 1926-1937.
  72. Ellis, D.E. Painter, G.S. (1970). Discrete variational method for the energy-band problem with general crystal potentials. Phys. Rev. B., 2, 2887-2898.
  73. Stephan, O., Taverna, D., Kociak, M., Suenaga, K., Henrard, L., Colliex, C. (2002). Discretic response of isolated carbon nanotubes investigated by spatially resolved electron energy-loss spectroscopy: From multi-walled to single-walled nanotubes. Phys. Rev. B., 66, 155422-155433.
  74. Garcia-Vidal, F.J., Pitarke, J.M., Pendry, J.B. (1997). Effective medium theory of the optical properties of aligned carbon nanotubes. Phys. Rev. Lett., 78, 4289-4292.
  75. Lu, W., Dong, J., Li, Z.Y. (2000). Optical properties of aligned carbon nanotube systems studied by effective-medium approximation method. Phys. Rev. B., 63, 033401-033404.
  76. Tanaka, K., Yamabe, T., Fukui, K. (1999). The Science and Technology of Carbon Nanotubes. New York: Elsevier, 199.
  77. Baylis, A., Gunzburger, M., Turkel, M. (1980). Boundary Conditions for the Numerical Solutions of Elliptic Equations in Exterior regions. SIAM J. Appl. Math., 1, 371-385.
  78. Matveev, A.N. (1985). Optics. Moscow, USSR: Vysshaia Shkola, 342.
  79. Volakis, J.L., Cbatterjee, A., Kempel, L.C. (1998). Finite Element Method for Electromagnetics. IEEE Press, 344.
  80. Jin, J. (2002). The Finite Element Method in Electromagnetics. Second Edition. New York: Willey, 753.
  81. Chew, W.C., Weedon, W.C. (1994). A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates. Micro-wave Opt. Tech. Lett., 7, 599-604.
  82. Sacks, Z.S., Kingsland, D.M., Lee, R., Lee, J.F. (1995). A perfectly matched anisotropic absorber for use as an absorbing boundary condition. IEEE Trans. Antennas Propagat, 43, 1460-1463.

Downloads

Published

2013-06-20

How to Cite

Канєвський, В. І., Розенбаум, В. М., & Шкода, Н. Г. (2013). Scattering of plane electromagnetic waves on carbon nanotube. Eastern-European Journal of Enterprise Technologies, 3(5(63), 38–46. https://doi.org/10.15587/1729-4061.2013.14506

Issue

Vol. 3 No. 5(63) (2013): The applied physics and materials technology

Section

Applied physics

License

Copyright (c) 2014 Василь Іванович Канєвський, Віктор Михайлович Розенбаум, Наталія Григорівна Шкода

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.