Abstract

An anomalous resonant behavior is observed in the transmission through composite layers of randomly oriented conducting fibers at frequencies above the primary one-half wavelength dipole resonance. The echo of radiation from the encounter of waves propagating along fibers, which are oriented in the direction of the incident wave, with the discontinuity at the end, is found to be the cause of the anomaly. This end-fire echo dominates the dipole radiation pattern for electrically long conductors at oblique angles. Layers of randomly distributed 1cm long fibers having a 0.8/cm3 number density are examined from 1 to 50GHz through a series of numerical experiments using the finite difference time domain method. Composites made from the same fibers aligned with the incident electric field do not exhibit the anomalous resonant behavior. Transmission for these aligned fibers is well-explained using Beer’s law, given the total cross section for a single dipole.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. D. Jackson, in Classical Electrodynamics (Wiley, 1975), pp. 152–155.
  2. J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Phil. Trans. R. Soc. London Ser. A 203, 385–420 (1904).
    [CrossRef]
  3. J. A. Roberts, T. Imholt, Z. Ye, C. A. Dyke, D. W. Price, Jr., and J. M. Tour, “Electromagnetic wave properties of polymer blends of single wall carbon nanotubes using a resonant microwave cavity as a probe,” J. Appl. Phys. 95, 4352–4356 (2004).
    [CrossRef]
  4. Y. Wang, K. Kempa, B. Kimball, J. B. Carlson, G. Benham, W. Z. Li, T. Kempa, J. Rybczynski, A. Herczynski, and Z. F. Ren, “Receiving and transmitting light-like radio waves: Antenna effect in arrays of aligned carbon nanotubes,” Appl. Phys. Lett. 85, 2607–2609 (2004).
    [CrossRef]
  5. H. Überall, B. F. Howell, and E. L. Diamond, “Effective medium theory and the attenuation of graphite fiber composites,” J. Appl. Phys. 73, 3441–3445 (1993).
    [CrossRef]
  6. L. Liu, S. M. Matitsine, Y. B. Gan, and K. N. Rozanov, “Effective permittivity of planar composites with randomly or periodically distributed conducting fibers,” J. Appl. Phys. 98, 063512 (2005).
    [CrossRef]
  7. P. Loschialpo, D. Smith, and D. Zabetakis, “Effective medium theory for strongly coupled randomly oriented conducting fibers on a planar surface,” J. Appl. Phys. 104, 104903 (2008).
    [CrossRef]
  8. L. N. Medgyesi-Mitschang, J. M. Putnam, and M. B. Gedara, “Generalized method of moments for three-dimensional penetrable scatterers,” J. Opt. Soc. Am. A 11, 1383–1398 (1994).
    [CrossRef]
  9. J. M. Hollas, in Modern Spectroscopy (Wiley, 2004), pp. 382–383.
  10. P. F. Loschialpo, D. L. Smith, D. W. Forester, F. J. Rachford, and J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 026502(2003).
    [CrossRef]
  11. P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, C. Monzon, and J. S. Schelleng, “Optical properties of an ideal homogeneous, causal “left handed” material slab,” Phys. Rev. E 70, 036605 (2004).
    [CrossRef]
  12. L. Peters, Jr., “End-fire echo of long, thin bodies,” IRE Transactions on Antennas and Propagation 6, 133–139 (1958).
    [CrossRef]
  13. L. N. Medgyesi-Mitschang and J. M. Putnam, “Electromagnetic scattering from extended wires and two- and three dimensional surfaces,” IEEE Trans. Antennas Propag. AP-33, 1090–1100(1985).
    [CrossRef]
  14. G. T. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, “Traveling waves,” in Radar Cross Section Handbook, G.T.Ruck (ed.) (Plenum Press, 1970), pp. 130–133.
  15. E. F. Knott, J. F. Shaeffer, and M. T. Tuley, in Radar Cross Section (Artech House, 1993), p. 228.
  16. J. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comp. Physiol. 114, 185–200(1994).

2008 (1)

P. Loschialpo, D. Smith, and D. Zabetakis, “Effective medium theory for strongly coupled randomly oriented conducting fibers on a planar surface,” J. Appl. Phys. 104, 104903 (2008).
[CrossRef]

2005 (1)

L. Liu, S. M. Matitsine, Y. B. Gan, and K. N. Rozanov, “Effective permittivity of planar composites with randomly or periodically distributed conducting fibers,” J. Appl. Phys. 98, 063512 (2005).
[CrossRef]

2004 (3)

J. A. Roberts, T. Imholt, Z. Ye, C. A. Dyke, D. W. Price, Jr., and J. M. Tour, “Electromagnetic wave properties of polymer blends of single wall carbon nanotubes using a resonant microwave cavity as a probe,” J. Appl. Phys. 95, 4352–4356 (2004).
[CrossRef]

Y. Wang, K. Kempa, B. Kimball, J. B. Carlson, G. Benham, W. Z. Li, T. Kempa, J. Rybczynski, A. Herczynski, and Z. F. Ren, “Receiving and transmitting light-like radio waves: Antenna effect in arrays of aligned carbon nanotubes,” Appl. Phys. Lett. 85, 2607–2609 (2004).
[CrossRef]

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, C. Monzon, and J. S. Schelleng, “Optical properties of an ideal homogeneous, causal “left handed” material slab,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

2003 (1)

P. F. Loschialpo, D. L. Smith, D. W. Forester, F. J. Rachford, and J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 026502(2003).
[CrossRef]

1994 (2)

J. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comp. Physiol. 114, 185–200(1994).

L. N. Medgyesi-Mitschang, J. M. Putnam, and M. B. Gedara, “Generalized method of moments for three-dimensional penetrable scatterers,” J. Opt. Soc. Am. A 11, 1383–1398 (1994).
[CrossRef]

1993 (1)

H. Überall, B. F. Howell, and E. L. Diamond, “Effective medium theory and the attenuation of graphite fiber composites,” J. Appl. Phys. 73, 3441–3445 (1993).
[CrossRef]

1985 (1)

L. N. Medgyesi-Mitschang and J. M. Putnam, “Electromagnetic scattering from extended wires and two- and three dimensional surfaces,” IEEE Trans. Antennas Propag. AP-33, 1090–1100(1985).
[CrossRef]

1958 (1)

L. Peters, Jr., “End-fire echo of long, thin bodies,” IRE Transactions on Antennas and Propagation 6, 133–139 (1958).
[CrossRef]

1904 (1)

J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Phil. Trans. R. Soc. London Ser. A 203, 385–420 (1904).
[CrossRef]

Barrick, D. E.

G. T. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, “Traveling waves,” in Radar Cross Section Handbook, G.T.Ruck (ed.) (Plenum Press, 1970), pp. 130–133.

Benham, G.

Y. Wang, K. Kempa, B. Kimball, J. B. Carlson, G. Benham, W. Z. Li, T. Kempa, J. Rybczynski, A. Herczynski, and Z. F. Ren, “Receiving and transmitting light-like radio waves: Antenna effect in arrays of aligned carbon nanotubes,” Appl. Phys. Lett. 85, 2607–2609 (2004).
[CrossRef]

Berenger, J.

J. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comp. Physiol. 114, 185–200(1994).

Carlson, J. B.

Y. Wang, K. Kempa, B. Kimball, J. B. Carlson, G. Benham, W. Z. Li, T. Kempa, J. Rybczynski, A. Herczynski, and Z. F. Ren, “Receiving and transmitting light-like radio waves: Antenna effect in arrays of aligned carbon nanotubes,” Appl. Phys. Lett. 85, 2607–2609 (2004).
[CrossRef]

Diamond, E. L.

H. Überall, B. F. Howell, and E. L. Diamond, “Effective medium theory and the attenuation of graphite fiber composites,” J. Appl. Phys. 73, 3441–3445 (1993).
[CrossRef]

Dyke, C. A.

J. A. Roberts, T. Imholt, Z. Ye, C. A. Dyke, D. W. Price, Jr., and J. M. Tour, “Electromagnetic wave properties of polymer blends of single wall carbon nanotubes using a resonant microwave cavity as a probe,” J. Appl. Phys. 95, 4352–4356 (2004).
[CrossRef]

Forester, D. W.

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, C. Monzon, and J. S. Schelleng, “Optical properties of an ideal homogeneous, causal “left handed” material slab,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

P. F. Loschialpo, D. L. Smith, D. W. Forester, F. J. Rachford, and J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 026502(2003).
[CrossRef]

Gan, Y. B.

L. Liu, S. M. Matitsine, Y. B. Gan, and K. N. Rozanov, “Effective permittivity of planar composites with randomly or periodically distributed conducting fibers,” J. Appl. Phys. 98, 063512 (2005).
[CrossRef]

Gedara, M. B.

Herczynski, A.

Y. Wang, K. Kempa, B. Kimball, J. B. Carlson, G. Benham, W. Z. Li, T. Kempa, J. Rybczynski, A. Herczynski, and Z. F. Ren, “Receiving and transmitting light-like radio waves: Antenna effect in arrays of aligned carbon nanotubes,” Appl. Phys. Lett. 85, 2607–2609 (2004).
[CrossRef]

Hollas, J. M.

J. M. Hollas, in Modern Spectroscopy (Wiley, 2004), pp. 382–383.

Howell, B. F.

H. Überall, B. F. Howell, and E. L. Diamond, “Effective medium theory and the attenuation of graphite fiber composites,” J. Appl. Phys. 73, 3441–3445 (1993).
[CrossRef]

Imholt, T.

J. A. Roberts, T. Imholt, Z. Ye, C. A. Dyke, D. W. Price, Jr., and J. M. Tour, “Electromagnetic wave properties of polymer blends of single wall carbon nanotubes using a resonant microwave cavity as a probe,” J. Appl. Phys. 95, 4352–4356 (2004).
[CrossRef]

Jackson, J. D.

J. D. Jackson, in Classical Electrodynamics (Wiley, 1975), pp. 152–155.

Kempa, K.

Y. Wang, K. Kempa, B. Kimball, J. B. Carlson, G. Benham, W. Z. Li, T. Kempa, J. Rybczynski, A. Herczynski, and Z. F. Ren, “Receiving and transmitting light-like radio waves: Antenna effect in arrays of aligned carbon nanotubes,” Appl. Phys. Lett. 85, 2607–2609 (2004).
[CrossRef]

Kempa, T.

Y. Wang, K. Kempa, B. Kimball, J. B. Carlson, G. Benham, W. Z. Li, T. Kempa, J. Rybczynski, A. Herczynski, and Z. F. Ren, “Receiving and transmitting light-like radio waves: Antenna effect in arrays of aligned carbon nanotubes,” Appl. Phys. Lett. 85, 2607–2609 (2004).
[CrossRef]

Kimball, B.

Y. Wang, K. Kempa, B. Kimball, J. B. Carlson, G. Benham, W. Z. Li, T. Kempa, J. Rybczynski, A. Herczynski, and Z. F. Ren, “Receiving and transmitting light-like radio waves: Antenna effect in arrays of aligned carbon nanotubes,” Appl. Phys. Lett. 85, 2607–2609 (2004).
[CrossRef]

Knott, E. F.

E. F. Knott, J. F. Shaeffer, and M. T. Tuley, in Radar Cross Section (Artech House, 1993), p. 228.

Krichbaum, C. K.

G. T. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, “Traveling waves,” in Radar Cross Section Handbook, G.T.Ruck (ed.) (Plenum Press, 1970), pp. 130–133.

Li, W. Z.

Y. Wang, K. Kempa, B. Kimball, J. B. Carlson, G. Benham, W. Z. Li, T. Kempa, J. Rybczynski, A. Herczynski, and Z. F. Ren, “Receiving and transmitting light-like radio waves: Antenna effect in arrays of aligned carbon nanotubes,” Appl. Phys. Lett. 85, 2607–2609 (2004).
[CrossRef]

Liu, L.

L. Liu, S. M. Matitsine, Y. B. Gan, and K. N. Rozanov, “Effective permittivity of planar composites with randomly or periodically distributed conducting fibers,” J. Appl. Phys. 98, 063512 (2005).
[CrossRef]

Loschialpo, P.

P. Loschialpo, D. Smith, and D. Zabetakis, “Effective medium theory for strongly coupled randomly oriented conducting fibers on a planar surface,” J. Appl. Phys. 104, 104903 (2008).
[CrossRef]

Loschialpo, P. F.

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, C. Monzon, and J. S. Schelleng, “Optical properties of an ideal homogeneous, causal “left handed” material slab,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

P. F. Loschialpo, D. L. Smith, D. W. Forester, F. J. Rachford, and J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 026502(2003).
[CrossRef]

Matitsine, S. M.

L. Liu, S. M. Matitsine, Y. B. Gan, and K. N. Rozanov, “Effective permittivity of planar composites with randomly or periodically distributed conducting fibers,” J. Appl. Phys. 98, 063512 (2005).
[CrossRef]

Maxwell Garnett, J. C.

J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Phil. Trans. R. Soc. London Ser. A 203, 385–420 (1904).
[CrossRef]

Medgyesi-Mitschang, L. N.

L. N. Medgyesi-Mitschang, J. M. Putnam, and M. B. Gedara, “Generalized method of moments for three-dimensional penetrable scatterers,” J. Opt. Soc. Am. A 11, 1383–1398 (1994).
[CrossRef]

L. N. Medgyesi-Mitschang and J. M. Putnam, “Electromagnetic scattering from extended wires and two- and three dimensional surfaces,” IEEE Trans. Antennas Propag. AP-33, 1090–1100(1985).
[CrossRef]

Monzon, C.

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, C. Monzon, and J. S. Schelleng, “Optical properties of an ideal homogeneous, causal “left handed” material slab,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

Peters, L.

L. Peters, Jr., “End-fire echo of long, thin bodies,” IRE Transactions on Antennas and Propagation 6, 133–139 (1958).
[CrossRef]

Price, D. W.

J. A. Roberts, T. Imholt, Z. Ye, C. A. Dyke, D. W. Price, Jr., and J. M. Tour, “Electromagnetic wave properties of polymer blends of single wall carbon nanotubes using a resonant microwave cavity as a probe,” J. Appl. Phys. 95, 4352–4356 (2004).
[CrossRef]

Putnam, J. M.

L. N. Medgyesi-Mitschang, J. M. Putnam, and M. B. Gedara, “Generalized method of moments for three-dimensional penetrable scatterers,” J. Opt. Soc. Am. A 11, 1383–1398 (1994).
[CrossRef]

L. N. Medgyesi-Mitschang and J. M. Putnam, “Electromagnetic scattering from extended wires and two- and three dimensional surfaces,” IEEE Trans. Antennas Propag. AP-33, 1090–1100(1985).
[CrossRef]

Rachford, F. J.

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, C. Monzon, and J. S. Schelleng, “Optical properties of an ideal homogeneous, causal “left handed” material slab,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

P. F. Loschialpo, D. L. Smith, D. W. Forester, F. J. Rachford, and J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 026502(2003).
[CrossRef]

Ren, Z. F.

Y. Wang, K. Kempa, B. Kimball, J. B. Carlson, G. Benham, W. Z. Li, T. Kempa, J. Rybczynski, A. Herczynski, and Z. F. Ren, “Receiving and transmitting light-like radio waves: Antenna effect in arrays of aligned carbon nanotubes,” Appl. Phys. Lett. 85, 2607–2609 (2004).
[CrossRef]

Roberts, J. A.

J. A. Roberts, T. Imholt, Z. Ye, C. A. Dyke, D. W. Price, Jr., and J. M. Tour, “Electromagnetic wave properties of polymer blends of single wall carbon nanotubes using a resonant microwave cavity as a probe,” J. Appl. Phys. 95, 4352–4356 (2004).
[CrossRef]

Rozanov, K. N.

L. Liu, S. M. Matitsine, Y. B. Gan, and K. N. Rozanov, “Effective permittivity of planar composites with randomly or periodically distributed conducting fibers,” J. Appl. Phys. 98, 063512 (2005).
[CrossRef]

Ruck, G. T.

G. T. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, “Traveling waves,” in Radar Cross Section Handbook, G.T.Ruck (ed.) (Plenum Press, 1970), pp. 130–133.

Rybczynski, J.

Y. Wang, K. Kempa, B. Kimball, J. B. Carlson, G. Benham, W. Z. Li, T. Kempa, J. Rybczynski, A. Herczynski, and Z. F. Ren, “Receiving and transmitting light-like radio waves: Antenna effect in arrays of aligned carbon nanotubes,” Appl. Phys. Lett. 85, 2607–2609 (2004).
[CrossRef]

Schelleng, J.

P. F. Loschialpo, D. L. Smith, D. W. Forester, F. J. Rachford, and J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 026502(2003).
[CrossRef]

Schelleng, J. S.

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, C. Monzon, and J. S. Schelleng, “Optical properties of an ideal homogeneous, causal “left handed” material slab,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

Shaeffer, J. F.

E. F. Knott, J. F. Shaeffer, and M. T. Tuley, in Radar Cross Section (Artech House, 1993), p. 228.

Smith, D.

P. Loschialpo, D. Smith, and D. Zabetakis, “Effective medium theory for strongly coupled randomly oriented conducting fibers on a planar surface,” J. Appl. Phys. 104, 104903 (2008).
[CrossRef]

Smith, D. L.

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, C. Monzon, and J. S. Schelleng, “Optical properties of an ideal homogeneous, causal “left handed” material slab,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

P. F. Loschialpo, D. L. Smith, D. W. Forester, F. J. Rachford, and J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 026502(2003).
[CrossRef]

Stuart, W. D.

G. T. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, “Traveling waves,” in Radar Cross Section Handbook, G.T.Ruck (ed.) (Plenum Press, 1970), pp. 130–133.

Tour, J. M.

J. A. Roberts, T. Imholt, Z. Ye, C. A. Dyke, D. W. Price, Jr., and J. M. Tour, “Electromagnetic wave properties of polymer blends of single wall carbon nanotubes using a resonant microwave cavity as a probe,” J. Appl. Phys. 95, 4352–4356 (2004).
[CrossRef]

Tuley, M. T.

E. F. Knott, J. F. Shaeffer, and M. T. Tuley, in Radar Cross Section (Artech House, 1993), p. 228.

Überall, H.

H. Überall, B. F. Howell, and E. L. Diamond, “Effective medium theory and the attenuation of graphite fiber composites,” J. Appl. Phys. 73, 3441–3445 (1993).
[CrossRef]

Wang, Y.

Y. Wang, K. Kempa, B. Kimball, J. B. Carlson, G. Benham, W. Z. Li, T. Kempa, J. Rybczynski, A. Herczynski, and Z. F. Ren, “Receiving and transmitting light-like radio waves: Antenna effect in arrays of aligned carbon nanotubes,” Appl. Phys. Lett. 85, 2607–2609 (2004).
[CrossRef]

Ye, Z.

J. A. Roberts, T. Imholt, Z. Ye, C. A. Dyke, D. W. Price, Jr., and J. M. Tour, “Electromagnetic wave properties of polymer blends of single wall carbon nanotubes using a resonant microwave cavity as a probe,” J. Appl. Phys. 95, 4352–4356 (2004).
[CrossRef]

Zabetakis, D.

P. Loschialpo, D. Smith, and D. Zabetakis, “Effective medium theory for strongly coupled randomly oriented conducting fibers on a planar surface,” J. Appl. Phys. 104, 104903 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

Y. Wang, K. Kempa, B. Kimball, J. B. Carlson, G. Benham, W. Z. Li, T. Kempa, J. Rybczynski, A. Herczynski, and Z. F. Ren, “Receiving and transmitting light-like radio waves: Antenna effect in arrays of aligned carbon nanotubes,” Appl. Phys. Lett. 85, 2607–2609 (2004).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

L. N. Medgyesi-Mitschang and J. M. Putnam, “Electromagnetic scattering from extended wires and two- and three dimensional surfaces,” IEEE Trans. Antennas Propag. AP-33, 1090–1100(1985).
[CrossRef]

IRE Transactions on Antennas and Propagation (1)

L. Peters, Jr., “End-fire echo of long, thin bodies,” IRE Transactions on Antennas and Propagation 6, 133–139 (1958).
[CrossRef]

J. Appl. Phys. (4)

J. A. Roberts, T. Imholt, Z. Ye, C. A. Dyke, D. W. Price, Jr., and J. M. Tour, “Electromagnetic wave properties of polymer blends of single wall carbon nanotubes using a resonant microwave cavity as a probe,” J. Appl. Phys. 95, 4352–4356 (2004).
[CrossRef]

H. Überall, B. F. Howell, and E. L. Diamond, “Effective medium theory and the attenuation of graphite fiber composites,” J. Appl. Phys. 73, 3441–3445 (1993).
[CrossRef]

L. Liu, S. M. Matitsine, Y. B. Gan, and K. N. Rozanov, “Effective permittivity of planar composites with randomly or periodically distributed conducting fibers,” J. Appl. Phys. 98, 063512 (2005).
[CrossRef]

P. Loschialpo, D. Smith, and D. Zabetakis, “Effective medium theory for strongly coupled randomly oriented conducting fibers on a planar surface,” J. Appl. Phys. 104, 104903 (2008).
[CrossRef]

J. Comp. Physiol. (1)

J. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comp. Physiol. 114, 185–200(1994).

J. Opt. Soc. Am. A (1)

Phil. Trans. R. Soc. London Ser. A (1)

J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Phil. Trans. R. Soc. London Ser. A 203, 385–420 (1904).
[CrossRef]

Phys. Rev. E (2)

P. F. Loschialpo, D. L. Smith, D. W. Forester, F. J. Rachford, and J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 026502(2003).
[CrossRef]

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, C. Monzon, and J. S. Schelleng, “Optical properties of an ideal homogeneous, causal “left handed” material slab,” Phys. Rev. E 70, 036605 (2004).
[CrossRef]

Other (4)

J. D. Jackson, in Classical Electrodynamics (Wiley, 1975), pp. 152–155.

J. M. Hollas, in Modern Spectroscopy (Wiley, 2004), pp. 382–383.

G. T. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, “Traveling waves,” in Radar Cross Section Handbook, G.T.Ruck (ed.) (Plenum Press, 1970), pp. 130–133.

E. F. Knott, J. F. Shaeffer, and M. T. Tuley, in Radar Cross Section (Artech House, 1993), p. 228.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

MOM computation of differential cross section for 1 cm long fibers tilted in a plane transverse to the direction of an incident plane wave at angles 0 ° , 15 ° , 30 ° , 45 ° , 60 ° , and 75 ° .

Fig. 2
Fig. 2

Schematic on top shows the orientation of the fibers with respect to the incident wave. The graph shows the total cross section computed with MOM (dots) of fibers tilted at angles 0 ° , 15 ° , 30 ° , 45 ° , 60 ° , and 75 ° in a plane transverse to the direction of an incident plane wave. Solid curves depict the product of the cross section of an aligned fiber and cos 2 θ .

Fig. 3
Fig. 3

Transmission through a 10 cm thick layer of the same fibers having a density of 0.8 / cm 3 that are aligned with the electric field of an incident plane wave. Averaged results of two FDTD simulations are shown by the solid curve and the results of a calculation using Beer’s law are given by the smooth dashed curve.

Fig. 4
Fig. 4

Schematic on top depicts the positioning of the aligned fiber layers inside the 20 cm long discretized volume used for FDTD simulations. Bar charts on the bottom show the distribution of distances between each fiber and its nearest neighbor for the two sample distributions.

Fig. 5
Fig. 5

Transmission through a 10 cm thick layer of fibers having a density of 0.8 / cm 3 that are randomly oriented with respect to the electric field of an incident plane wave. The smooth dashed curve represents the result of a Beer’s law calculation with an average cross section obtained by dividing the aligned fiber cross section by three. The solid curve shows the average transmission from FDTD simulations performed for two sample distributions of randomly oriented fibers having the same density.

Fig. 6
Fig. 6

Schematic on top depicts the positioning of the randomly oriented fiber layers inside the 20 cm long discretized vol ume used for FDTD simulations. Bar charts on the bottom show the distribution of distances between each fiber and its nearest neighbor for the two sample distributions.

Fig. 7
Fig. 7

MOM computation of differential cross section for 1 cm long fibers tilted forward in the direction of propagation at angles 0 ° , 15 ° , 30 ° , 45 ° , 60 ° , and 75 ° .

Fig. 8
Fig. 8

Radiation pattern of fibers tilted 45 ° from the electric field of an incident wave at 43 GHz . (a) The typical dipole pattern at ( 3 / 2 ) λ resonance for a fiber tilted in a plane transverse to the direction of incidence. (b) The radiation pattern dominated by the end-fire echo for a fiber tilted in the forward direction.

Fig. 9
Fig. 9

Schematic on top shows the orientation of the fibers with respect to the incident wave. The graph shows the total cross section computed with MOM (dots) of fibers tilted forward in the direction of propagation at angles 0 ° , 15 ° , 30 ° , 45 ° , 60 ° , and 75 ° . Solid lines depict the product of the cross section of an aligned fiber and cos 2 θ .

Fig. 10
Fig. 10

Schematic defining the coordinates used to compute the weighted average cross section of a fiber that can have an arbitrary orientation with respect to the electric field of an incident plane wave.

Fig. 11
Fig. 11

Transmission through a 10 cm thick layer of fibers having a density of 0.8 / cm 3 that are randomly oriented with respect to the electric field of an incident plane wave. The smooth dashed curve represents the result of a Beer’s law calculation with the cross section computed using the weighted-averaging procedure described by Eq. (4). The large improvement in accuracy due to the inclusion of end-fire radiation is evident by comparing the smooth dashed curve with the FDTD result (solid curve repeated from Fig. 5).

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

T = e ( n σ 1 d ) .
α = 90 ° 49 ° λ L ,
σ avg = 1 2 π 0 π 2 0 2 π σ 1 ( θ , ϕ ) sin ( θ ) d θ d ϕ .
σ avg = 1 2 0 π 2 σ ( θ , ϕ = 0 ) sin ( θ ) d θ + 1 2 0 π 2 σ ( θ , ϕ = π 2 ) sin ( θ ) d θ .
0 π 2 f ( θ ) d θ π 12 [ 1 3 f ( 0 ) + 4 3 f ( π 12 ) + 2 3 f ( 2 π 12 ) + 4 3 f ( 3 π 12 ) + 2 3 f ( 4 π 12 ) + 4 3 f ( 5 π 12 ) + 1 3 f ( 6 π 12 ) ] .

Metrics