Abstract

We demonstrate the use of a full-wave electromagnetic field simulator to verify terahertz (THz) transmission-mode spectroscopic measurements of periodic arrays containing subwavelength cylindrical scatterers. Many existing THz scattering studies utilize analytical solutions, which were developed for a single scatterer. For multiple scatterers, a scaling factor equal to the number of scatterers is applied, accounting for interference between far-field radiative contributions from those scatterers but not their near-field mutual coupling. Consequently, analytical solutions do not accurately verify measurements. Conversely, results from the full-wave electromagnetic field simulator elucidate our measurements well, and provide an important insight into how the scattering behavior of cylindrical scatterers is influenced by test conditions.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983).
  2. L. M. Zurk, B. Orlowski, D. P. Winebrenner, E. I. Thorsos, M. R. Leahy-Hoppa, and L. M. Hayden, “Terahertz scattering from granular material,” J. Opt. Soc. Am. B 24, 2238–2243 (2007).
    [CrossRef]
  3. A. Bandyopadhyay, A. Sengupta, R. B. Barat, D. E. Gary, J. F. Federici, M. Chen, and D. B. Tanner, “Effects of scattering on THz spectra of granular solids,” Int. J. Infrared Millim. Waves 28, 969–978 (2007).
    [CrossRef]
  4. Y.-C. Shen, P. F. Taday, and M. Pepper, “Elimination of scattering effects in spectral measurement of granulated materials using terahertz pulsed spectroscopy,” Appl. Phys. Lett. 92, 051103 (2008).
    [CrossRef]
  5. M. Franz, B. M. Fischer, and M. Walther, “The Christiansen effect in terahertz time-domain spectra of coarse-grained powders,” Appl. Phys. Lett. 92, 021107 (2008).
    [CrossRef]
  6. J. E. Bjarnason, T. L. J. Chan, A. W. M. Lee, M. A. Celis, and E. R. Brown, “Millimeter-wave, terahertz, and mid-infrared transmission through common clothing,” Appl. Phys. Lett. 85, 519–521 (2004).
    [CrossRef]
  7. M. A. Kaliteevski, D. M. Beggs, S. Brand, R. A. Abram, J. R. Fletcher, G. P. Swift, and J. M. Chamberlain, “Propagation of electromagnetic waves through a system of randomly placed cylinders: The partial scattering wave resonance,” J. Mod. Opt. 53, 2089–2097 (2006).
    [CrossRef]
  8. J. R. Fletcher, G. P. Swift, D. C. Dai, J. A. Levitt, and J. M. Chamberlain, “Propagation of terahertz radiation through random structures: An alternative theoretical approach and experimental validation,” J. Appl. Phys. 101, 013102 (2007).
    [CrossRef]
  9. Y. L. Hor, J. F. Federici, and R. L. Wample, “Nondestructive evaluation of cork enclosures using terahertz/millimeter wave spectroscopy and imaging,” Appl. Opt. 47, 72–78 (2008).
    [CrossRef]
  10. P. Y. Han, G. C. Cho, and X.-C. Zhang, “Time-domain transillumination of biological tissues with terahertz pulses,” Opt. Lett. 25, 242–244 (2000).
    [CrossRef]
  11. M. Reid and R. Fedosejevs, “Terahertz birefringence and attenuation properties of wood and paper,” Appl. Opt. 45, 2766–2772 (2006).
    [CrossRef] [PubMed]
  12. J. Beckmann, H. Richter, U. Zscherpel, U. Ewert, J. Weinzierl, L.-P. Schmidt, F. Rutz, M. Koch, H. Richter, and H.-W. Hübers, “Imaging capability of terahertz and millimeter-wave instrumentations for NDT of polymer materials,” in Proceedings of 9th European Conference on Nondestructive Testing (NDT) , R. Diederichs, ed. (The e-Journal of Nondestructive Testing, 2006).
  13. K. Naito, Y. Kagawa, S. Utsuno, T. Naganuma, and K. Kurihara, “Dielectric properties of eight-harness-stain fabric glass fiber reinforced polyimide matrix composite in the THz frequency range,” NDT & E Int. 42, 441–445 (2009).
    [CrossRef]
  14. K. Naito, Y. Kagawa, S. Utsuno, T. Naganuma, and K. Kurihara, “Dielectric properties of woven fabric glass fiber reinforced polymer matrix composites in the THz frequency range,” Compos. Sci. Technol. 69, 2027–2029 (2009).
    [CrossRef]
  15. X.-L. Tang, Y.-W. Shi, Y. Matsuura, K. Iwai, and M. Miyagi, “Transmission characteristics of terahertz hollow fiber with an absorptive dielectric inner-coating film,” Opt. Lett. 34, 2231–2233 (2009).
    [CrossRef] [PubMed]
  16. Y. Dikmelik, J. B. Spicer, M. J. Fitch, and R. Osiander, “Effects of surface roughness on reflection spectra obtained by terahertz time-domain spectroscopy,” Opt. Lett. 31, 3653–3655 (2006).
    [CrossRef] [PubMed]
  17. T. Kleine-Ostmann, C. Jansen, R. Piesiewicz, D. Mittleman, M. Koch, and T. Kürner, “Propagation modeling based on measurements and simulations of surface scattering in specular direction,” in Proceedings of Joint 32nd International Conference on Infrared and Millimetre Waves, and 15th International Conference on Terahertz Electronics , M. J. Griffin, P. C. Hargrave, T. J. Parker, and K. P. Wood, eds., vol. 1, pp. 408–410 (2007).
  18. R. Piesiewicz, C. Jansen, D. Mittleman, T. Kleine-Ostmann, M. Koch, and T. Kürner, “Scattering analysis for the modeling of THz communication systems,” IEEE Trans. Antennas Propag . 55, 3002–3009 (2007).
    [CrossRef]
  19. J. Pearce, Z. Jian, and D. M. Mittleman, “Statistics of multiply scattered broadband terahertz pulses,” Phys. Rev. Lett. 91, 043903 (2003).
    [CrossRef] [PubMed]
  20. J. Pearce and D. M. Mittleman, “Using terahertz pulses to study light scattering,” Phys. B 338, 92–96 (2003).
    [CrossRef]
  21. Z. Jian, J. Pearce, and D. M. Mittleman, “Characterizing individual scattering events by measuring the amplitude and phase of the electric field diffusing through a random medium,” Phys. Rev. Lett. 91, 033903 (2003).
    [CrossRef] [PubMed]
  22. S. Mujumdar, K. J. Chau, and A. Y. Elezzabi, “Experimental and numerical investigation of terahertz transmission through strongly scattering sub-wavelength size spheres,” Appl. Phys. Lett. 85, 6284–6286 (2004).
    [CrossRef]
  23. X. J. Zhong, T. J. Cui, Z. Li, Y. B. Tao, and H. Lin, “Terahertz-wave scattering by perfectly electrical conducting objects,” J. Electromagn. Waves Appl. 21, 2331–2340 (2007).
    [CrossRef]
  24. R. A. Cheville, M. T. Reiten, R. McGowan, and D. R. Grischkowsky, Applications of Optically Generated Terahertz Pulses to Time Domain Ranging and Scattering (Springer-Verlag, 2003).
  25. G. M. Png, R. J. Falconer, B. M. Fischer, H. A. Zakaria, S. P. Mickan, A. P. J. Middelberg, and D. Abbott, “Terahertz spectroscopic differentiation of microstructures in protein gels,” Opt. Express 17, 13102–13115 (2009).
    [CrossRef] [PubMed]
  26. C. A. Balanis, Antenna Theory: Analysis and Design (Harper & Row Publishers, 1982).
  27. E. Hecht, Optics (Addison-Wesley Publishing Company, 2002).
  28. H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., 1957).
  29. M. Kerker, Scattering of Light and Other Electromagnetic Radiation (Academic Press, New York, 1969).
  30. E. F. Knott, J. F. Shaeffer, and M. T. Tuley, Radar Cross Section (SciTech Publishing Inc., 2004).
  31. R. Piesiewicz, T. Kleine-Ostmann, N. Krumbholz, D. Mittleman, M. Koch, and T. Kürner, “Terahertz characterisation of building materials,” Electron. Lett. 41, 1002–1004 (2005).
    [CrossRef]
  32. M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy of silicate glasses and the relationship to material properties,” J. Appl. Phys. 102, 043517 (2007).
    [CrossRef]
  33. C. A. Balanis, Advanced Engineering Electromagnetics (John Wiley & Sons, 1989).
  34. G. Chattopadhyay, J. Glenn, J. J. Bock, B. K. Rownd, M. Caldwell, and M. J. Griffin, “Feed horn coupled bolometer arrays for SPIRE—design, simulations, and measurements,” IEEE Trans. Microwave Theory Tech . 51, 2139–2146 (2003).
    [CrossRef]
  35. 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]
  36. C. Hafner, The Multiple Multipole Program (MMP) and the Generalized Multipole Technique (GMT) , pp. 21–38 (Elsevier Science B.V., 1999).

2009 (4)

K. Naito, Y. Kagawa, S. Utsuno, T. Naganuma, and K. Kurihara, “Dielectric properties of eight-harness-stain fabric glass fiber reinforced polyimide matrix composite in the THz frequency range,” NDT & E Int. 42, 441–445 (2009).
[CrossRef]

K. Naito, Y. Kagawa, S. Utsuno, T. Naganuma, and K. Kurihara, “Dielectric properties of woven fabric glass fiber reinforced polymer matrix composites in the THz frequency range,” Compos. Sci. Technol. 69, 2027–2029 (2009).
[CrossRef]

X.-L. Tang, Y.-W. Shi, Y. Matsuura, K. Iwai, and M. Miyagi, “Transmission characteristics of terahertz hollow fiber with an absorptive dielectric inner-coating film,” Opt. Lett. 34, 2231–2233 (2009).
[CrossRef] [PubMed]

G. M. Png, R. J. Falconer, B. M. Fischer, H. A. Zakaria, S. P. Mickan, A. P. J. Middelberg, and D. Abbott, “Terahertz spectroscopic differentiation of microstructures in protein gels,” Opt. Express 17, 13102–13115 (2009).
[CrossRef] [PubMed]

2008 (3)

Y.-C. Shen, P. F. Taday, and M. Pepper, “Elimination of scattering effects in spectral measurement of granulated materials using terahertz pulsed spectroscopy,” Appl. Phys. Lett. 92, 051103 (2008).
[CrossRef]

M. Franz, B. M. Fischer, and M. Walther, “The Christiansen effect in terahertz time-domain spectra of coarse-grained powders,” Appl. Phys. Lett. 92, 021107 (2008).
[CrossRef]

Y. L. Hor, J. F. Federici, and R. L. Wample, “Nondestructive evaluation of cork enclosures using terahertz/millimeter wave spectroscopy and imaging,” Appl. Opt. 47, 72–78 (2008).
[CrossRef]

2007 (6)

L. M. Zurk, B. Orlowski, D. P. Winebrenner, E. I. Thorsos, M. R. Leahy-Hoppa, and L. M. Hayden, “Terahertz scattering from granular material,” J. Opt. Soc. Am. B 24, 2238–2243 (2007).
[CrossRef]

A. Bandyopadhyay, A. Sengupta, R. B. Barat, D. E. Gary, J. F. Federici, M. Chen, and D. B. Tanner, “Effects of scattering on THz spectra of granular solids,” Int. J. Infrared Millim. Waves 28, 969–978 (2007).
[CrossRef]

R. Piesiewicz, C. Jansen, D. Mittleman, T. Kleine-Ostmann, M. Koch, and T. Kürner, “Scattering analysis for the modeling of THz communication systems,” IEEE Trans. Antennas Propag . 55, 3002–3009 (2007).
[CrossRef]

J. R. Fletcher, G. P. Swift, D. C. Dai, J. A. Levitt, and J. M. Chamberlain, “Propagation of terahertz radiation through random structures: An alternative theoretical approach and experimental validation,” J. Appl. Phys. 101, 013102 (2007).
[CrossRef]

X. J. Zhong, T. J. Cui, Z. Li, Y. B. Tao, and H. Lin, “Terahertz-wave scattering by perfectly electrical conducting objects,” J. Electromagn. Waves Appl. 21, 2331–2340 (2007).
[CrossRef]

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy of silicate glasses and the relationship to material properties,” J. Appl. Phys. 102, 043517 (2007).
[CrossRef]

2006 (3)

M. Reid and R. Fedosejevs, “Terahertz birefringence and attenuation properties of wood and paper,” Appl. Opt. 45, 2766–2772 (2006).
[CrossRef] [PubMed]

Y. Dikmelik, J. B. Spicer, M. J. Fitch, and R. Osiander, “Effects of surface roughness on reflection spectra obtained by terahertz time-domain spectroscopy,” Opt. Lett. 31, 3653–3655 (2006).
[CrossRef] [PubMed]

M. A. Kaliteevski, D. M. Beggs, S. Brand, R. A. Abram, J. R. Fletcher, G. P. Swift, and J. M. Chamberlain, “Propagation of electromagnetic waves through a system of randomly placed cylinders: The partial scattering wave resonance,” J. Mod. Opt. 53, 2089–2097 (2006).
[CrossRef]

2005 (2)

R. Piesiewicz, T. Kleine-Ostmann, N. Krumbholz, D. Mittleman, M. Koch, and T. Kürner, “Terahertz characterisation of building materials,” Electron. Lett. 41, 1002–1004 (2005).
[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]

2004 (2)

S. Mujumdar, K. J. Chau, and A. Y. Elezzabi, “Experimental and numerical investigation of terahertz transmission through strongly scattering sub-wavelength size spheres,” Appl. Phys. Lett. 85, 6284–6286 (2004).
[CrossRef]

J. E. Bjarnason, T. L. J. Chan, A. W. M. Lee, M. A. Celis, and E. R. Brown, “Millimeter-wave, terahertz, and mid-infrared transmission through common clothing,” Appl. Phys. Lett. 85, 519–521 (2004).
[CrossRef]

2003 (5)

J. Pearce, Z. Jian, and D. M. Mittleman, “Statistics of multiply scattered broadband terahertz pulses,” Phys. Rev. Lett. 91, 043903 (2003).
[CrossRef] [PubMed]

J. Pearce and D. M. Mittleman, “Using terahertz pulses to study light scattering,” Phys. B 338, 92–96 (2003).
[CrossRef]

Z. Jian, J. Pearce, and D. M. Mittleman, “Characterizing individual scattering events by measuring the amplitude and phase of the electric field diffusing through a random medium,” Phys. Rev. Lett. 91, 033903 (2003).
[CrossRef] [PubMed]

G. Chattopadhyay, J. Glenn, J. J. Bock, B. K. Rownd, M. Caldwell, and M. J. Griffin, “Feed horn coupled bolometer arrays for SPIRE—design, simulations, and measurements,” IEEE Trans. Microwave Theory Tech . 51, 2139–2146 (2003).
[CrossRef]

R. A. Cheville, M. T. Reiten, R. McGowan, and D. R. Grischkowsky, Applications of Optically Generated Terahertz Pulses to Time Domain Ranging and Scattering (Springer-Verlag, 2003).

2002 (1)

E. Hecht, Optics (Addison-Wesley Publishing Company, 2002).

2000 (1)

1999 (1)

C. Hafner, The Multiple Multipole Program (MMP) and the Generalized Multipole Technique (GMT) , pp. 21–38 (Elsevier Science B.V., 1999).

1989 (1)

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

1983 (1)

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

1982 (1)

C. A. Balanis, Antenna Theory: Analysis and Design (Harper & Row Publishers, 1982).

1969 (1)

M. Kerker, Scattering of Light and Other Electromagnetic Radiation (Academic Press, New York, 1969).

1957 (1)

H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., 1957).

Abbott, D.

Abram, R. A.

M. A. Kaliteevski, D. M. Beggs, S. Brand, R. A. Abram, J. R. Fletcher, G. P. Swift, and J. M. Chamberlain, “Propagation of electromagnetic waves through a system of randomly placed cylinders: The partial scattering wave resonance,” J. Mod. Opt. 53, 2089–2097 (2006).
[CrossRef]

Balanis, C. A.

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

C. A. Balanis, Antenna Theory: Analysis and Design (Harper & Row Publishers, 1982).

Bandyopadhyay, A.

A. Bandyopadhyay, A. Sengupta, R. B. Barat, D. E. Gary, J. F. Federici, M. Chen, and D. B. Tanner, “Effects of scattering on THz spectra of granular solids,” Int. J. Infrared Millim. Waves 28, 969–978 (2007).
[CrossRef]

Barat, R. B.

A. Bandyopadhyay, A. Sengupta, R. B. Barat, D. E. Gary, J. F. Federici, M. Chen, and D. B. Tanner, “Effects of scattering on THz spectra of granular solids,” Int. J. Infrared Millim. Waves 28, 969–978 (2007).
[CrossRef]

Beggs, D. M.

M. A. Kaliteevski, D. M. Beggs, S. Brand, R. A. Abram, J. R. Fletcher, G. P. Swift, and J. M. Chamberlain, “Propagation of electromagnetic waves through a system of randomly placed cylinders: The partial scattering wave resonance,” J. Mod. Opt. 53, 2089–2097 (2006).
[CrossRef]

Bjarnason, J. E.

J. E. Bjarnason, T. L. J. Chan, A. W. M. Lee, M. A. Celis, and E. R. Brown, “Millimeter-wave, terahertz, and mid-infrared transmission through common clothing,” Appl. Phys. Lett. 85, 519–521 (2004).
[CrossRef]

Bock, J. J.

G. Chattopadhyay, J. Glenn, J. J. Bock, B. K. Rownd, M. Caldwell, and M. J. Griffin, “Feed horn coupled bolometer arrays for SPIRE—design, simulations, and measurements,” IEEE Trans. Microwave Theory Tech . 51, 2139–2146 (2003).
[CrossRef]

Bohren, C. F.

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

Brand, S.

M. A. Kaliteevski, D. M. Beggs, S. Brand, R. A. Abram, J. R. Fletcher, G. P. Swift, and J. M. Chamberlain, “Propagation of electromagnetic waves through a system of randomly placed cylinders: The partial scattering wave resonance,” J. Mod. Opt. 53, 2089–2097 (2006).
[CrossRef]

Brown, E. R.

J. E. Bjarnason, T. L. J. Chan, A. W. M. Lee, M. A. Celis, and E. R. Brown, “Millimeter-wave, terahertz, and mid-infrared transmission through common clothing,” Appl. Phys. Lett. 85, 519–521 (2004).
[CrossRef]

Caldwell, M.

G. Chattopadhyay, J. Glenn, J. J. Bock, B. K. Rownd, M. Caldwell, and M. J. Griffin, “Feed horn coupled bolometer arrays for SPIRE—design, simulations, and measurements,” IEEE Trans. Microwave Theory Tech . 51, 2139–2146 (2003).
[CrossRef]

Celis, M. A.

J. E. Bjarnason, T. L. J. Chan, A. W. M. Lee, M. A. Celis, and E. R. Brown, “Millimeter-wave, terahertz, and mid-infrared transmission through common clothing,” Appl. Phys. Lett. 85, 519–521 (2004).
[CrossRef]

Chamberlain, J. M.

J. R. Fletcher, G. P. Swift, D. C. Dai, J. A. Levitt, and J. M. Chamberlain, “Propagation of terahertz radiation through random structures: An alternative theoretical approach and experimental validation,” J. Appl. Phys. 101, 013102 (2007).
[CrossRef]

M. A. Kaliteevski, D. M. Beggs, S. Brand, R. A. Abram, J. R. Fletcher, G. P. Swift, and J. M. Chamberlain, “Propagation of electromagnetic waves through a system of randomly placed cylinders: The partial scattering wave resonance,” J. Mod. Opt. 53, 2089–2097 (2006).
[CrossRef]

Chan, T. L. J.

J. E. Bjarnason, T. L. J. Chan, A. W. M. Lee, M. A. Celis, and E. R. Brown, “Millimeter-wave, terahertz, and mid-infrared transmission through common clothing,” Appl. Phys. Lett. 85, 519–521 (2004).
[CrossRef]

Chattopadhyay, G.

G. Chattopadhyay, J. Glenn, J. J. Bock, B. K. Rownd, M. Caldwell, and M. J. Griffin, “Feed horn coupled bolometer arrays for SPIRE—design, simulations, and measurements,” IEEE Trans. Microwave Theory Tech . 51, 2139–2146 (2003).
[CrossRef]

Chau, K. J.

S. Mujumdar, K. J. Chau, and A. Y. Elezzabi, “Experimental and numerical investigation of terahertz transmission through strongly scattering sub-wavelength size spheres,” Appl. Phys. Lett. 85, 6284–6286 (2004).
[CrossRef]

Chen, M.

A. Bandyopadhyay, A. Sengupta, R. B. Barat, D. E. Gary, J. F. Federici, M. Chen, and D. B. Tanner, “Effects of scattering on THz spectra of granular solids,” Int. J. Infrared Millim. Waves 28, 969–978 (2007).
[CrossRef]

Cheville, R. A.

R. A. Cheville, M. T. Reiten, R. McGowan, and D. R. Grischkowsky, Applications of Optically Generated Terahertz Pulses to Time Domain Ranging and Scattering (Springer-Verlag, 2003).

Cho, G. C.

Cui, T. J.

X. J. Zhong, T. J. Cui, Z. Li, Y. B. Tao, and H. Lin, “Terahertz-wave scattering by perfectly electrical conducting objects,” J. Electromagn. Waves Appl. 21, 2331–2340 (2007).
[CrossRef]

Dai, D. C.

J. R. Fletcher, G. P. Swift, D. C. Dai, J. A. Levitt, and J. M. Chamberlain, “Propagation of terahertz radiation through random structures: An alternative theoretical approach and experimental validation,” J. Appl. Phys. 101, 013102 (2007).
[CrossRef]

Dikmelik, Y.

Elezzabi, A. Y.

S. Mujumdar, K. J. Chau, and A. Y. Elezzabi, “Experimental and numerical investigation of terahertz transmission through strongly scattering sub-wavelength size spheres,” Appl. Phys. Lett. 85, 6284–6286 (2004).
[CrossRef]

Falconer, R. J.

Federici, J. F.

Y. L. Hor, J. F. Federici, and R. L. Wample, “Nondestructive evaluation of cork enclosures using terahertz/millimeter wave spectroscopy and imaging,” Appl. Opt. 47, 72–78 (2008).
[CrossRef]

A. Bandyopadhyay, A. Sengupta, R. B. Barat, D. E. Gary, J. F. Federici, M. Chen, and D. B. Tanner, “Effects of scattering on THz spectra of granular solids,” Int. J. Infrared Millim. Waves 28, 969–978 (2007).
[CrossRef]

Fedosejevs, R.

Fischer, B. M.

Fitch, M. J.

Fletcher, J. R.

J. R. Fletcher, G. P. Swift, D. C. Dai, J. A. Levitt, and J. M. Chamberlain, “Propagation of terahertz radiation through random structures: An alternative theoretical approach and experimental validation,” J. Appl. Phys. 101, 013102 (2007).
[CrossRef]

M. A. Kaliteevski, D. M. Beggs, S. Brand, R. A. Abram, J. R. Fletcher, G. P. Swift, and J. M. Chamberlain, “Propagation of electromagnetic waves through a system of randomly placed cylinders: The partial scattering wave resonance,” J. Mod. Opt. 53, 2089–2097 (2006).
[CrossRef]

Franz, M.

M. Franz, B. M. Fischer, and M. Walther, “The Christiansen effect in terahertz time-domain spectra of coarse-grained powders,” Appl. Phys. Lett. 92, 021107 (2008).
[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]

Gary, D. E.

A. Bandyopadhyay, A. Sengupta, R. B. Barat, D. E. Gary, J. F. Federici, M. Chen, and D. B. Tanner, “Effects of scattering on THz spectra of granular solids,” Int. J. Infrared Millim. Waves 28, 969–978 (2007).
[CrossRef]

Glenn, J.

G. Chattopadhyay, J. Glenn, J. J. Bock, B. K. Rownd, M. Caldwell, and M. J. Griffin, “Feed horn coupled bolometer arrays for SPIRE—design, simulations, and measurements,” IEEE Trans. Microwave Theory Tech . 51, 2139–2146 (2003).
[CrossRef]

Griffin, M. J.

G. Chattopadhyay, J. Glenn, J. J. Bock, B. K. Rownd, M. Caldwell, and M. J. Griffin, “Feed horn coupled bolometer arrays for SPIRE—design, simulations, and measurements,” IEEE Trans. Microwave Theory Tech . 51, 2139–2146 (2003).
[CrossRef]

Grischkowsky, D. R.

R. A. Cheville, M. T. Reiten, R. McGowan, and D. R. Grischkowsky, Applications of Optically Generated Terahertz Pulses to Time Domain Ranging and Scattering (Springer-Verlag, 2003).

Hafner, C.

C. Hafner, The Multiple Multipole Program (MMP) and the Generalized Multipole Technique (GMT) , pp. 21–38 (Elsevier Science B.V., 1999).

Han, P. Y.

Hayden, L. M.

Hecht, E.

E. Hecht, Optics (Addison-Wesley Publishing Company, 2002).

Hor, Y. L.

Huffman, D. R.

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

Iwai, K.

Jansen, C.

R. Piesiewicz, C. Jansen, D. Mittleman, T. Kleine-Ostmann, M. Koch, and T. Kürner, “Scattering analysis for the modeling of THz communication systems,” IEEE Trans. Antennas Propag . 55, 3002–3009 (2007).
[CrossRef]

Jian, Z.

J. Pearce, Z. Jian, and D. M. Mittleman, “Statistics of multiply scattered broadband terahertz pulses,” Phys. Rev. Lett. 91, 043903 (2003).
[CrossRef] [PubMed]

Z. Jian, J. Pearce, and D. M. Mittleman, “Characterizing individual scattering events by measuring the amplitude and phase of the electric field diffusing through a random medium,” Phys. Rev. Lett. 91, 033903 (2003).
[CrossRef] [PubMed]

Kagawa, Y.

K. Naito, Y. Kagawa, S. Utsuno, T. Naganuma, and K. Kurihara, “Dielectric properties of woven fabric glass fiber reinforced polymer matrix composites in the THz frequency range,” Compos. Sci. Technol. 69, 2027–2029 (2009).
[CrossRef]

K. Naito, Y. Kagawa, S. Utsuno, T. Naganuma, and K. Kurihara, “Dielectric properties of eight-harness-stain fabric glass fiber reinforced polyimide matrix composite in the THz frequency range,” NDT & E Int. 42, 441–445 (2009).
[CrossRef]

Kaliteevski, M. A.

M. A. Kaliteevski, D. M. Beggs, S. Brand, R. A. Abram, J. R. Fletcher, G. P. Swift, and J. M. Chamberlain, “Propagation of electromagnetic waves through a system of randomly placed cylinders: The partial scattering wave resonance,” J. Mod. Opt. 53, 2089–2097 (2006).
[CrossRef]

Kerker, M.

M. Kerker, Scattering of Light and Other Electromagnetic Radiation (Academic Press, New York, 1969).

Kleine-Ostmann, T.

R. Piesiewicz, C. Jansen, D. Mittleman, T. Kleine-Ostmann, M. Koch, and T. Kürner, “Scattering analysis for the modeling of THz communication systems,” IEEE Trans. Antennas Propag . 55, 3002–3009 (2007).
[CrossRef]

R. Piesiewicz, T. Kleine-Ostmann, N. Krumbholz, D. Mittleman, M. Koch, and T. Kürner, “Terahertz characterisation of building materials,” Electron. Lett. 41, 1002–1004 (2005).
[CrossRef]

Koch, M.

R. Piesiewicz, C. Jansen, D. Mittleman, T. Kleine-Ostmann, M. Koch, and T. Kürner, “Scattering analysis for the modeling of THz communication systems,” IEEE Trans. Antennas Propag . 55, 3002–3009 (2007).
[CrossRef]

R. Piesiewicz, T. Kleine-Ostmann, N. Krumbholz, D. Mittleman, M. Koch, and T. Kürner, “Terahertz characterisation of building materials,” Electron. Lett. 41, 1002–1004 (2005).
[CrossRef]

Krumbholz, N.

R. Piesiewicz, T. Kleine-Ostmann, N. Krumbholz, D. Mittleman, M. Koch, and T. Kürner, “Terahertz characterisation of building materials,” Electron. Lett. 41, 1002–1004 (2005).
[CrossRef]

Kurihara, K.

K. Naito, Y. Kagawa, S. Utsuno, T. Naganuma, and K. Kurihara, “Dielectric properties of woven fabric glass fiber reinforced polymer matrix composites in the THz frequency range,” Compos. Sci. Technol. 69, 2027–2029 (2009).
[CrossRef]

K. Naito, Y. Kagawa, S. Utsuno, T. Naganuma, and K. Kurihara, “Dielectric properties of eight-harness-stain fabric glass fiber reinforced polyimide matrix composite in the THz frequency range,” NDT & E Int. 42, 441–445 (2009).
[CrossRef]

Kürner, T.

R. Piesiewicz, C. Jansen, D. Mittleman, T. Kleine-Ostmann, M. Koch, and T. Kürner, “Scattering analysis for the modeling of THz communication systems,” IEEE Trans. Antennas Propag . 55, 3002–3009 (2007).
[CrossRef]

R. Piesiewicz, T. Kleine-Ostmann, N. Krumbholz, D. Mittleman, M. Koch, and T. Kürner, “Terahertz characterisation of building materials,” Electron. Lett. 41, 1002–1004 (2005).
[CrossRef]

Leahy-Hoppa, M. R.

Lee, A. W. M.

J. E. Bjarnason, T. L. J. Chan, A. W. M. Lee, M. A. Celis, and E. R. Brown, “Millimeter-wave, terahertz, and mid-infrared transmission through common clothing,” Appl. Phys. Lett. 85, 519–521 (2004).
[CrossRef]

Levitt, J. A.

J. R. Fletcher, G. P. Swift, D. C. Dai, J. A. Levitt, and J. M. Chamberlain, “Propagation of terahertz radiation through random structures: An alternative theoretical approach and experimental validation,” J. Appl. Phys. 101, 013102 (2007).
[CrossRef]

Li, Z.

X. J. Zhong, T. J. Cui, Z. Li, Y. B. Tao, and H. Lin, “Terahertz-wave scattering by perfectly electrical conducting objects,” J. Electromagn. Waves Appl. 21, 2331–2340 (2007).
[CrossRef]

Lin, H.

X. J. Zhong, T. J. Cui, Z. Li, Y. B. Tao, and H. Lin, “Terahertz-wave scattering by perfectly electrical conducting objects,” J. Electromagn. Waves Appl. 21, 2331–2340 (2007).
[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]

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]

Matsuura, Y.

McGowan, R.

R. A. Cheville, M. T. Reiten, R. McGowan, and D. R. Grischkowsky, Applications of Optically Generated Terahertz Pulses to Time Domain Ranging and Scattering (Springer-Verlag, 2003).

Mickan, S. P.

Middelberg, A. P. J.

Miles, R. E.

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy of silicate glasses and the relationship to material properties,” J. Appl. Phys. 102, 043517 (2007).
[CrossRef]

Mittleman, D.

R. Piesiewicz, C. Jansen, D. Mittleman, T. Kleine-Ostmann, M. Koch, and T. Kürner, “Scattering analysis for the modeling of THz communication systems,” IEEE Trans. Antennas Propag . 55, 3002–3009 (2007).
[CrossRef]

R. Piesiewicz, T. Kleine-Ostmann, N. Krumbholz, D. Mittleman, M. Koch, and T. Kürner, “Terahertz characterisation of building materials,” Electron. Lett. 41, 1002–1004 (2005).
[CrossRef]

Mittleman, D. M.

J. Pearce, Z. Jian, and D. M. Mittleman, “Statistics of multiply scattered broadband terahertz pulses,” Phys. Rev. Lett. 91, 043903 (2003).
[CrossRef] [PubMed]

J. Pearce and D. M. Mittleman, “Using terahertz pulses to study light scattering,” Phys. B 338, 92–96 (2003).
[CrossRef]

Z. Jian, J. Pearce, and D. M. Mittleman, “Characterizing individual scattering events by measuring the amplitude and phase of the electric field diffusing through a random medium,” Phys. Rev. Lett. 91, 033903 (2003).
[CrossRef] [PubMed]

Miyagi, M.

Mujumdar, S.

S. Mujumdar, K. J. Chau, and A. Y. Elezzabi, “Experimental and numerical investigation of terahertz transmission through strongly scattering sub-wavelength size spheres,” Appl. Phys. Lett. 85, 6284–6286 (2004).
[CrossRef]

Naftaly, M.

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy of silicate glasses and the relationship to material properties,” J. Appl. Phys. 102, 043517 (2007).
[CrossRef]

Naganuma, T.

K. Naito, Y. Kagawa, S. Utsuno, T. Naganuma, and K. Kurihara, “Dielectric properties of woven fabric glass fiber reinforced polymer matrix composites in the THz frequency range,” Compos. Sci. Technol. 69, 2027–2029 (2009).
[CrossRef]

K. Naito, Y. Kagawa, S. Utsuno, T. Naganuma, and K. Kurihara, “Dielectric properties of eight-harness-stain fabric glass fiber reinforced polyimide matrix composite in the THz frequency range,” NDT & E Int. 42, 441–445 (2009).
[CrossRef]

Naito, K.

K. Naito, Y. Kagawa, S. Utsuno, T. Naganuma, and K. Kurihara, “Dielectric properties of woven fabric glass fiber reinforced polymer matrix composites in the THz frequency range,” Compos. Sci. Technol. 69, 2027–2029 (2009).
[CrossRef]

K. Naito, Y. Kagawa, S. Utsuno, T. Naganuma, and K. Kurihara, “Dielectric properties of eight-harness-stain fabric glass fiber reinforced polyimide matrix composite in the THz frequency range,” NDT & E Int. 42, 441–445 (2009).
[CrossRef]

Orlowski, B.

Osiander, R.

Pearce, J.

J. Pearce, Z. Jian, and D. M. Mittleman, “Statistics of multiply scattered broadband terahertz pulses,” Phys. Rev. Lett. 91, 043903 (2003).
[CrossRef] [PubMed]

Z. Jian, J. Pearce, and D. M. Mittleman, “Characterizing individual scattering events by measuring the amplitude and phase of the electric field diffusing through a random medium,” Phys. Rev. Lett. 91, 033903 (2003).
[CrossRef] [PubMed]

J. Pearce and D. M. Mittleman, “Using terahertz pulses to study light scattering,” Phys. B 338, 92–96 (2003).
[CrossRef]

Pepper, M.

Y.-C. Shen, P. F. Taday, and M. Pepper, “Elimination of scattering effects in spectral measurement of granulated materials using terahertz pulsed spectroscopy,” Appl. Phys. Lett. 92, 051103 (2008).
[CrossRef]

Piesiewicz, R.

R. Piesiewicz, C. Jansen, D. Mittleman, T. Kleine-Ostmann, M. Koch, and T. Kürner, “Scattering analysis for the modeling of THz communication systems,” IEEE Trans. Antennas Propag . 55, 3002–3009 (2007).
[CrossRef]

R. Piesiewicz, T. Kleine-Ostmann, N. Krumbholz, D. Mittleman, M. Koch, and T. Kürner, “Terahertz characterisation of building materials,” Electron. Lett. 41, 1002–1004 (2005).
[CrossRef]

Png, G. M.

Reid, M.

Reiten, M. T.

R. A. Cheville, M. T. Reiten, R. McGowan, and D. R. Grischkowsky, Applications of Optically Generated Terahertz Pulses to Time Domain Ranging and Scattering (Springer-Verlag, 2003).

Rownd, B. K.

G. Chattopadhyay, J. Glenn, J. J. Bock, B. K. Rownd, M. Caldwell, and M. J. Griffin, “Feed horn coupled bolometer arrays for SPIRE—design, simulations, and measurements,” IEEE Trans. Microwave Theory Tech . 51, 2139–2146 (2003).
[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]

Sengupta, A.

A. Bandyopadhyay, A. Sengupta, R. B. Barat, D. E. Gary, J. F. Federici, M. Chen, and D. B. Tanner, “Effects of scattering on THz spectra of granular solids,” Int. J. Infrared Millim. Waves 28, 969–978 (2007).
[CrossRef]

Shen, Y.-C.

Y.-C. Shen, P. F. Taday, and M. Pepper, “Elimination of scattering effects in spectral measurement of granulated materials using terahertz pulsed spectroscopy,” Appl. Phys. Lett. 92, 051103 (2008).
[CrossRef]

Shi, Y.-W.

Spicer, J. B.

Swift, G. P.

J. R. Fletcher, G. P. Swift, D. C. Dai, J. A. Levitt, and J. M. Chamberlain, “Propagation of terahertz radiation through random structures: An alternative theoretical approach and experimental validation,” J. Appl. Phys. 101, 013102 (2007).
[CrossRef]

M. A. Kaliteevski, D. M. Beggs, S. Brand, R. A. Abram, J. R. Fletcher, G. P. Swift, and J. M. Chamberlain, “Propagation of electromagnetic waves through a system of randomly placed cylinders: The partial scattering wave resonance,” J. Mod. Opt. 53, 2089–2097 (2006).
[CrossRef]

Taday, P. F.

Y.-C. Shen, P. F. Taday, and M. Pepper, “Elimination of scattering effects in spectral measurement of granulated materials using terahertz pulsed spectroscopy,” Appl. Phys. Lett. 92, 051103 (2008).
[CrossRef]

Tang, X.-L.

Tanner, D. B.

A. Bandyopadhyay, A. Sengupta, R. B. Barat, D. E. Gary, J. F. Federici, M. Chen, and D. B. Tanner, “Effects of scattering on THz spectra of granular solids,” Int. J. Infrared Millim. Waves 28, 969–978 (2007).
[CrossRef]

Tao, Y. B.

X. J. Zhong, T. J. Cui, Z. Li, Y. B. Tao, and H. Lin, “Terahertz-wave scattering by perfectly electrical conducting objects,” J. Electromagn. Waves Appl. 21, 2331–2340 (2007).
[CrossRef]

Thorsos, E. I.

Utsuno, S.

K. Naito, Y. Kagawa, S. Utsuno, T. Naganuma, and K. Kurihara, “Dielectric properties of woven fabric glass fiber reinforced polymer matrix composites in the THz frequency range,” Compos. Sci. Technol. 69, 2027–2029 (2009).
[CrossRef]

K. Naito, Y. Kagawa, S. Utsuno, T. Naganuma, and K. Kurihara, “Dielectric properties of eight-harness-stain fabric glass fiber reinforced polyimide matrix composite in the THz frequency range,” NDT & E Int. 42, 441–445 (2009).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., 1957).

Walther, M.

M. Franz, B. M. Fischer, and M. Walther, “The Christiansen effect in terahertz time-domain spectra of coarse-grained powders,” Appl. Phys. Lett. 92, 021107 (2008).
[CrossRef]

Wample, R. L.

Winebrenner, D. P.

Zakaria, H. A.

Zhang, X.-C.

Zhong, X. J.

X. J. Zhong, T. J. Cui, Z. Li, Y. B. Tao, and H. Lin, “Terahertz-wave scattering by perfectly electrical conducting objects,” J. Electromagn. Waves Appl. 21, 2331–2340 (2007).
[CrossRef]

Zurk, L. M.

Appl. Opt. (2)

Appl. Phys. Lett. (4)

Y.-C. Shen, P. F. Taday, and M. Pepper, “Elimination of scattering effects in spectral measurement of granulated materials using terahertz pulsed spectroscopy,” Appl. Phys. Lett. 92, 051103 (2008).
[CrossRef]

M. Franz, B. M. Fischer, and M. Walther, “The Christiansen effect in terahertz time-domain spectra of coarse-grained powders,” Appl. Phys. Lett. 92, 021107 (2008).
[CrossRef]

J. E. Bjarnason, T. L. J. Chan, A. W. M. Lee, M. A. Celis, and E. R. Brown, “Millimeter-wave, terahertz, and mid-infrared transmission through common clothing,” Appl. Phys. Lett. 85, 519–521 (2004).
[CrossRef]

S. Mujumdar, K. J. Chau, and A. Y. Elezzabi, “Experimental and numerical investigation of terahertz transmission through strongly scattering sub-wavelength size spheres,” Appl. Phys. Lett. 85, 6284–6286 (2004).
[CrossRef]

Compos. Sci. Technol. (1)

K. Naito, Y. Kagawa, S. Utsuno, T. Naganuma, and K. Kurihara, “Dielectric properties of woven fabric glass fiber reinforced polymer matrix composites in the THz frequency range,” Compos. Sci. Technol. 69, 2027–2029 (2009).
[CrossRef]

Electron. Lett. (1)

R. Piesiewicz, T. Kleine-Ostmann, N. Krumbholz, D. Mittleman, M. Koch, and T. Kürner, “Terahertz characterisation of building materials,” Electron. Lett. 41, 1002–1004 (2005).
[CrossRef]

IEEE Trans. Antennas Propag (1)

R. Piesiewicz, C. Jansen, D. Mittleman, T. Kleine-Ostmann, M. Koch, and T. Kürner, “Scattering analysis for the modeling of THz communication systems,” IEEE Trans. Antennas Propag . 55, 3002–3009 (2007).
[CrossRef]

IEEE Trans. Microwave Theory Tech (1)

G. Chattopadhyay, J. Glenn, J. J. Bock, B. K. Rownd, M. Caldwell, and M. J. Griffin, “Feed horn coupled bolometer arrays for SPIRE—design, simulations, and measurements,” IEEE Trans. Microwave Theory Tech . 51, 2139–2146 (2003).
[CrossRef]

Int. J. Infrared Millim. Waves (1)

A. Bandyopadhyay, A. Sengupta, R. B. Barat, D. E. Gary, J. F. Federici, M. Chen, and D. B. Tanner, “Effects of scattering on THz spectra of granular solids,” Int. J. Infrared Millim. Waves 28, 969–978 (2007).
[CrossRef]

J. Appl. Phys. (3)

J. R. Fletcher, G. P. Swift, D. C. Dai, J. A. Levitt, and J. M. Chamberlain, “Propagation of terahertz radiation through random structures: An alternative theoretical approach and experimental validation,” J. Appl. Phys. 101, 013102 (2007).
[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]

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy of silicate glasses and the relationship to material properties,” J. Appl. Phys. 102, 043517 (2007).
[CrossRef]

J. Electromagn. Waves Appl. (1)

X. J. Zhong, T. J. Cui, Z. Li, Y. B. Tao, and H. Lin, “Terahertz-wave scattering by perfectly electrical conducting objects,” J. Electromagn. Waves Appl. 21, 2331–2340 (2007).
[CrossRef]

J. Mod. Opt. (1)

M. A. Kaliteevski, D. M. Beggs, S. Brand, R. A. Abram, J. R. Fletcher, G. P. Swift, and J. M. Chamberlain, “Propagation of electromagnetic waves through a system of randomly placed cylinders: The partial scattering wave resonance,” J. Mod. Opt. 53, 2089–2097 (2006).
[CrossRef]

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

NDT & E Int. (1)

K. Naito, Y. Kagawa, S. Utsuno, T. Naganuma, and K. Kurihara, “Dielectric properties of eight-harness-stain fabric glass fiber reinforced polyimide matrix composite in the THz frequency range,” NDT & E Int. 42, 441–445 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. B (1)

J. Pearce and D. M. Mittleman, “Using terahertz pulses to study light scattering,” Phys. B 338, 92–96 (2003).
[CrossRef]

Phys. Rev. Lett. (2)

Z. Jian, J. Pearce, and D. M. Mittleman, “Characterizing individual scattering events by measuring the amplitude and phase of the electric field diffusing through a random medium,” Phys. Rev. Lett. 91, 033903 (2003).
[CrossRef] [PubMed]

J. Pearce, Z. Jian, and D. M. Mittleman, “Statistics of multiply scattered broadband terahertz pulses,” Phys. Rev. Lett. 91, 043903 (2003).
[CrossRef] [PubMed]

Other (11)

C. A. Balanis, Antenna Theory: Analysis and Design (Harper & Row Publishers, 1982).

E. Hecht, Optics (Addison-Wesley Publishing Company, 2002).

H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., 1957).

M. Kerker, Scattering of Light and Other Electromagnetic Radiation (Academic Press, New York, 1969).

E. F. Knott, J. F. Shaeffer, and M. T. Tuley, Radar Cross Section (SciTech Publishing Inc., 2004).

C. Hafner, The Multiple Multipole Program (MMP) and the Generalized Multipole Technique (GMT) , pp. 21–38 (Elsevier Science B.V., 1999).

R. A. Cheville, M. T. Reiten, R. McGowan, and D. R. Grischkowsky, Applications of Optically Generated Terahertz Pulses to Time Domain Ranging and Scattering (Springer-Verlag, 2003).

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

J. Beckmann, H. Richter, U. Zscherpel, U. Ewert, J. Weinzierl, L.-P. Schmidt, F. Rutz, M. Koch, H. Richter, and H.-W. Hübers, “Imaging capability of terahertz and millimeter-wave instrumentations for NDT of polymer materials,” in Proceedings of 9th European Conference on Nondestructive Testing (NDT) , R. Diederichs, ed. (The e-Journal of Nondestructive Testing, 2006).

T. Kleine-Ostmann, C. Jansen, R. Piesiewicz, D. Mittleman, M. Koch, and T. Kürner, “Propagation modeling based on measurements and simulations of surface scattering in specular direction,” in Proceedings of Joint 32nd International Conference on Infrared and Millimetre Waves, and 15th International Conference on Terahertz Electronics , M. J. Griffin, P. C. Hargrave, T. J. Parker, and K. P. Wood, eds., vol. 1, pp. 408–410 (2007).

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

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 (7)

Fig. 1
Fig. 1

(a–b) Strands of fiberglass are taken from woven fiberglass cloth (plain weave E glass, weight 7.5 oz/yd2), and aligned as a near-periodic array. (c) The array is clamped between two polyethylene frames, with a square aperture of size 20 mm×21 mm. One of the polyethylene frames is covered with aluminum foil to prevent transmission of THz through the frames. The frame is placed orthogonal to the incident THz beam, which is vertically polarized. The red circle with a cross illustrates the incident THz beam into the plane of the fibers. The beamwidth is ≈ 5 mm. (d) The parallel and perpendicular orientations of the arrays with respect to the THz beam. (e) Schematic diagram of an infinite circular cylinder in the parallel or transverse magnetic (TM) orientation, illuminated by a plane wave at θ = 90°, with propagation vector k normal to the long axis of the cylinder (z-axis). The electric field vector E is parallel to the z-axis. After [1].

Fig. 2
Fig. 2

Frequency response and measured optical properties of the arrays described in Fig. 1, in the parallel and perpendicular orientations. (a) Terahertz transmission magnitudes (normalized) of two of the four arrays. The perpendicular arrays have similar magnitudes, unlike the parallel arrays where the magnitudes vary from sample to sample. (b) The measured effective refractive indices n of the fiberglass arrays vary slightly between the two orientations, suggesting geometry-induced birefringence. The error bars account for uncertainties in the samples’ thicknesses. (c) The measured extinction coefficients α of sample 1 changes directions beyond 2 THz, raising the question of whether this change is an artifact.

Fig. 3
Fig. 3

(a) C sca,|| and C sca, ⊥ normalized by 1 m2, and plotted on a logarithmic y-axis. (b) By multiplying C sca with AF, a scaling effect across all frequencies is observed.

Fig. 4
Fig. 4

(a) Overview of the HFSS simulation with the cylinders located about the origin, and the surrounding airbox highlighted in purple. The incident wave propagates in the x-direction. (b) Schematic of the radiation boundaries assigned on the walls of the airbox. The airbox walls, which are parallel to the y-z plane, are λ max/2 away from the cylinders, where the minimum frequency ν min = 0.088 THz. The two airbox walls that lie parallel to the x-z plane are assigned master/slave boundaries in order to model the periodic array that extends to infinity along the y-z plane. In order to model each cylinder’s infinite length with respect to its diameter, the walls parallel to the x-y plane are assigned symmetrical electric field E boundaries for the parallel case (symmetrical magnetic field H boundaries for the perpendicular case). (c) One of the two PML boundaries with depth of λ max/6; this depth ensures that fields incident on the PML boundaries are nearly completely absorbed and are not reflected back into the problem space. (d–e) Zoomed view showing two cylinders enclosed inside the airbox for both the parallel and perpendicular cases. (f) Plan view of the double cylinder structure with a 2 μm offset to account for misalignments between adjacent strands in the fiberglass arrays used in the THz experiment. To create a small 1 μm gap between adjacent strands, a 0.5 μm wallspace is introduced between each cylinder and the airbox walls which are parallel to the x-z plane. The master/slave boundaries replicates the double cylinder structure along the y axis. The grid spacing in this specific figure is set to 0.5 μm along both the x and y-axes.

Fig. 5
Fig. 5

(a) The larger S 21 values for the perpendicular case indicates stronger THz transmission than for the parallel case, agreeing well with the THz transmission magnitude plots in Fig. 2(a) particularly for frequencies below 1 THz. (b) When the space between adjacent strands increases, the S 21 plots for both orientations shift upwards, indicating stronger THz transmission due to “leakage” through the wider spacing. However, the parallel case appears to be more sensitive to the change in strand spacing, shifting more significantly than for the perpendicular case. This resembles the inconsistencies seen in Fig. 2(a) for the two parallel samples.

Fig. 6
Fig. 6

The grid spacing of the geometries in figures a–c is set to 0.5 μm along both the x and y-axes. (a) Simplest periodic model containing only one cylinder. (b) Periodic model containing two cylinder layers. The gap between the cylinders is equal to twice the wallspace to ensure that gaps are uniform in both the x and y directions. (c) Periodic model containing four cylinder layers. (d) For the parallel orientation, each cylinder layer decreases the S 21 value by ≈ 1 dB for frequencies above 0.5 THz. There is good quantitative agreement between the model with 24 layers with the normalized THz transmission magnitude of parallel sample 2. (e) For the perpendicular orientation, each cylinder layer decreases the S 21 value by ≈ 0.5 dB for frequencies above 0.5 THz. There is good quantitative agreement between the model with 24 layers with the normalized THz transmission magnitude of both perpendicular samples up to ≈ 1.8 THz.

Fig. 7
Fig. 7

(a) Alternative periodic models: model i is the simplest periodic model containing only one cylinder; model ii is equivalent to model i but with two cylinders with no offset between them; model iii, which is the same as that shown in Fig. 4(d), comprises of two cylinders with an offset between them. (b) Comparison between the S 21 plots from: model i, model ii, and model iii. The plots from all 3 models mostly overlap with only slight displacement due to meshing differences between the models. The overlap shows consistency in the HFSS simulations, with no unexpected artifacts arising from the presence of multiple cylinders in the problem space.

Equations (8)

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

C sca , | | = 4 l k [ | b 0 | | | 2 + 2 s = 1 | b s , | | | 2 ]
C sca , = 4 l k [ | a 0 | 2 + 2 s = 1 | a s , | 2 ]
a s , = { [ D s ( m k r ) m + s k r ] J s ( k r ) - J s - 1 ( k r ) } { [ D s ( m k r ) m + s k r ] H s ( 1 ) ( k r ) - H s - 1 ( 1 ) ( k r ) } - 1
b s , | | = { [ m D s ( m k r ) + s k r ] J s ( k r ) - J s - 1 ( k r ) } { [ m D s ( m k r ) + s k r ] H s ( 1 ) ( k r ) - H s - 1 ( 1 ) ( k r ) } - 1
D s ( m k r ) = { J s ' ( m k r ) } { J s ( m k r ) } - 1 ,
AF  = s = 1 N e i ( s - 1 ) [ k d cos ( ϕ ) + β ]
S 11 = E reflected E incident = - H reflected H incident , 0 S 11 1
S 21 = E transmitted E incident = η 2 H transmitted η 1 H incident , 0 S 21 1 ,

Metrics