Abstract

The far-infrared properties of spruce wood are examined with a terahertz time-domain spectrometer. The solid wood is shown to exhibit both birefringence and diattenuation. The birefringence properties are sufficient for construction of a quarter-wave plate operating at 0.36  THz, and a half-wave plate operating at 0.71  THz. The origin of the birefringence is attributed to preferential fiber orientation within the wood. Similar birefringence is observed in lens paper in which the fibers are preferentially oriented in one direction.

© 2006 Optical Society of America

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  1. G. C. Walker, E. Berry, N. N. Zinov'ev, A. J. Fitzgerald, R. E. Miles, M. Chamberlain, and M. A. Smith, " Teraherz imaging and international safety guidelines," in Medical Imaging 2002: Physics of Medical Imaging, L.E.Antonuk and M.J.Yaffe, eds., Proc. SPIE 4682, 683- 690 ( 2002).
  2. D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, " Recent advances in terahertz imaging," Appl. Phys. B 68, 1085- 1094 ( 1999).
    [CrossRef]
  3. M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, " Security applications of terahertz imaging," in Terahertz for Military and Security Applications, R.J.Hwu and D.L.Woolard, eds., Proc. SPIE 5070, 44- 52 ( 2003).
  4. W. R. Tribe, D. A. Newnham, P. F. Taday, and M. C. Kemp, " Hidden object detection: security applications of terahertz technology," in Terahertz and Gigahertz Electronics and Photonics III, R.J.Hwu, ed., Proc. SPIE 5354, 168- 176 ( 2004).
  5. M. Koch, S. Hunsche, P. Schaucher, M. C. Nuss, J. Feldmann, and J. Fromm, " THz-imaging: a new method for density mapping of wood," Wood Sci. Technol. 32, 421- 427 ( 1998).
  6. S. Hunsche and M. C. Nuss, " Terahertz T-ray tomography," in Millimeter and Submillimeter Waves IV, M.N.Afsar, ed., Proc. SPIE 3465, 426- 433 ( 1998).
  7. Y. W. Lim, A. Sarko, and R. H. Marchessault, " Light scattering by cellulose. II. Oriented condensed paper," TAPPI J. 53, 2314- 2319 ( 1970).
  8. P. H. Friedlander, " The measurement of fibre orientation in newsprint with respect to the machine direction by x-ray diffraction," Pulp Paper Mag. Canada (January 1958), pp. 102- 103.
  9. H. Ruck and H. Krässig, " The determination of fiber orientation in paper," Pulp Paper Mag. Canada (June 1958), pp. 183- 190 ( 1958).
  10. C. M. Crosby, A. R. K. Eusufazi, R. E. Mark, R. W. Perkins, J. S. Chang, and N. V. Uplekar, " A digitizing system for quantitative measurement of structural parameters in paper," TAPPI J. 64, 103- 106 ( 1981).
  11. M. Reid and R. Fedosejevs, " Quantitative comparison of THz emission from (100) InAs surfaces and GaAs large-aperture photoconductive switch at high fluences," Appl. Opt. 44, 149- 153 ( 2004).
  12. G. Zhao, R. N. Schouten, N. van der Valk, W. T. Wenckebach, and P. C. M. Planken, " Design and performance of THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715- 1719 ( 2002).
    [CrossRef]
  13. P. C. M. Planken, H. -K. Nienhuys, H. J. Bakker, and T. Wenckebach, " Measurement and calculation of the orientation dependence of terahertz pulse detection in ZnTe," J. Opt. Soc. Am. B 18, 313- 317 ( 2001).
    [CrossRef]
  14. L. Duvillaret, F. Garet, and J. -L. Coutaz, " A reliable method for extraction of material parameters in terahetz time-domain spectroscopy," IEEE J. Sel. Top. Quantum Electron. 2, 739- 746 ( 1996).
    [CrossRef]
  15. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).
  16. A. J. Stamm, Wood and Cellulose Science, 1st ed. (Ronald Press, 1964).
  17. For a long solid cylinder, with an index of refraction of 1.5, numerical calculations are shown in Fig. 67 of Ref. 18 for values of 0.1 < p < 1, corresponding to a frequency range of 0.1-1 THz for a cylinder radius of 50 μm.
  18. H. C. van de Hulst, Light Scattering by Small Particles, 1st ed. (Dover, 1981).

2004 (1)

2002 (1)

G. Zhao, R. N. Schouten, N. van der Valk, W. T. Wenckebach, and P. C. M. Planken, " Design and performance of THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715- 1719 ( 2002).
[CrossRef]

2001 (1)

1999 (1)

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, " Recent advances in terahertz imaging," Appl. Phys. B 68, 1085- 1094 ( 1999).
[CrossRef]

1998 (1)

M. Koch, S. Hunsche, P. Schaucher, M. C. Nuss, J. Feldmann, and J. Fromm, " THz-imaging: a new method for density mapping of wood," Wood Sci. Technol. 32, 421- 427 ( 1998).

1996 (1)

L. Duvillaret, F. Garet, and J. -L. Coutaz, " A reliable method for extraction of material parameters in terahetz time-domain spectroscopy," IEEE J. Sel. Top. Quantum Electron. 2, 739- 746 ( 1996).
[CrossRef]

1981 (1)

C. M. Crosby, A. R. K. Eusufazi, R. E. Mark, R. W. Perkins, J. S. Chang, and N. V. Uplekar, " A digitizing system for quantitative measurement of structural parameters in paper," TAPPI J. 64, 103- 106 ( 1981).

1970 (1)

Y. W. Lim, A. Sarko, and R. H. Marchessault, " Light scattering by cellulose. II. Oriented condensed paper," TAPPI J. 53, 2314- 2319 ( 1970).

1958 (1)

H. Ruck and H. Krässig, " The determination of fiber orientation in paper," Pulp Paper Mag. Canada (June 1958), pp. 183- 190 ( 1958).

Bakker, H. J.

Baraniuk, R. G.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, " Recent advances in terahertz imaging," Appl. Phys. B 68, 1085- 1094 ( 1999).
[CrossRef]

Berry, E.

G. C. Walker, E. Berry, N. N. Zinov'ev, A. J. Fitzgerald, R. E. Miles, M. Chamberlain, and M. A. Smith, " Teraherz imaging and international safety guidelines," in Medical Imaging 2002: Physics of Medical Imaging, L.E.Antonuk and M.J.Yaffe, eds., Proc. SPIE 4682, 683- 690 ( 2002).

Chamberlain, M.

G. C. Walker, E. Berry, N. N. Zinov'ev, A. J. Fitzgerald, R. E. Miles, M. Chamberlain, and M. A. Smith, " Teraherz imaging and international safety guidelines," in Medical Imaging 2002: Physics of Medical Imaging, L.E.Antonuk and M.J.Yaffe, eds., Proc. SPIE 4682, 683- 690 ( 2002).

Chang, J. S.

C. M. Crosby, A. R. K. Eusufazi, R. E. Mark, R. W. Perkins, J. S. Chang, and N. V. Uplekar, " A digitizing system for quantitative measurement of structural parameters in paper," TAPPI J. 64, 103- 106 ( 1981).

Cluff, J. A.

M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, " Security applications of terahertz imaging," in Terahertz for Military and Security Applications, R.J.Hwu and D.L.Woolard, eds., Proc. SPIE 5070, 44- 52 ( 2003).

Cole, B. E.

M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, " Security applications of terahertz imaging," in Terahertz for Military and Security Applications, R.J.Hwu and D.L.Woolard, eds., Proc. SPIE 5070, 44- 52 ( 2003).

Coutaz, J. -L.

L. Duvillaret, F. Garet, and J. -L. Coutaz, " A reliable method for extraction of material parameters in terahetz time-domain spectroscopy," IEEE J. Sel. Top. Quantum Electron. 2, 739- 746 ( 1996).
[CrossRef]

Crosby, C. M.

C. M. Crosby, A. R. K. Eusufazi, R. E. Mark, R. W. Perkins, J. S. Chang, and N. V. Uplekar, " A digitizing system for quantitative measurement of structural parameters in paper," TAPPI J. 64, 103- 106 ( 1981).

Duvillaret, L.

L. Duvillaret, F. Garet, and J. -L. Coutaz, " A reliable method for extraction of material parameters in terahetz time-domain spectroscopy," IEEE J. Sel. Top. Quantum Electron. 2, 739- 746 ( 1996).
[CrossRef]

Eusufazi, A. R. K.

C. M. Crosby, A. R. K. Eusufazi, R. E. Mark, R. W. Perkins, J. S. Chang, and N. V. Uplekar, " A digitizing system for quantitative measurement of structural parameters in paper," TAPPI J. 64, 103- 106 ( 1981).

Fedosejevs, R.

Feldmann, J.

M. Koch, S. Hunsche, P. Schaucher, M. C. Nuss, J. Feldmann, and J. Fromm, " THz-imaging: a new method for density mapping of wood," Wood Sci. Technol. 32, 421- 427 ( 1998).

Fitzgerald, A. J.

M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, " Security applications of terahertz imaging," in Terahertz for Military and Security Applications, R.J.Hwu and D.L.Woolard, eds., Proc. SPIE 5070, 44- 52 ( 2003).

G. C. Walker, E. Berry, N. N. Zinov'ev, A. J. Fitzgerald, R. E. Miles, M. Chamberlain, and M. A. Smith, " Teraherz imaging and international safety guidelines," in Medical Imaging 2002: Physics of Medical Imaging, L.E.Antonuk and M.J.Yaffe, eds., Proc. SPIE 4682, 683- 690 ( 2002).

Friedlander, P. H.

P. H. Friedlander, " The measurement of fibre orientation in newsprint with respect to the machine direction by x-ray diffraction," Pulp Paper Mag. Canada (January 1958), pp. 102- 103.

Fromm, J.

M. Koch, S. Hunsche, P. Schaucher, M. C. Nuss, J. Feldmann, and J. Fromm, " THz-imaging: a new method for density mapping of wood," Wood Sci. Technol. 32, 421- 427 ( 1998).

Garet, F.

L. Duvillaret, F. Garet, and J. -L. Coutaz, " A reliable method for extraction of material parameters in terahetz time-domain spectroscopy," IEEE J. Sel. Top. Quantum Electron. 2, 739- 746 ( 1996).
[CrossRef]

Gupta, M.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, " Recent advances in terahertz imaging," Appl. Phys. B 68, 1085- 1094 ( 1999).
[CrossRef]

Hunsche, S.

M. Koch, S. Hunsche, P. Schaucher, M. C. Nuss, J. Feldmann, and J. Fromm, " THz-imaging: a new method for density mapping of wood," Wood Sci. Technol. 32, 421- 427 ( 1998).

S. Hunsche and M. C. Nuss, " Terahertz T-ray tomography," in Millimeter and Submillimeter Waves IV, M.N.Afsar, ed., Proc. SPIE 3465, 426- 433 ( 1998).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

Kemp, M. C.

W. R. Tribe, D. A. Newnham, P. F. Taday, and M. C. Kemp, " Hidden object detection: security applications of terahertz technology," in Terahertz and Gigahertz Electronics and Photonics III, R.J.Hwu, ed., Proc. SPIE 5354, 168- 176 ( 2004).

M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, " Security applications of terahertz imaging," in Terahertz for Military and Security Applications, R.J.Hwu and D.L.Woolard, eds., Proc. SPIE 5070, 44- 52 ( 2003).

Koch, M.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, " Recent advances in terahertz imaging," Appl. Phys. B 68, 1085- 1094 ( 1999).
[CrossRef]

M. Koch, S. Hunsche, P. Schaucher, M. C. Nuss, J. Feldmann, and J. Fromm, " THz-imaging: a new method for density mapping of wood," Wood Sci. Technol. 32, 421- 427 ( 1998).

Krässig, H.

H. Ruck and H. Krässig, " The determination of fiber orientation in paper," Pulp Paper Mag. Canada (June 1958), pp. 183- 190 ( 1958).

Lim, Y. W.

Y. W. Lim, A. Sarko, and R. H. Marchessault, " Light scattering by cellulose. II. Oriented condensed paper," TAPPI J. 53, 2314- 2319 ( 1970).

Marchessault, R. H.

Y. W. Lim, A. Sarko, and R. H. Marchessault, " Light scattering by cellulose. II. Oriented condensed paper," TAPPI J. 53, 2314- 2319 ( 1970).

Mark, R. E.

C. M. Crosby, A. R. K. Eusufazi, R. E. Mark, R. W. Perkins, J. S. Chang, and N. V. Uplekar, " A digitizing system for quantitative measurement of structural parameters in paper," TAPPI J. 64, 103- 106 ( 1981).

Miles, R. E.

G. C. Walker, E. Berry, N. N. Zinov'ev, A. J. Fitzgerald, R. E. Miles, M. Chamberlain, and M. A. Smith, " Teraherz imaging and international safety guidelines," in Medical Imaging 2002: Physics of Medical Imaging, L.E.Antonuk and M.J.Yaffe, eds., Proc. SPIE 4682, 683- 690 ( 2002).

Mittleman, D. M.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, " Recent advances in terahertz imaging," Appl. Phys. B 68, 1085- 1094 ( 1999).
[CrossRef]

Neelamani, R.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, " Recent advances in terahertz imaging," Appl. Phys. B 68, 1085- 1094 ( 1999).
[CrossRef]

Newnham, D. A.

W. R. Tribe, D. A. Newnham, P. F. Taday, and M. C. Kemp, " Hidden object detection: security applications of terahertz technology," in Terahertz and Gigahertz Electronics and Photonics III, R.J.Hwu, ed., Proc. SPIE 5354, 168- 176 ( 2004).

Nienhuys, H. -K.

Nuss, M. C.

M. Koch, S. Hunsche, P. Schaucher, M. C. Nuss, J. Feldmann, and J. Fromm, " THz-imaging: a new method for density mapping of wood," Wood Sci. Technol. 32, 421- 427 ( 1998).

S. Hunsche and M. C. Nuss, " Terahertz T-ray tomography," in Millimeter and Submillimeter Waves IV, M.N.Afsar, ed., Proc. SPIE 3465, 426- 433 ( 1998).

Perkins, R. W.

C. M. Crosby, A. R. K. Eusufazi, R. E. Mark, R. W. Perkins, J. S. Chang, and N. V. Uplekar, " A digitizing system for quantitative measurement of structural parameters in paper," TAPPI J. 64, 103- 106 ( 1981).

Planken, P. C. M.

G. Zhao, R. N. Schouten, N. van der Valk, W. T. Wenckebach, and P. C. M. Planken, " Design and performance of THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715- 1719 ( 2002).
[CrossRef]

P. C. M. Planken, H. -K. Nienhuys, H. J. Bakker, and T. Wenckebach, " Measurement and calculation of the orientation dependence of terahertz pulse detection in ZnTe," J. Opt. Soc. Am. B 18, 313- 317 ( 2001).
[CrossRef]

Reid, M.

Ruck, H.

H. Ruck and H. Krässig, " The determination of fiber orientation in paper," Pulp Paper Mag. Canada (June 1958), pp. 183- 190 ( 1958).

Rudd, J. V.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, " Recent advances in terahertz imaging," Appl. Phys. B 68, 1085- 1094 ( 1999).
[CrossRef]

Sarko, A.

Y. W. Lim, A. Sarko, and R. H. Marchessault, " Light scattering by cellulose. II. Oriented condensed paper," TAPPI J. 53, 2314- 2319 ( 1970).

Schaucher, P.

M. Koch, S. Hunsche, P. Schaucher, M. C. Nuss, J. Feldmann, and J. Fromm, " THz-imaging: a new method for density mapping of wood," Wood Sci. Technol. 32, 421- 427 ( 1998).

Schouten, R. N.

G. Zhao, R. N. Schouten, N. van der Valk, W. T. Wenckebach, and P. C. M. Planken, " Design and performance of THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715- 1719 ( 2002).
[CrossRef]

Smith, M. A.

G. C. Walker, E. Berry, N. N. Zinov'ev, A. J. Fitzgerald, R. E. Miles, M. Chamberlain, and M. A. Smith, " Teraherz imaging and international safety guidelines," in Medical Imaging 2002: Physics of Medical Imaging, L.E.Antonuk and M.J.Yaffe, eds., Proc. SPIE 4682, 683- 690 ( 2002).

Stamm, A. J.

A. J. Stamm, Wood and Cellulose Science, 1st ed. (Ronald Press, 1964).

Taday, P. F.

M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, " Security applications of terahertz imaging," in Terahertz for Military and Security Applications, R.J.Hwu and D.L.Woolard, eds., Proc. SPIE 5070, 44- 52 ( 2003).

W. R. Tribe, D. A. Newnham, P. F. Taday, and M. C. Kemp, " Hidden object detection: security applications of terahertz technology," in Terahertz and Gigahertz Electronics and Photonics III, R.J.Hwu, ed., Proc. SPIE 5354, 168- 176 ( 2004).

Tribe, W. R.

M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, " Security applications of terahertz imaging," in Terahertz for Military and Security Applications, R.J.Hwu and D.L.Woolard, eds., Proc. SPIE 5070, 44- 52 ( 2003).

W. R. Tribe, D. A. Newnham, P. F. Taday, and M. C. Kemp, " Hidden object detection: security applications of terahertz technology," in Terahertz and Gigahertz Electronics and Photonics III, R.J.Hwu, ed., Proc. SPIE 5354, 168- 176 ( 2004).

Uplekar, N. V.

C. M. Crosby, A. R. K. Eusufazi, R. E. Mark, R. W. Perkins, J. S. Chang, and N. V. Uplekar, " A digitizing system for quantitative measurement of structural parameters in paper," TAPPI J. 64, 103- 106 ( 1981).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles, 1st ed. (Dover, 1981).

van der Valk, N.

G. Zhao, R. N. Schouten, N. van der Valk, W. T. Wenckebach, and P. C. M. Planken, " Design and performance of THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715- 1719 ( 2002).
[CrossRef]

Walker, G. C.

G. C. Walker, E. Berry, N. N. Zinov'ev, A. J. Fitzgerald, R. E. Miles, M. Chamberlain, and M. A. Smith, " Teraherz imaging and international safety guidelines," in Medical Imaging 2002: Physics of Medical Imaging, L.E.Antonuk and M.J.Yaffe, eds., Proc. SPIE 4682, 683- 690 ( 2002).

Wenckebach, T.

Wenckebach, W. T.

G. Zhao, R. N. Schouten, N. van der Valk, W. T. Wenckebach, and P. C. M. Planken, " Design and performance of THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715- 1719 ( 2002).
[CrossRef]

Zhao, G.

G. Zhao, R. N. Schouten, N. van der Valk, W. T. Wenckebach, and P. C. M. Planken, " Design and performance of THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715- 1719 ( 2002).
[CrossRef]

Zinov'ev, N. N.

G. C. Walker, E. Berry, N. N. Zinov'ev, A. J. Fitzgerald, R. E. Miles, M. Chamberlain, and M. A. Smith, " Teraherz imaging and international safety guidelines," in Medical Imaging 2002: Physics of Medical Imaging, L.E.Antonuk and M.J.Yaffe, eds., Proc. SPIE 4682, 683- 690 ( 2002).

Appl. Opt. (1)

Appl. Phys. B (1)

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, " Recent advances in terahertz imaging," Appl. Phys. B 68, 1085- 1094 ( 1999).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

L. Duvillaret, F. Garet, and J. -L. Coutaz, " A reliable method for extraction of material parameters in terahetz time-domain spectroscopy," IEEE J. Sel. Top. Quantum Electron. 2, 739- 746 ( 1996).
[CrossRef]

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

Pulp Paper Mag. Canada (2)

P. H. Friedlander, " The measurement of fibre orientation in newsprint with respect to the machine direction by x-ray diffraction," Pulp Paper Mag. Canada (January 1958), pp. 102- 103.

H. Ruck and H. Krässig, " The determination of fiber orientation in paper," Pulp Paper Mag. Canada (June 1958), pp. 183- 190 ( 1958).

Rev. Sci. Instrum. (1)

G. Zhao, R. N. Schouten, N. van der Valk, W. T. Wenckebach, and P. C. M. Planken, " Design and performance of THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715- 1719 ( 2002).
[CrossRef]

TAPPI J. (2)

C. M. Crosby, A. R. K. Eusufazi, R. E. Mark, R. W. Perkins, J. S. Chang, and N. V. Uplekar, " A digitizing system for quantitative measurement of structural parameters in paper," TAPPI J. 64, 103- 106 ( 1981).

Y. W. Lim, A. Sarko, and R. H. Marchessault, " Light scattering by cellulose. II. Oriented condensed paper," TAPPI J. 53, 2314- 2319 ( 1970).

Wood Sci. Technol. (1)

M. Koch, S. Hunsche, P. Schaucher, M. C. Nuss, J. Feldmann, and J. Fromm, " THz-imaging: a new method for density mapping of wood," Wood Sci. Technol. 32, 421- 427 ( 1998).

Other (8)

S. Hunsche and M. C. Nuss, " Terahertz T-ray tomography," in Millimeter and Submillimeter Waves IV, M.N.Afsar, ed., Proc. SPIE 3465, 426- 433 ( 1998).

M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, " Security applications of terahertz imaging," in Terahertz for Military and Security Applications, R.J.Hwu and D.L.Woolard, eds., Proc. SPIE 5070, 44- 52 ( 2003).

W. R. Tribe, D. A. Newnham, P. F. Taday, and M. C. Kemp, " Hidden object detection: security applications of terahertz technology," in Terahertz and Gigahertz Electronics and Photonics III, R.J.Hwu, ed., Proc. SPIE 5354, 168- 176 ( 2004).

G. C. Walker, E. Berry, N. N. Zinov'ev, A. J. Fitzgerald, R. E. Miles, M. Chamberlain, and M. A. Smith, " Teraherz imaging and international safety guidelines," in Medical Imaging 2002: Physics of Medical Imaging, L.E.Antonuk and M.J.Yaffe, eds., Proc. SPIE 4682, 683- 690 ( 2002).

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

A. J. Stamm, Wood and Cellulose Science, 1st ed. (Ronald Press, 1964).

For a long solid cylinder, with an index of refraction of 1.5, numerical calculations are shown in Fig. 67 of Ref. 18 for values of 0.1 < p < 1, corresponding to a frequency range of 0.1-1 THz for a cylinder radius of 50 μm.

H. C. van de Hulst, Light Scattering by Small Particles, 1st ed. (Dover, 1981).

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of the setup: BS, beam splitter; λ∕2, half-wave plate; POL, polarizer; M's, mirrors; ODL, optical delay line; PLs, positive lenses; PMs, parabolic mirrors; LPF, low-pass filter blocking the optical leakage and passing the far-infrared radiation; λ∕4, quarter-wave plate; WP, Wollaston prism; PDs, are photodiodes; LIA, lock-in amplifier; SLAPCS, semi-large aperture photoconductive switch.

Fig. 2
Fig. 2

Reference and transmitted terahertz time-domain waveforms transmitted through an 8.3 mm piece of spruce wood measured with the terahertz polarization making an angle θ with respect to the visible grain direction. Each scan is labeled by the corresponding value of θ used in the measurement, and the scans are offset for clarity. tfast and tslow , time delay for propagation with terahertz polarization perpendicular and parallel to the visible grain, leading to fast and slow axes, respectively. Δτ, time difference between terahertz propagation polarized parallel and perpendicular to the grain.

Fig. 3
Fig. 3

Frequency-resolved index of refraction (n) and absorption coefficient (α) obtained in transmission spectroscopy of a 3.025 mm thick piece of spruce wood. Measurements were taken with the terahertz polarization parallel to the grain (solid curves) and perpendicular to the grain (dashed curves).

Fig. 4
Fig. 4

Schematic diagram of the orientation of the wood with respect to analyzer axes (vertical and horizontal) for the input terahertz fields. Directions â and â are parallel and perpendicular, respectively, to the wood grain.

Fig. 5
Fig. 5

Measured THz transmission for the 365 GHz frequency bin data as a function of wood orientation. The data for vertically (squares) and horizontally (circles) polarized terahertz fields are shown for transmission through 3.025 mm thick spruce, along with the expected angular dependence for behavior as a quarter-wave plate [Eqs. (11)]. The angle is defined as the angle that the grain direction makes with the vertical axis.

Fig. 6
Fig. 6

THz transmission for the 711 GHz frequency bin data as a function of wood orientation. The data for vertically (squares) and horizontally (circles) polarized terahertz fields are shown for transmission through 3.025 mm thick spruce, along with the expected angular dependence for behavior as a half-wave plate [Eq. (11)]. The angle is defined as the angle that the grain direction makes with the vertical axis.

Fig. 7
Fig. 7

Operating point for mapping the time delay of terahertz radiation to birefringence data. The figure shows a typical terahertz time-domain waveform, and the orientation of the operating point is shown in the inset. The lock-in amplifier (LIA) signal is zeroed at the operating point, and the lens paper sample is rotated about its surface normal to map the time delay to amplitude information.

Fig. 8
Fig. 8

Lock-in amplifier (LIA) signal as a function of orientation for transmission of terahertz radiation through 27 pieces of aligned lens paper. The lens paper oriented with its fiber alignment vertical corresponds to 0° here. The input terahertz field is polarized horizontally. The measured signal corresponds to mapping time delay to birefringence (see text for details).

Fig. 9
Fig. 9

Index of refraction of a 21 μm thick piece of lens paper obtained with terahertz polarization perpendicular (long-dashed curve) and parallel (solid curve) to the fiber orientation. nf, ns , fast and slow axes, respectively.

Equations (19)

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Δ n = c Δ τ / L ,
E wood ( ν ) E ref ( ν ) = t ̂ AW t ̂ WA exp [ i 2 πν L c ( n ^ W n ^ A ) ] ,
t ^ i j = 2 n ^ i n ^ i + n ^ j
n ^ W = n W i k W ,
R exp ( i θ ) = E wood ( ν ) E ref ( ν ) 4 n W ( n W + 1 ) exp ( 2 π ν L c k W ) × exp [ i 2 π ν L c ( n W 1 ) ] .
n W = θ c 2 π ν L + 1 ,
α W = 2 L ln [ R ( n W + 1 ) 2 4 n W ] ,
E out = E in cos ( θ ) exp ( i Γ ) exp ( ½ α d ) ,
E out = E in sin ( θ ) exp ( i Γ ) exp ( ½ α d ) ,
E vert out = E out cos ( θ ) E out sin ( θ ) ,
E horiz out = E out cos ( θ ) + E out sin ( θ ) .
| E vert out | = | E in | exp ( ½ α d ) × | sin ( θ ) cos ( θ ) | × | 1 exp ( i Δ Γ ) exp ( Δ α d ) | ,
| E horiz out | = | E in | exp ( ½ α d ) × | cos 2 ( θ ) exp ( Δ α d ) exp ( i Δ Γ ) + sin 2 ( θ ) | ,
E vert out,   QWP = E in exp ( ½ α d ) | sin ( θ ) cos ( θ ) | × [ 1 + exp ( 2 Δ α ) ] 1 / 2 ,
E vert out,   HWP = E in exp ( ½ α d ) | sin ( θ ) cos ( θ ) | × [ 1 + exp ( Δ α d ) ] ,
E horiz out,   QWP = E in exp ( ½ α d ) × [ sin 4 ( θ ) + cos 4 ( θ ) × exp ( 2 Δ α d ) ] 1 / 2 ,
E horiz out,   HWP = E in exp ( ½ α d ) × ( { sin 2 ( θ ) [ 1 + exp ( Δ α d ) ] exp ( Δ α d ) } 2 ) ½ .
λ match = 2 π L Δ Γ Δ n ,
Δ τ = d lens c [ n cos ( θ ) + n sin ( θ ) ] ,

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