Abstract

A system has been developed to measure the absorption cross section for a single carbon fiber at 35 GHz as a function of length, orientation, and diameter. Typical lengths of the fibers considered ranged from 1 to 20 mm, and diameters ranged from 3 to 8 μm. The results were compared with the modified integral equation calculations of Waterman and Pedersen that describe the scattering and absorption behavior for a wire of finite length and conductivity. Good agreement was found for all lengths, orientations, and diameters studied.

© 1995 Optical Society of America

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  1. C. W. Bruce, A. V. Jelinek, R. M. Halonen, M. J. Stehling, J. C. Pedersen, P. C. Waterman, “Millimeter wavelength attenuation efficiencies of fiberous aerosols,” J. Appl. Phys. 74, 3688–3691 (1993).
    [Crossref]
  2. C. W. Bruce, T. F. Stromberg, K. P. Gurton, J. B. Mozer, “Trans-spectral absorption and scattering of electromagnetic radiation by diesel soot,” Appl. Opt. 30, 1537–1546 (1991).
    [Crossref] [PubMed]
  3. M. F. Iskander, H. Y. Chen, J. E. Penner, “Optical scattering and absorption by branched chains of aerosols,” Appl. Opt. 28, 3083–3091 (1989).
    [Crossref] [PubMed]
  4. B. L. Drolen, C. L. Tien, “Absorption and scattering of agglomerated soot particulate,” J. Quantum Spectrosc. Radiat. Transfer 37, 433–448 (1987).
    [Crossref]
  5. P. C. Waterman, J. C. Pedersen, “Scattering by finite wires,” J. Appl. Phys. 72, 349–359 (1992).
    [Crossref]
  6. E. H. Newman, “A unified theory of thin material wires,” IEEE Trans. Antennas Propag. 39, 1488–1496 (1991).
    [Crossref]
  7. J. H. Richmond, “Scattering by imperfectly conducting wires,” IEEE Trans. Antennas Propag. AP-15, 802–806 (1967).
    [Crossref]
  8. S. Hong, S. L. Borison, D. P. Ford, “Short-pulse scattering by a long wire,” IEEE Trans. Antennas Propag. AP-16, 338–342 (1968).
    [Crossref]
  9. L. Peters, “End-fire echo area of long, thin bodies,” IRE Trans. Antennas Propag. 6, 133–139 (1958).
    [Crossref]
  10. H. Scharfman, D. D. King, “Antenna measurements by modulation of the scatterer,” Proc. IRE 42, 854–858 (1954).
    [Crossref]
  11. C. W. Bruce, D. R. Ashmore, P. C. Pittman, N. E. Pedersen, J. C. Pedersen, P. C. Waterman, “Attenuation at a wavelength of 0.86 cm due to fiberous aerosols,” Appl. Phys. Lett. 56, 791–796 (1990).
    [Crossref]
  12. A. V. Jelinek, C. B. Bruce, “Extinction spectra of highly conductive fiberous aerosols,” J. Appl. Phys. (to be published).
  13. E. K. Kerr, J. G. Attwood, “The laser illuminated absorptivity spectrophone: a method for weak absorptivity in gases at laser wavelengths,” Appl. Opt. 7, 915–921 (1968).
    [Crossref] [PubMed]
  14. C. Bruce, “Development of spectrophones for cw and pulsed radiation sources,” ASL-TR-5802 (U.S. Army Atmospheric Science Laboratory, White Sands Missile Range, N.M., 1976).
  15. T. F. Dalton, D. A. Depatie, T. W. Walker, “Absorption coefficient measurements of nitrous oxide and methane at DF laser wavelengths,” Appl. Phys. Lett. 26, 300–306 (1975).
    [Crossref]
  16. G. Hänel, C. Hillenbrand, “Calorimetric measurement of optical absorption,” Appl. Opt. 28, 510–516 (1989).
    [Crossref] [PubMed]
  17. A. V. Luikov, Analytical Heat Diffusion Theory, J. P. Hartnett, ed. (Academic, New York, 1968), Chap. 8, pp. 371–376.
  18. H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford Press, Oxford, England, 1959), Chap. 13, pp. 346–347.

1993 (1)

C. W. Bruce, A. V. Jelinek, R. M. Halonen, M. J. Stehling, J. C. Pedersen, P. C. Waterman, “Millimeter wavelength attenuation efficiencies of fiberous aerosols,” J. Appl. Phys. 74, 3688–3691 (1993).
[Crossref]

1992 (1)

P. C. Waterman, J. C. Pedersen, “Scattering by finite wires,” J. Appl. Phys. 72, 349–359 (1992).
[Crossref]

1991 (2)

1990 (1)

C. W. Bruce, D. R. Ashmore, P. C. Pittman, N. E. Pedersen, J. C. Pedersen, P. C. Waterman, “Attenuation at a wavelength of 0.86 cm due to fiberous aerosols,” Appl. Phys. Lett. 56, 791–796 (1990).
[Crossref]

1989 (2)

1987 (1)

B. L. Drolen, C. L. Tien, “Absorption and scattering of agglomerated soot particulate,” J. Quantum Spectrosc. Radiat. Transfer 37, 433–448 (1987).
[Crossref]

1975 (1)

T. F. Dalton, D. A. Depatie, T. W. Walker, “Absorption coefficient measurements of nitrous oxide and methane at DF laser wavelengths,” Appl. Phys. Lett. 26, 300–306 (1975).
[Crossref]

1968 (2)

1967 (1)

J. H. Richmond, “Scattering by imperfectly conducting wires,” IEEE Trans. Antennas Propag. AP-15, 802–806 (1967).
[Crossref]

1958 (1)

L. Peters, “End-fire echo area of long, thin bodies,” IRE Trans. Antennas Propag. 6, 133–139 (1958).
[Crossref]

1954 (1)

H. Scharfman, D. D. King, “Antenna measurements by modulation of the scatterer,” Proc. IRE 42, 854–858 (1954).
[Crossref]

Ashmore, D. R.

C. W. Bruce, D. R. Ashmore, P. C. Pittman, N. E. Pedersen, J. C. Pedersen, P. C. Waterman, “Attenuation at a wavelength of 0.86 cm due to fiberous aerosols,” Appl. Phys. Lett. 56, 791–796 (1990).
[Crossref]

Attwood, J. G.

Borison, S. L.

S. Hong, S. L. Borison, D. P. Ford, “Short-pulse scattering by a long wire,” IEEE Trans. Antennas Propag. AP-16, 338–342 (1968).
[Crossref]

Bruce, C.

C. Bruce, “Development of spectrophones for cw and pulsed radiation sources,” ASL-TR-5802 (U.S. Army Atmospheric Science Laboratory, White Sands Missile Range, N.M., 1976).

Bruce, C. B.

A. V. Jelinek, C. B. Bruce, “Extinction spectra of highly conductive fiberous aerosols,” J. Appl. Phys. (to be published).

Bruce, C. W.

C. W. Bruce, A. V. Jelinek, R. M. Halonen, M. J. Stehling, J. C. Pedersen, P. C. Waterman, “Millimeter wavelength attenuation efficiencies of fiberous aerosols,” J. Appl. Phys. 74, 3688–3691 (1993).
[Crossref]

C. W. Bruce, T. F. Stromberg, K. P. Gurton, J. B. Mozer, “Trans-spectral absorption and scattering of electromagnetic radiation by diesel soot,” Appl. Opt. 30, 1537–1546 (1991).
[Crossref] [PubMed]

C. W. Bruce, D. R. Ashmore, P. C. Pittman, N. E. Pedersen, J. C. Pedersen, P. C. Waterman, “Attenuation at a wavelength of 0.86 cm due to fiberous aerosols,” Appl. Phys. Lett. 56, 791–796 (1990).
[Crossref]

Carslaw, H. S.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford Press, Oxford, England, 1959), Chap. 13, pp. 346–347.

Chen, H. Y.

Dalton, T. F.

T. F. Dalton, D. A. Depatie, T. W. Walker, “Absorption coefficient measurements of nitrous oxide and methane at DF laser wavelengths,” Appl. Phys. Lett. 26, 300–306 (1975).
[Crossref]

Depatie, D. A.

T. F. Dalton, D. A. Depatie, T. W. Walker, “Absorption coefficient measurements of nitrous oxide and methane at DF laser wavelengths,” Appl. Phys. Lett. 26, 300–306 (1975).
[Crossref]

Drolen, B. L.

B. L. Drolen, C. L. Tien, “Absorption and scattering of agglomerated soot particulate,” J. Quantum Spectrosc. Radiat. Transfer 37, 433–448 (1987).
[Crossref]

Ford, D. P.

S. Hong, S. L. Borison, D. P. Ford, “Short-pulse scattering by a long wire,” IEEE Trans. Antennas Propag. AP-16, 338–342 (1968).
[Crossref]

Gurton, K. P.

Halonen, R. M.

C. W. Bruce, A. V. Jelinek, R. M. Halonen, M. J. Stehling, J. C. Pedersen, P. C. Waterman, “Millimeter wavelength attenuation efficiencies of fiberous aerosols,” J. Appl. Phys. 74, 3688–3691 (1993).
[Crossref]

Hänel, G.

Hillenbrand, C.

Hong, S.

S. Hong, S. L. Borison, D. P. Ford, “Short-pulse scattering by a long wire,” IEEE Trans. Antennas Propag. AP-16, 338–342 (1968).
[Crossref]

Iskander, M. F.

Jaeger, J. C.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford Press, Oxford, England, 1959), Chap. 13, pp. 346–347.

Jelinek, A. V.

C. W. Bruce, A. V. Jelinek, R. M. Halonen, M. J. Stehling, J. C. Pedersen, P. C. Waterman, “Millimeter wavelength attenuation efficiencies of fiberous aerosols,” J. Appl. Phys. 74, 3688–3691 (1993).
[Crossref]

A. V. Jelinek, C. B. Bruce, “Extinction spectra of highly conductive fiberous aerosols,” J. Appl. Phys. (to be published).

Kerr, E. K.

King, D. D.

H. Scharfman, D. D. King, “Antenna measurements by modulation of the scatterer,” Proc. IRE 42, 854–858 (1954).
[Crossref]

Luikov, A. V.

A. V. Luikov, Analytical Heat Diffusion Theory, J. P. Hartnett, ed. (Academic, New York, 1968), Chap. 8, pp. 371–376.

Mozer, J. B.

Newman, E. H.

E. H. Newman, “A unified theory of thin material wires,” IEEE Trans. Antennas Propag. 39, 1488–1496 (1991).
[Crossref]

Pedersen, J. C.

C. W. Bruce, A. V. Jelinek, R. M. Halonen, M. J. Stehling, J. C. Pedersen, P. C. Waterman, “Millimeter wavelength attenuation efficiencies of fiberous aerosols,” J. Appl. Phys. 74, 3688–3691 (1993).
[Crossref]

P. C. Waterman, J. C. Pedersen, “Scattering by finite wires,” J. Appl. Phys. 72, 349–359 (1992).
[Crossref]

C. W. Bruce, D. R. Ashmore, P. C. Pittman, N. E. Pedersen, J. C. Pedersen, P. C. Waterman, “Attenuation at a wavelength of 0.86 cm due to fiberous aerosols,” Appl. Phys. Lett. 56, 791–796 (1990).
[Crossref]

Pedersen, N. E.

C. W. Bruce, D. R. Ashmore, P. C. Pittman, N. E. Pedersen, J. C. Pedersen, P. C. Waterman, “Attenuation at a wavelength of 0.86 cm due to fiberous aerosols,” Appl. Phys. Lett. 56, 791–796 (1990).
[Crossref]

Penner, J. E.

Peters, L.

L. Peters, “End-fire echo area of long, thin bodies,” IRE Trans. Antennas Propag. 6, 133–139 (1958).
[Crossref]

Pittman, P. C.

C. W. Bruce, D. R. Ashmore, P. C. Pittman, N. E. Pedersen, J. C. Pedersen, P. C. Waterman, “Attenuation at a wavelength of 0.86 cm due to fiberous aerosols,” Appl. Phys. Lett. 56, 791–796 (1990).
[Crossref]

Richmond, J. H.

J. H. Richmond, “Scattering by imperfectly conducting wires,” IEEE Trans. Antennas Propag. AP-15, 802–806 (1967).
[Crossref]

Scharfman, H.

H. Scharfman, D. D. King, “Antenna measurements by modulation of the scatterer,” Proc. IRE 42, 854–858 (1954).
[Crossref]

Stehling, M. J.

C. W. Bruce, A. V. Jelinek, R. M. Halonen, M. J. Stehling, J. C. Pedersen, P. C. Waterman, “Millimeter wavelength attenuation efficiencies of fiberous aerosols,” J. Appl. Phys. 74, 3688–3691 (1993).
[Crossref]

Stromberg, T. F.

Tien, C. L.

B. L. Drolen, C. L. Tien, “Absorption and scattering of agglomerated soot particulate,” J. Quantum Spectrosc. Radiat. Transfer 37, 433–448 (1987).
[Crossref]

Walker, T. W.

T. F. Dalton, D. A. Depatie, T. W. Walker, “Absorption coefficient measurements of nitrous oxide and methane at DF laser wavelengths,” Appl. Phys. Lett. 26, 300–306 (1975).
[Crossref]

Waterman, P. C.

C. W. Bruce, A. V. Jelinek, R. M. Halonen, M. J. Stehling, J. C. Pedersen, P. C. Waterman, “Millimeter wavelength attenuation efficiencies of fiberous aerosols,” J. Appl. Phys. 74, 3688–3691 (1993).
[Crossref]

P. C. Waterman, J. C. Pedersen, “Scattering by finite wires,” J. Appl. Phys. 72, 349–359 (1992).
[Crossref]

C. W. Bruce, D. R. Ashmore, P. C. Pittman, N. E. Pedersen, J. C. Pedersen, P. C. Waterman, “Attenuation at a wavelength of 0.86 cm due to fiberous aerosols,” Appl. Phys. Lett. 56, 791–796 (1990).
[Crossref]

Appl. Opt. (4)

Appl. Phys. Lett. (2)

T. F. Dalton, D. A. Depatie, T. W. Walker, “Absorption coefficient measurements of nitrous oxide and methane at DF laser wavelengths,” Appl. Phys. Lett. 26, 300–306 (1975).
[Crossref]

C. W. Bruce, D. R. Ashmore, P. C. Pittman, N. E. Pedersen, J. C. Pedersen, P. C. Waterman, “Attenuation at a wavelength of 0.86 cm due to fiberous aerosols,” Appl. Phys. Lett. 56, 791–796 (1990).
[Crossref]

IEEE Trans. Antennas Propag. (3)

E. H. Newman, “A unified theory of thin material wires,” IEEE Trans. Antennas Propag. 39, 1488–1496 (1991).
[Crossref]

J. H. Richmond, “Scattering by imperfectly conducting wires,” IEEE Trans. Antennas Propag. AP-15, 802–806 (1967).
[Crossref]

S. Hong, S. L. Borison, D. P. Ford, “Short-pulse scattering by a long wire,” IEEE Trans. Antennas Propag. AP-16, 338–342 (1968).
[Crossref]

IRE Trans. Antennas Propag. (1)

L. Peters, “End-fire echo area of long, thin bodies,” IRE Trans. Antennas Propag. 6, 133–139 (1958).
[Crossref]

J. Appl. Phys. (2)

C. W. Bruce, A. V. Jelinek, R. M. Halonen, M. J. Stehling, J. C. Pedersen, P. C. Waterman, “Millimeter wavelength attenuation efficiencies of fiberous aerosols,” J. Appl. Phys. 74, 3688–3691 (1993).
[Crossref]

P. C. Waterman, J. C. Pedersen, “Scattering by finite wires,” J. Appl. Phys. 72, 349–359 (1992).
[Crossref]

J. Quantum Spectrosc. Radiat. Transfer (1)

B. L. Drolen, C. L. Tien, “Absorption and scattering of agglomerated soot particulate,” J. Quantum Spectrosc. Radiat. Transfer 37, 433–448 (1987).
[Crossref]

Proc. IRE (1)

H. Scharfman, D. D. King, “Antenna measurements by modulation of the scatterer,” Proc. IRE 42, 854–858 (1954).
[Crossref]

Other (4)

A. V. Jelinek, C. B. Bruce, “Extinction spectra of highly conductive fiberous aerosols,” J. Appl. Phys. (to be published).

C. Bruce, “Development of spectrophones for cw and pulsed radiation sources,” ASL-TR-5802 (U.S. Army Atmospheric Science Laboratory, White Sands Missile Range, N.M., 1976).

A. V. Luikov, Analytical Heat Diffusion Theory, J. P. Hartnett, ed. (Academic, New York, 1968), Chap. 8, pp. 371–376.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford Press, Oxford, England, 1959), Chap. 13, pp. 346–347.

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Figures (7)

Fig. 1
Fig. 1

Absorption device schematic: 1, 1-w impatt oscillator; 2, isolator; 3, switch; 4, directional coupler; 5, variable attenuator; 6, detector diode; 7, E–H tuner; 8, variable leak; 9, pressure head.

Fig. 2
Fig. 2

Irradiance for the H-plane study.

Fig. 3
Fig. 3

Irradiance for the E-plane study.

Fig. 4
Fig. 4

Rotation of a 20-mm carbon fiber in the H plane.

Fig. 5
Fig. 5

Length-dependence study.

Fig. 6
Fig. 6

Rotation of a 20-mm carbon fiber in the E plane.

Fig. 7
Fig. 7

Diameter-dependence study.

Equations (5)

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( d Δ p d t ) = ( d Δ p d t ) abs - { ( d Δ p d t ) drift + ( d Δ p d t ) loss + ( d Δ p d t ) leak } .
d Q d t = σ abs I rad ,
d Q d t = n a c ν [ d T d t ] air ,
( d Δ p d t ) abs = ρ R [ d T d t ] air ,
σ abs = V c ν R I rad ( d Δ p d t ) abs ,

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