Abstract

The measurements here are used to examine agreement with a recently developed theory for long-wavelength fibrous aerosol attenuative properties (extinction and components absorption, scattering). This is intended to be the final phase of a long and systematic examination of the theory’s key features. In this case the parameters are high conductivities coupled with a broad range of fiber diameters. It is clear that there is a limit on the extinction efficiency or effective extinction cross section per unit fiber volume. This limit is represented by the fiber diameter of translucency, that is, the diameter at which the fiber is not completely opaque to the electromagnetic energy. The transition is approximated by the classical skin depth of the fiber. Above this diameter the peak extinction efficiency decreases with an increase in diameter at approximately the same rate for all conductors. The scattering resonance producing this peak becomes stronger as the diameter increases. Our data confirm that for fiber diameters below the skin depth the character of the attenuation is that of absorption.

© 2004 Optical Society of America

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References

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  1. P. C. Waterman, J. C. Pedersen, “Electromagnetic scattering and absorption by finite wires,” J. Appl. Phys. 78, 656–667 (1995).
    [CrossRef]
  2. P. C. Waterman, J. C. Pedersen, “Scattering by finite wires of arbitrary epsilon, mu and sigma,” J. Opt. Soc. Am. A 15, 174–184 (1998).
    [CrossRef]
  3. K. P. Gurton, C. W. Bruce, “Parametric study of the absorption cross section for a moderately conducting thin cylinder,” Appl. Opt. 34, 2822–2828 (1995).
    [CrossRef] [PubMed]
  4. K. P. Gurton, C. W. Bruce, “Measured backscatter from conductive thin films deposited on fibrous substrates,” IEEE Trans. Antennas Propag. 46, 1674–1678 (1998).
    [CrossRef]
  5. M. Hart, C. W. Bruce, “Backscatter measurements of thin nickel-coated graphite fibers,” IEEE Trans. Antennas Propag. 48, 842–843 (2000).
    [CrossRef]
  6. 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 ccm due to fibrous aerosols,” Appl. Phys. Lett. 56, 791–792 (1990).
    [CrossRef]
  7. A. V. Jelinek, C. W. Bruce, “Extinction spectra of high conductivity fibrous aerosols,” J. Appl. Phys. 78, 2675–2678 (1995).
    [CrossRef]
  8. C. T. Tai, “Electromagnetic backscattering from cylindrical wires,” J. Appl. Phys. 23, 909–916 (1952).
    [CrossRef]
  9. C. W. Bruce, A. V. Jelinek, R. M. Halonen, M. J. Stehling, J. C. Pedersen, P. C. Waterman, “Millimeter wavelength attenuation efficiencies of fibrous aerosols,” J. Appl. Phys. 74, 3688–3691 (1993).
    [CrossRef]
  10. A. V. Jelinek, C. W. Bruce, “Absorption by moderately conducting fibrous aerosols at millimeter wavelengths,” Appl. Opt. (to be published).
  11. A. Miller, New Mexico State University, Las Cruces, N. Mex., 88003 (personal communication, 2003).

2000

M. Hart, C. W. Bruce, “Backscatter measurements of thin nickel-coated graphite fibers,” IEEE Trans. Antennas Propag. 48, 842–843 (2000).
[CrossRef]

1998

P. C. Waterman, J. C. Pedersen, “Scattering by finite wires of arbitrary epsilon, mu and sigma,” J. Opt. Soc. Am. A 15, 174–184 (1998).
[CrossRef]

K. P. Gurton, C. W. Bruce, “Measured backscatter from conductive thin films deposited on fibrous substrates,” IEEE Trans. Antennas Propag. 46, 1674–1678 (1998).
[CrossRef]

1995

P. C. Waterman, J. C. Pedersen, “Electromagnetic scattering and absorption by finite wires,” J. Appl. Phys. 78, 656–667 (1995).
[CrossRef]

K. P. Gurton, C. W. Bruce, “Parametric study of the absorption cross section for a moderately conducting thin cylinder,” Appl. Opt. 34, 2822–2828 (1995).
[CrossRef] [PubMed]

A. V. Jelinek, C. W. Bruce, “Extinction spectra of high conductivity fibrous aerosols,” J. Appl. Phys. 78, 2675–2678 (1995).
[CrossRef]

1993

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

1990

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 ccm due to fibrous aerosols,” Appl. Phys. Lett. 56, 791–792 (1990).
[CrossRef]

1952

C. T. Tai, “Electromagnetic backscattering from cylindrical wires,” J. Appl. Phys. 23, 909–916 (1952).
[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 ccm due to fibrous aerosols,” Appl. Phys. Lett. 56, 791–792 (1990).
[CrossRef]

Bruce, C. W.

M. Hart, C. W. Bruce, “Backscatter measurements of thin nickel-coated graphite fibers,” IEEE Trans. Antennas Propag. 48, 842–843 (2000).
[CrossRef]

K. P. Gurton, C. W. Bruce, “Measured backscatter from conductive thin films deposited on fibrous substrates,” IEEE Trans. Antennas Propag. 46, 1674–1678 (1998).
[CrossRef]

K. P. Gurton, C. W. Bruce, “Parametric study of the absorption cross section for a moderately conducting thin cylinder,” Appl. Opt. 34, 2822–2828 (1995).
[CrossRef] [PubMed]

A. V. Jelinek, C. W. Bruce, “Extinction spectra of high conductivity fibrous aerosols,” J. Appl. Phys. 78, 2675–2678 (1995).
[CrossRef]

C. W. Bruce, A. V. Jelinek, R. M. Halonen, M. J. Stehling, J. C. Pedersen, P. C. Waterman, “Millimeter wavelength attenuation efficiencies of fibrous aerosols,” J. Appl. Phys. 74, 3688–3691 (1993).
[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 ccm due to fibrous aerosols,” Appl. Phys. Lett. 56, 791–792 (1990).
[CrossRef]

A. V. Jelinek, C. W. Bruce, “Absorption by moderately conducting fibrous aerosols at millimeter wavelengths,” Appl. Opt. (to be published).

Gurton, K. P.

K. P. Gurton, C. W. Bruce, “Measured backscatter from conductive thin films deposited on fibrous substrates,” IEEE Trans. Antennas Propag. 46, 1674–1678 (1998).
[CrossRef]

K. P. Gurton, C. W. Bruce, “Parametric study of the absorption cross section for a moderately conducting thin cylinder,” Appl. Opt. 34, 2822–2828 (1995).
[CrossRef] [PubMed]

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 fibrous aerosols,” J. Appl. Phys. 74, 3688–3691 (1993).
[CrossRef]

Hart, M.

M. Hart, C. W. Bruce, “Backscatter measurements of thin nickel-coated graphite fibers,” IEEE Trans. Antennas Propag. 48, 842–843 (2000).
[CrossRef]

Jelinek, A. V.

A. V. Jelinek, C. W. Bruce, “Extinction spectra of high conductivity fibrous aerosols,” J. Appl. Phys. 78, 2675–2678 (1995).
[CrossRef]

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

A. V. Jelinek, C. W. Bruce, “Absorption by moderately conducting fibrous aerosols at millimeter wavelengths,” Appl. Opt. (to be published).

Miller, A.

A. Miller, New Mexico State University, Las Cruces, N. Mex., 88003 (personal communication, 2003).

Pedersen, J. C.

P. C. Waterman, J. C. Pedersen, “Scattering by finite wires of arbitrary epsilon, mu and sigma,” J. Opt. Soc. Am. A 15, 174–184 (1998).
[CrossRef]

P. C. Waterman, J. C. Pedersen, “Electromagnetic scattering and absorption by finite wires,” J. Appl. Phys. 78, 656–667 (1995).
[CrossRef]

C. W. Bruce, A. V. Jelinek, R. M. Halonen, M. J. Stehling, J. C. Pedersen, P. C. Waterman, “Millimeter wavelength attenuation efficiencies of fibrous aerosols,” J. Appl. Phys. 74, 3688–3691 (1993).
[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 ccm due to fibrous aerosols,” Appl. Phys. Lett. 56, 791–792 (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 ccm due to fibrous aerosols,” Appl. Phys. Lett. 56, 791–792 (1990).
[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 ccm due to fibrous aerosols,” Appl. Phys. Lett. 56, 791–792 (1990).
[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 fibrous aerosols,” J. Appl. Phys. 74, 3688–3691 (1993).
[CrossRef]

Tai, C. T.

C. T. Tai, “Electromagnetic backscattering from cylindrical wires,” J. Appl. Phys. 23, 909–916 (1952).
[CrossRef]

Waterman, P. C.

P. C. Waterman, J. C. Pedersen, “Scattering by finite wires of arbitrary epsilon, mu and sigma,” J. Opt. Soc. Am. A 15, 174–184 (1998).
[CrossRef]

P. C. Waterman, J. C. Pedersen, “Electromagnetic scattering and absorption by finite wires,” J. Appl. Phys. 78, 656–667 (1995).
[CrossRef]

C. W. Bruce, A. V. Jelinek, R. M. Halonen, M. J. Stehling, J. C. Pedersen, P. C. Waterman, “Millimeter wavelength attenuation efficiencies of fibrous aerosols,” J. Appl. Phys. 74, 3688–3691 (1993).
[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 ccm due to fibrous aerosols,” Appl. Phys. Lett. 56, 791–792 (1990).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

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 ccm due to fibrous aerosols,” Appl. Phys. Lett. 56, 791–792 (1990).
[CrossRef]

IEEE Trans. Antennas Propag.

K. P. Gurton, C. W. Bruce, “Measured backscatter from conductive thin films deposited on fibrous substrates,” IEEE Trans. Antennas Propag. 46, 1674–1678 (1998).
[CrossRef]

M. Hart, C. W. Bruce, “Backscatter measurements of thin nickel-coated graphite fibers,” IEEE Trans. Antennas Propag. 48, 842–843 (2000).
[CrossRef]

J. Appl. Phys.

P. C. Waterman, J. C. Pedersen, “Electromagnetic scattering and absorption by finite wires,” J. Appl. Phys. 78, 656–667 (1995).
[CrossRef]

A. V. Jelinek, C. W. Bruce, “Extinction spectra of high conductivity fibrous aerosols,” J. Appl. Phys. 78, 2675–2678 (1995).
[CrossRef]

C. T. Tai, “Electromagnetic backscattering from cylindrical wires,” J. Appl. Phys. 23, 909–916 (1952).
[CrossRef]

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

J. Opt. Soc. Am. A

Other

A. V. Jelinek, C. W. Bruce, “Absorption by moderately conducting fibrous aerosols at millimeter wavelengths,” Appl. Opt. (to be published).

A. Miller, New Mexico State University, Las Cruces, N. Mex., 88003 (personal communication, 2003).

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Figures (9)

Fig. 1
Fig. 1

Peak extinction effective cross section per unit volume plotted for several conductivities, computed from the Waterman-Pedersen formulation for a wavelength of 8.57 mm (35 GHz). The vertical lines represent the values of the skin depth for the materials cited. The conductivities are in 107 mho/m: Cu, 5.9; Fe,Ni, 1.1,1.4; graphite, heat treated, 0.06; graphite, 0.007.

Fig. 2
Fig. 2

Computed width of the principal extinction resonance as a function of fiber conductivity for three diameters, again for a wavelength of 8.57 mm. The inset shows a sample resonance spectrum.

Fig. 3
Fig. 3

End-on sketch of the fiber as mounted on a sheath attached to a nylon line. The outside and inside diameters of the sheath are 944 and 687 μm, respectively. The diameter of the nylon line is 306 μm.

Fig. 4
Fig. 4

Rotating platform single-fiber extinction measurement system. Millimeter wavelength energy enters below the unit. The detector is at the top. The Impatt diode and attendant microwave components are behind the unit.

Fig. 5
Fig. 5

Rotating platform of the single-fiber extinction measurement.

Fig. 6
Fig. 6

Examples of fiber-length spectra: radar cross sections for type 316L stainless steel as functions of fiber length measured and computed for a wavelength of 8.57 mm. Each plot represents a given diameter. The first plot (a) exhibits the flat spectrum (when normalized to fiber volume) of the translucent domain.

Fig. 7
Fig. 7

Peak radar cross section per unit fiber volume as a function of the diameter for a set of conductivities, measured and computed for a wavelength of 8.57 mm. The diameter ranges for two conductivities, high and low metallic (molybdenum/tungsten and stainless steel), are much more complete than for several other materials included.

Fig. 8
Fig. 8

Peak extinction cross section per unit fiber volume as a function of diameter for a set of conductivities, measured and computed for a wavelength of 8.57 mm. Measurement results are presented for nearly the same set of materials as used for the results of Fig. 7.

Fig. 9
Fig. 9

Angular scattering in relative units for gold fibers through a limited range of angles.

Equations (7)

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

δ=2/μσω,
ηs=2μ/μ0J0κa/κaJ1κa,
kn=ω2μnεn+iωμnσn,
k0=ω2μ0ε0h=ω2h.
kh=ω2εh.
T=I2/I1=exp-ρvxσ3xdx,
T=exp-ρaσ2.

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