Abstract

The light-scattering Mueller matrix is experimentally determined for a 0.26-μm-radius quartz fiber mounted on an aluminum surface at five different incident angles. The results are compared with those for the experimental scattering elements of the lone fiber and the lone surface and with theoretical results derived from a simple fiber–surface model. The experimental matrix elements of the fiber–surface system do not resemble the matrix elements from any of these other systems.

© 1992 Optical Society of America

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References

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  1. Rayleigh, “On the electromagnetic theory of light,” Philos. Mag. 12, 81–101 (1881).
  2. A. J. Hunt, D. R. Huffman, “A new polarization-modulated light scattering instrument,” Rev. Sci. Instrum. 44, 1753–1762 (1973).
    [Crossref]
  3. R. J. Perry, A. J. Hunt, D. R. Huffman, “Experimental determinations of Mueller scattering matrices for nonspherical particles,” Appl. Opt. 17, 2700–2710 (1978).
    [Crossref] [PubMed]
  4. W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of polarization effects in light scattering: a new biophysical tool,” Proc. Natl. Acad. Sci. USA 73, 486–490 (1976).
    [Crossref] [PubMed]
  5. W. S. Bickel, W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized scattered light,” Am. J. Phys. 53, 468–478 (1985).
    [Crossref]
  6. V. J. Iafelice, W. S. Bickel, “Polarized light scattering matrix elements for select perfect and perturbed optical surfaces,” Appl. Opt. 26, 2410–2415 (1987).
    [Crossref]
  7. B. W. Bell, W. S. Bickel, “Single fiber light scattering matrix: an experimental determination,” Appl. Opt. 20, 3874–3879 (1981).
    [Crossref] [PubMed]
  8. C. F. Bohren, D. R. Huffman, Adsorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  9. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  10. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  11. K. B. Nahm, W. L. Wolfe, “Light-scattering models for spheres on a conducting plane: comparison with experiment,” Appl. Opt. 26, 2995–2999 (1987).
    [Crossref] [PubMed]
  12. D. E. Gray, ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972).

1987 (2)

1985 (1)

W. S. Bickel, W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized scattered light,” Am. J. Phys. 53, 468–478 (1985).
[Crossref]

1981 (1)

1978 (1)

1976 (1)

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of polarization effects in light scattering: a new biophysical tool,” Proc. Natl. Acad. Sci. USA 73, 486–490 (1976).
[Crossref] [PubMed]

1973 (1)

A. J. Hunt, D. R. Huffman, “A new polarization-modulated light scattering instrument,” Rev. Sci. Instrum. 44, 1753–1762 (1973).
[Crossref]

1881 (1)

Rayleigh, “On the electromagnetic theory of light,” Philos. Mag. 12, 81–101 (1881).

Bailey, W. M.

W. S. Bickel, W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized scattered light,” Am. J. Phys. 53, 468–478 (1985).
[Crossref]

Bell, B. W.

Bickel, W. S.

V. J. Iafelice, W. S. Bickel, “Polarized light scattering matrix elements for select perfect and perturbed optical surfaces,” Appl. Opt. 26, 2410–2415 (1987).
[Crossref]

W. S. Bickel, W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized scattered light,” Am. J. Phys. 53, 468–478 (1985).
[Crossref]

B. W. Bell, W. S. Bickel, “Single fiber light scattering matrix: an experimental determination,” Appl. Opt. 20, 3874–3879 (1981).
[Crossref] [PubMed]

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of polarization effects in light scattering: a new biophysical tool,” Proc. Natl. Acad. Sci. USA 73, 486–490 (1976).
[Crossref] [PubMed]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Adsorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Davidson, J. F.

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of polarization effects in light scattering: a new biophysical tool,” Proc. Natl. Acad. Sci. USA 73, 486–490 (1976).
[Crossref] [PubMed]

Huffman, D. R.

R. J. Perry, A. J. Hunt, D. R. Huffman, “Experimental determinations of Mueller scattering matrices for nonspherical particles,” Appl. Opt. 17, 2700–2710 (1978).
[Crossref] [PubMed]

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of polarization effects in light scattering: a new biophysical tool,” Proc. Natl. Acad. Sci. USA 73, 486–490 (1976).
[Crossref] [PubMed]

A. J. Hunt, D. R. Huffman, “A new polarization-modulated light scattering instrument,” Rev. Sci. Instrum. 44, 1753–1762 (1973).
[Crossref]

C. F. Bohren, D. R. Huffman, Adsorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Hunt, A. J.

R. J. Perry, A. J. Hunt, D. R. Huffman, “Experimental determinations of Mueller scattering matrices for nonspherical particles,” Appl. Opt. 17, 2700–2710 (1978).
[Crossref] [PubMed]

A. J. Hunt, D. R. Huffman, “A new polarization-modulated light scattering instrument,” Rev. Sci. Instrum. 44, 1753–1762 (1973).
[Crossref]

Iafelice, V. J.

Kerker, M.

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

Kilkson, R.

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of polarization effects in light scattering: a new biophysical tool,” Proc. Natl. Acad. Sci. USA 73, 486–490 (1976).
[Crossref] [PubMed]

Nahm, K. B.

Perry, R. J.

Rayleigh,

Rayleigh, “On the electromagnetic theory of light,” Philos. Mag. 12, 81–101 (1881).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Wolfe, W. L.

Am. J. Phys. (1)

W. S. Bickel, W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized scattered light,” Am. J. Phys. 53, 468–478 (1985).
[Crossref]

Appl. Opt. (4)

Philos. Mag. (1)

Rayleigh, “On the electromagnetic theory of light,” Philos. Mag. 12, 81–101 (1881).

Proc. Natl. Acad. Sci. USA (1)

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of polarization effects in light scattering: a new biophysical tool,” Proc. Natl. Acad. Sci. USA 73, 486–490 (1976).
[Crossref] [PubMed]

Rev. Sci. Instrum. (1)

A. J. Hunt, D. R. Huffman, “A new polarization-modulated light scattering instrument,” Rev. Sci. Instrum. 44, 1753–1762 (1973).
[Crossref]

Other (4)

C. F. Bohren, D. R. Huffman, Adsorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

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

D. E. Gray, ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972).

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Figures (9)

Fig. 1
Fig. 1

Schematic of the light-scattering apparatus used to measure the Mueller matrix elements.

Fig. 2
Fig. 2

The four unique experimental Mueller matrix elements for the quartz fiber (dotted curves) and the theoretical matrix elements for a 0.26-μm-radius quartz fiber (solid curves).

Fig. 3
Fig. 3

The four unique experimental Mueller matrix elements for a fiber–surface system illuminated at near-grazing incidence (α = 11.25°) from an aluminum surface (solid curves). The experimental Mueller matrix elements for the fiber are also shown (dotted curves).

Fig. 4
Fig. 4

The four unique Mueller matrix elements for a fiber–surface system illuminated at α = 22.5° from an aluminum surface.

Fig. 5
Fig. 5

The four unique Mueller matrix elements for a fiber–surface system illuminated at α = 45° from an aluminum surface.

Fig. 6
Fig. 6

The four unique Mueller matrix elements for a fiber–surface system illuminated at α = 67.5° from an aluminum surface.

Fig. 7
Fig. 7

The four unique Mueller matrix elements for a fiber–surface system illuminated at α = 78.75° from an aluminum surface.

Fig. 8
Fig. 8

Paths that an incident beam may follow to the fiber and after interaction before being detected on the incident side of the surface.

Fig. 9
Fig. 9

The four unique Mueller matrix elements calculated for a fiber–surface system (quartz fiber of radius 0.26 μm) illuminated at near-grazing incidence (α = 11.25°) from an aluminum surface (solid curves) are compared with the experimental Mueller matrix elements (dotted curves).

Equations (6)

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S 11 * = S 11             S 12 * = S 12 / S 11 , S 22 * = ( S 12 + S 22 ) / ( S 11 + S 21 ) , S 33 * = ( S 13 + S 33 ) / ( S 11 + S 31 ) , S 34 * = ( S 14 + S 34 ) / ( S 11 + S 31 ) .
S 11 * = S 11 ,             S 12 * = S 12 / S 11 ,             S 22 * = 1 , S 33 * = S 33 / S 11 ,             S 34 * = S 34 / S 11 .
T n tot ( ϑ ) = T n ( ϑ ) + R n ( π / 2 - α ) exp i δ ( α ) T n ( ϑ - 2 α ) + R n [ π / 2 - ( ϑ - α ) ] exp i δ ( ϑ - α ) T n ( ϑ - 2 α ) + R n [ π / 2 - ( ϑ - α ) ] R n ( π / 2 - α ) exp i [ δ ( α ) + δ ( ϑ - α ) ] T n ( ϑ ) .
δ ( ϑ ) = 4 π r sin ϑ λ
R 1 ( ϑ i ) = μ 2 n 1 cos ϑ i - μ 1 n 2 [ 1 - ( n 1 / n 2 ) 2 sin 2 ϑ i ] 1 / 2 μ 2 n 1 cos ϑ i + μ 1 n 2 [ 1 - ( n 1 / n 2 ) 2 sin 2 ϑ i ] 1 / 2 ,
R 2 ( ϑ i ) = μ 1 n 2 cos ϑ i - μ 2 n 1 [ 1 - ( n 1 / n 2 ) 2 sin 2 ϑ i ] 1 / 2 μ 1 n 2 cos ϑ i + μ 2 n 1 [ 1 - ( n 1 / n 2 ) 2 sin 2 ϑ i ] 1 / 2 ,

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