Abstract

The so-called sum rule for the extinction cross section has been the subject of several publications. However, it has not been obtained directly from the macroscopic Maxwell equations but rather follows from heuristic causality considerations. It is argued that these causality considerations are, in fact, questionable and do not follow from the fundamental concept of electromagnetic scattering by a particle. Therefore, the resulting sum rule should be considered an unproven hypothesis rather than an outcome of a rigorous derivation from first principles.

© 2008 Optical Society of America

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  1. E. M. Purcell, “On the absorption and emission of light by interstellar grains,” Astrophys. J. 158, 433-440 (1969).
    [CrossRef]
  2. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  3. C. Sohl, M. Gustafsson, and G. Kristensson, “Physical limitations on broadband scattering by heterogeneous obstacles,” J. Phys. A 40, 11165-11182 (2007).
    [CrossRef]
  4. C. Sohl, M. Gustafsson, and G. Kristensson, “Physical limitations on metamaterials: restrictions on scattering and absorption over a frequency interval,” J. Phys. D 40, 7146-7151 (2007).
    [CrossRef]
  5. N. G. van Kampen, “S-matrix and causality conditions. I. Maxwell field,” Phys. Rev. 89, 1072-1079 (1953).
    [CrossRef]
  6. B. H. J. McKellar, M. A. Box, and C. F. Bohren, “Sum rules for optical scattering amplitudes,” J. Opt. Soc. Am. 72, 535-538 (1982).
    [CrossRef]
  7. J. C. Ku and J. D. Felske, “Determination of refractive indices of Mie scatterers from Kramers-Kronig analysis of spectral extinction data,” J. Opt. Soc. Am. A 3, 617-623 (1986).
    [CrossRef]
  8. M. A. Box, P. Attard, G. Bryant, and B. H. J. McKellar, “Sum rules for Mie scattering,” J. Opt. Soc. Am. A 4, 795-799 (1987).
    [CrossRef]
  9. Z.-F. Xing and J. M. Greenberg, “An efficient method for the calculation of mean extinction. I. The analyticity of the complex extinction efficiency of homogeneous spheres,” Astrophys. J. 399, 164-175 (1992).
    [CrossRef]
  10. A. J. Sievers, “Extinction sum rule and optical moment for an ellispsoidal particle of arbitrary size,” Opt. Commun. 109, 71-74 (1994).
    [CrossRef]
  11. R. Lai and A. J. Sievers, “Mie computational test of the extinction cross-section sum rules and optical moments for large dielectric spheres and shells,” Opt. Commun. 116, 72-76 (1995).
    [CrossRef]
  12. R. Lai and A. J. Sievers, “Sum rules and optical moments for a coarse scattering medium,” J. Opt. Soc. Am. A 13, 1036-1045 (1996).
    [CrossRef]
  13. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).
  14. E. J. Rothwell and M. J. Cloud, Electromagnetics (CRC, 2001).
    [CrossRef]
  15. V. Twersky, “On propagation in random media of discrete scatterers,” Proc. Symp. Appl. Math. 16, 84-116 (1964).
  16. A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1997).
  17. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge U. Press, 2006).
  18. R. Pike and P. Sabatier, Scattering: Scattering and Inverse Scattering in Pure and Applied Mathematics (Academic, 2002), p. xi.
  19. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of light by Small Particles (Cambridge U. Press, 2002) (available in the PDF format at http://www.giss.nasa.gov/~crmim/books.html).

2007 (2)

C. Sohl, M. Gustafsson, and G. Kristensson, “Physical limitations on broadband scattering by heterogeneous obstacles,” J. Phys. A 40, 11165-11182 (2007).
[CrossRef]

C. Sohl, M. Gustafsson, and G. Kristensson, “Physical limitations on metamaterials: restrictions on scattering and absorption over a frequency interval,” J. Phys. D 40, 7146-7151 (2007).
[CrossRef]

1996 (1)

1995 (1)

R. Lai and A. J. Sievers, “Mie computational test of the extinction cross-section sum rules and optical moments for large dielectric spheres and shells,” Opt. Commun. 116, 72-76 (1995).
[CrossRef]

1994 (1)

A. J. Sievers, “Extinction sum rule and optical moment for an ellispsoidal particle of arbitrary size,” Opt. Commun. 109, 71-74 (1994).
[CrossRef]

1992 (1)

Z.-F. Xing and J. M. Greenberg, “An efficient method for the calculation of mean extinction. I. The analyticity of the complex extinction efficiency of homogeneous spheres,” Astrophys. J. 399, 164-175 (1992).
[CrossRef]

1987 (1)

1986 (1)

1982 (1)

1969 (1)

E. M. Purcell, “On the absorption and emission of light by interstellar grains,” Astrophys. J. 158, 433-440 (1969).
[CrossRef]

1964 (1)

V. Twersky, “On propagation in random media of discrete scatterers,” Proc. Symp. Appl. Math. 16, 84-116 (1964).

1953 (1)

N. G. van Kampen, “S-matrix and causality conditions. I. Maxwell field,” Phys. Rev. 89, 1072-1079 (1953).
[CrossRef]

Attard, P.

Bohren, C. F.

B. H. J. McKellar, M. A. Box, and C. F. Bohren, “Sum rules for optical scattering amplitudes,” J. Opt. Soc. Am. 72, 535-538 (1982).
[CrossRef]

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

Box, M. A.

Bryant, G.

Cloud, M. J.

E. J. Rothwell and M. J. Cloud, Electromagnetics (CRC, 2001).
[CrossRef]

Felske, J. D.

Greenberg, J. M.

Z.-F. Xing and J. M. Greenberg, “An efficient method for the calculation of mean extinction. I. The analyticity of the complex extinction efficiency of homogeneous spheres,” Astrophys. J. 399, 164-175 (1992).
[CrossRef]

Gustafsson, M.

C. Sohl, M. Gustafsson, and G. Kristensson, “Physical limitations on broadband scattering by heterogeneous obstacles,” J. Phys. A 40, 11165-11182 (2007).
[CrossRef]

C. Sohl, M. Gustafsson, and G. Kristensson, “Physical limitations on metamaterials: restrictions on scattering and absorption over a frequency interval,” J. Phys. D 40, 7146-7151 (2007).
[CrossRef]

Huffman, D. R.

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

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1997).

Kristensson, G.

C. Sohl, M. Gustafsson, and G. Kristensson, “Physical limitations on broadband scattering by heterogeneous obstacles,” J. Phys. A 40, 11165-11182 (2007).
[CrossRef]

C. Sohl, M. Gustafsson, and G. Kristensson, “Physical limitations on metamaterials: restrictions on scattering and absorption over a frequency interval,” J. Phys. D 40, 7146-7151 (2007).
[CrossRef]

Ku, J. C.

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge U. Press, 2006).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of light by Small Particles (Cambridge U. Press, 2002) (available in the PDF format at http://www.giss.nasa.gov/~crmim/books.html).

Lai, R.

R. Lai and A. J. Sievers, “Sum rules and optical moments for a coarse scattering medium,” J. Opt. Soc. Am. A 13, 1036-1045 (1996).
[CrossRef]

R. Lai and A. J. Sievers, “Mie computational test of the extinction cross-section sum rules and optical moments for large dielectric spheres and shells,” Opt. Commun. 116, 72-76 (1995).
[CrossRef]

McKellar, B. H. J.

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of light by Small Particles (Cambridge U. Press, 2002) (available in the PDF format at http://www.giss.nasa.gov/~crmim/books.html).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge U. Press, 2006).

Pike, R.

R. Pike and P. Sabatier, Scattering: Scattering and Inverse Scattering in Pure and Applied Mathematics (Academic, 2002), p. xi.

Purcell, E. M.

E. M. Purcell, “On the absorption and emission of light by interstellar grains,” Astrophys. J. 158, 433-440 (1969).
[CrossRef]

Rothwell, E. J.

E. J. Rothwell and M. J. Cloud, Electromagnetics (CRC, 2001).
[CrossRef]

Sabatier, P.

R. Pike and P. Sabatier, Scattering: Scattering and Inverse Scattering in Pure and Applied Mathematics (Academic, 2002), p. xi.

Sievers, A. J.

R. Lai and A. J. Sievers, “Sum rules and optical moments for a coarse scattering medium,” J. Opt. Soc. Am. A 13, 1036-1045 (1996).
[CrossRef]

R. Lai and A. J. Sievers, “Mie computational test of the extinction cross-section sum rules and optical moments for large dielectric spheres and shells,” Opt. Commun. 116, 72-76 (1995).
[CrossRef]

A. J. Sievers, “Extinction sum rule and optical moment for an ellispsoidal particle of arbitrary size,” Opt. Commun. 109, 71-74 (1994).
[CrossRef]

Sohl, C.

C. Sohl, M. Gustafsson, and G. Kristensson, “Physical limitations on metamaterials: restrictions on scattering and absorption over a frequency interval,” J. Phys. D 40, 7146-7151 (2007).
[CrossRef]

C. Sohl, M. Gustafsson, and G. Kristensson, “Physical limitations on broadband scattering by heterogeneous obstacles,” J. Phys. A 40, 11165-11182 (2007).
[CrossRef]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of light by Small Particles (Cambridge U. Press, 2002) (available in the PDF format at http://www.giss.nasa.gov/~crmim/books.html).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge U. Press, 2006).

Twersky, V.

V. Twersky, “On propagation in random media of discrete scatterers,” Proc. Symp. Appl. Math. 16, 84-116 (1964).

van Kampen, N. G.

N. G. van Kampen, “S-matrix and causality conditions. I. Maxwell field,” Phys. Rev. 89, 1072-1079 (1953).
[CrossRef]

Xing, Z.-F.

Z.-F. Xing and J. M. Greenberg, “An efficient method for the calculation of mean extinction. I. The analyticity of the complex extinction efficiency of homogeneous spheres,” Astrophys. J. 399, 164-175 (1992).
[CrossRef]

Astrophys. J. (2)

E. M. Purcell, “On the absorption and emission of light by interstellar grains,” Astrophys. J. 158, 433-440 (1969).
[CrossRef]

Z.-F. Xing and J. M. Greenberg, “An efficient method for the calculation of mean extinction. I. The analyticity of the complex extinction efficiency of homogeneous spheres,” Astrophys. J. 399, 164-175 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

J. Phys. A (1)

C. Sohl, M. Gustafsson, and G. Kristensson, “Physical limitations on broadband scattering by heterogeneous obstacles,” J. Phys. A 40, 11165-11182 (2007).
[CrossRef]

J. Phys. D (1)

C. Sohl, M. Gustafsson, and G. Kristensson, “Physical limitations on metamaterials: restrictions on scattering and absorption over a frequency interval,” J. Phys. D 40, 7146-7151 (2007).
[CrossRef]

Opt. Commun. (2)

A. J. Sievers, “Extinction sum rule and optical moment for an ellispsoidal particle of arbitrary size,” Opt. Commun. 109, 71-74 (1994).
[CrossRef]

R. Lai and A. J. Sievers, “Mie computational test of the extinction cross-section sum rules and optical moments for large dielectric spheres and shells,” Opt. Commun. 116, 72-76 (1995).
[CrossRef]

Phys. Rev. (1)

N. G. van Kampen, “S-matrix and causality conditions. I. Maxwell field,” Phys. Rev. 89, 1072-1079 (1953).
[CrossRef]

Proc. Symp. Appl. Math. (1)

V. Twersky, “On propagation in random media of discrete scatterers,” Proc. Symp. Appl. Math. 16, 84-116 (1964).

Other (7)

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1997).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge U. Press, 2006).

R. Pike and P. Sabatier, Scattering: Scattering and Inverse Scattering in Pure and Applied Mathematics (Academic, 2002), p. xi.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of light by Small Particles (Cambridge U. Press, 2002) (available in the PDF format at http://www.giss.nasa.gov/~crmim/books.html).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

E. J. Rothwell and M. J. Cloud, Electromagnetics (CRC, 2001).
[CrossRef]

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

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