Abstract

The formalism of the quantum theory of angular momentum is used for orientational averaging of the T matrix, the Hermitian tensor T+T, and the direct product T*νν′ Tμμ′. These results are independent of the nature of waves and scatterers. Equations for 〈 T〉 and 〈 T+T〉 are interpreted as specific forms of the generalized Wigner–Eckart theorem for the matrix elements of operators T and T+T, which are calculated in terms of symmetrical top eigenfunctions. The averaged values of the above three types of tensor are used for the analytical calculation of a complete set of incoherent light-scattering observables, i.e., the total scattering and extinction cross sections and the Mueller matrix elements.

© 1992 Optical Society of America

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References

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  1. P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
    [CrossRef]
  2. B. Peterson, S. Ström, “T-matrix for electromagnetic scattering from an arbitrary number of scatterers and representation of E (3),” Phys. Rev. D 8, 3661–3678 (1973).
    [CrossRef]
  3. P. W. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrary shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
    [CrossRef] [PubMed]
  4. V. K. Varadan, V. V. Varadan, eds., Acoustic, Electromagnetic, and Elastic Wave Scattering: Focus on the T-matrix Approach (Pergamon, New York, 1980).
  5. M. F. Iskander, A. Lakhtakia, “Extension of the iterative EBCM to calculate scattering by low-loss or lossless elongated dielectric objects,” Appl. Opt. 23, 948–953 (1984).
    [CrossRef] [PubMed]
  6. V.Twersky Twersky, “Coherent electromagnetic waves in pair-correlated random distributions of aligned scatterers,” J. Math. Phys. 19, 215–230 (1978).
    [CrossRef]
  7. Y. Ma, V. V. Varadan, V. K. Varadan, “Scattered intensity of a wave propagating in a discrete random medium,” Appl. Opt. 27, 2469–2477 (1988).
    [CrossRef] [PubMed]
  8. V. V. Varadan, V. K. Varadan, Y. Ma, W. A. Steele, “Effects of nonspherical statistics on EM wave propagation in discrete random media,” Radio Sci. 22, 491–498 (1987).
    [CrossRef]
  9. V. K. Varadan, Y. Ma, V. V. Varadan, “Scattering and attenuation of elastic waves in random media,” Pure Appl. Geophys. 131, 577–603 (1989).
    [CrossRef]
  10. P. E. Geller, T. G. Tsuei, P. W. Barber, “Information content of the scattering matrix for spheroidal particles,” Appl. Opt. 24, 2391–2396 (1985).
    [CrossRef] [PubMed]
  11. V. N. Lopatin, F. Ya. Sidko, Introduction to Optics of Cell Suspensions (Nauka, Novosibirsk, 1988).
  12. E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
    [CrossRef]
  13. S. B. Singham, C. F. Bohren, “Hybrid method in light scattering by an arbitrary particle,” Appl. Opt. 28, 517–522 (1989).
    [CrossRef] [PubMed]
  14. M. K.Singham Singham, S. B.Singham Singham, G. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986).
    [CrossRef]
  15. W. M. McClain, W. A. Ghoul, “Elastic light scattering by randomly oriented macromolecules: computation of the complete set of observables,” J. Chem. Phys. 84, 6609–6622 (1986).
    [CrossRef]
  16. V. V. Varadan, V. K. Varadan, “Multiple scattering of electromagnetic waves by randomly distributed and oriented dielectric scatterers,” Phys. Rev. D 21, 388–394 (1980).
    [CrossRef]
  17. V. K. Varadan, Y.Ma Ma, V. V. Varadan, “Coherent electromagnetic wave propagation through randomly distributed and oriented pair-correlated dielectric scatterers,” Radio Sci. 19, 1445–1449 (1984).
    [CrossRef]
  18. M. I. Mishchenko, “The interstellar absorption of light by randomly oriented nonspherical grains,” Pis’ma Astron. Zh. 15, 694–700 (1989); “Extinction of light by randomly-oriented non-spherical grains,” Astrophys. Space Sci. 164, 1–13 (1990).
  19. M. I. Mishchenko, “Calculation of Integral Characteristics of Light Scattering for Ensemble of Randomly Oriented Non-spherical Particles,” Kinem. Fiz. Nebes. Tel’ 6, 95–96 (1990).
  20. N. G. Khlebtsov, A. G. Melnikov, V. A. Bogatyrev, D. A. Borovsky, “The optical effects in disperse systems induced by external field: light scattering, linear dichroism, and birefringence,” in Optics of Sea and Atmosphere, F. Ya. Sid’ko, ed. (Academy of Sciences of the USSR, Krasnoyarsk, 1990), p. 168.
  21. N. G. Khlebtsov, “Orientational averaging of the light scattering observables in the T-matrix method,” Opt. Spektrosk. 71, 151–153 (1991).
  22. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  23. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  24. M. I. Mishchenko, “Light scattering by randomly oriented nonspherical particles,” J. Opt. Soc. Am. A 8, 871–882 (1991).
    [CrossRef]
  25. D. A. Varshalovich, A. N. Moskalev, V. K. Khersonsky, Quantum Theory of Angular Momentum (Nauka, Leningrad, 1975).
  26. L. D. Landau, E. M. Lifschitz, Quantum Mechanics. Nonrelativistic Theory (Nauka, Moscow, 1989).
  27. A. R. Edmonds, Angular Momentum in Quantum Mechanics (CERN, Geneva, 1955).
  28. R. Newton, Scattering theory of waves and particles (McGraw-Hill, New York, 1969).
  29. D. S. Saxon, “Tensor scattering matrix for the electromagnetic fields,” Phys. Rev. 100, 1771–1775 (1955).
    [CrossRef]
  30. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. Press, Princeton, N.J., 1957).
  31. P. C. Waterman, “New formulation of acoustic scattering,” J. Acoust. Soc. Am. 45, 1417–1429 (1969).
    [CrossRef]
  32. P. C. Waterman, “Matrix theory of elastic wave scattering,” J. Acoust. Soc. Am. 60, 567–580 (1976).
    [CrossRef]

1991 (2)

N. G. Khlebtsov, “Orientational averaging of the light scattering observables in the T-matrix method,” Opt. Spektrosk. 71, 151–153 (1991).

M. I. Mishchenko, “Light scattering by randomly oriented nonspherical particles,” J. Opt. Soc. Am. A 8, 871–882 (1991).
[CrossRef]

1990 (1)

M. I. Mishchenko, “Calculation of Integral Characteristics of Light Scattering for Ensemble of Randomly Oriented Non-spherical Particles,” Kinem. Fiz. Nebes. Tel’ 6, 95–96 (1990).

1989 (3)

M. I. Mishchenko, “The interstellar absorption of light by randomly oriented nonspherical grains,” Pis’ma Astron. Zh. 15, 694–700 (1989); “Extinction of light by randomly-oriented non-spherical grains,” Astrophys. Space Sci. 164, 1–13 (1990).

S. B. Singham, C. F. Bohren, “Hybrid method in light scattering by an arbitrary particle,” Appl. Opt. 28, 517–522 (1989).
[CrossRef] [PubMed]

V. K. Varadan, Y. Ma, V. V. Varadan, “Scattering and attenuation of elastic waves in random media,” Pure Appl. Geophys. 131, 577–603 (1989).
[CrossRef]

1988 (1)

1987 (1)

V. V. Varadan, V. K. Varadan, Y. Ma, W. A. Steele, “Effects of nonspherical statistics on EM wave propagation in discrete random media,” Radio Sci. 22, 491–498 (1987).
[CrossRef]

1986 (2)

M. K.Singham Singham, S. B.Singham Singham, G. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986).
[CrossRef]

W. M. McClain, W. A. Ghoul, “Elastic light scattering by randomly oriented macromolecules: computation of the complete set of observables,” J. Chem. Phys. 84, 6609–6622 (1986).
[CrossRef]

1985 (1)

1984 (2)

M. F. Iskander, A. Lakhtakia, “Extension of the iterative EBCM to calculate scattering by low-loss or lossless elongated dielectric objects,” Appl. Opt. 23, 948–953 (1984).
[CrossRef] [PubMed]

V. K. Varadan, Y.Ma Ma, V. V. Varadan, “Coherent electromagnetic wave propagation through randomly distributed and oriented pair-correlated dielectric scatterers,” Radio Sci. 19, 1445–1449 (1984).
[CrossRef]

1980 (1)

V. V. Varadan, V. K. Varadan, “Multiple scattering of electromagnetic waves by randomly distributed and oriented dielectric scatterers,” Phys. Rev. D 21, 388–394 (1980).
[CrossRef]

1978 (1)

V.Twersky Twersky, “Coherent electromagnetic waves in pair-correlated random distributions of aligned scatterers,” J. Math. Phys. 19, 215–230 (1978).
[CrossRef]

1976 (1)

P. C. Waterman, “Matrix theory of elastic wave scattering,” J. Acoust. Soc. Am. 60, 567–580 (1976).
[CrossRef]

1975 (1)

1973 (2)

B. Peterson, S. Ström, “T-matrix for electromagnetic scattering from an arbitrary number of scatterers and representation of E (3),” Phys. Rev. D 8, 3661–3678 (1973).
[CrossRef]

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

1971 (1)

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

1969 (1)

P. C. Waterman, “New formulation of acoustic scattering,” J. Acoust. Soc. Am. 45, 1417–1429 (1969).
[CrossRef]

1955 (1)

D. S. Saxon, “Tensor scattering matrix for the electromagnetic fields,” Phys. Rev. 100, 1771–1775 (1955).
[CrossRef]

Barber, P. W.

Bogatyrev, V. A.

N. G. Khlebtsov, A. G. Melnikov, V. A. Bogatyrev, D. A. Borovsky, “The optical effects in disperse systems induced by external field: light scattering, linear dichroism, and birefringence,” in Optics of Sea and Atmosphere, F. Ya. Sid’ko, ed. (Academy of Sciences of the USSR, Krasnoyarsk, 1990), p. 168.

Bohren, C. F.

S. B. Singham, C. F. Bohren, “Hybrid method in light scattering by an arbitrary particle,” Appl. Opt. 28, 517–522 (1989).
[CrossRef] [PubMed]

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

Borovsky, D. A.

N. G. Khlebtsov, A. G. Melnikov, V. A. Bogatyrev, D. A. Borovsky, “The optical effects in disperse systems induced by external field: light scattering, linear dichroism, and birefringence,” in Optics of Sea and Atmosphere, F. Ya. Sid’ko, ed. (Academy of Sciences of the USSR, Krasnoyarsk, 1990), p. 168.

Edmonds, A. R.

A. R. Edmonds, Angular Momentum in Quantum Mechanics (CERN, Geneva, 1955).

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. Press, Princeton, N.J., 1957).

Geller, P. E.

Ghoul, W. A.

W. M. McClain, W. A. Ghoul, “Elastic light scattering by randomly oriented macromolecules: computation of the complete set of observables,” J. Chem. Phys. 84, 6609–6622 (1986).
[CrossRef]

Huffman, D. R.

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

Iskander, M. F.

Khersonsky, V. K.

D. A. Varshalovich, A. N. Moskalev, V. K. Khersonsky, Quantum Theory of Angular Momentum (Nauka, Leningrad, 1975).

Khlebtsov, N. G.

N. G. Khlebtsov, “Orientational averaging of the light scattering observables in the T-matrix method,” Opt. Spektrosk. 71, 151–153 (1991).

N. G. Khlebtsov, A. G. Melnikov, V. A. Bogatyrev, D. A. Borovsky, “The optical effects in disperse systems induced by external field: light scattering, linear dichroism, and birefringence,” in Optics of Sea and Atmosphere, F. Ya. Sid’ko, ed. (Academy of Sciences of the USSR, Krasnoyarsk, 1990), p. 168.

Lakhtakia, A.

Landau, L. D.

L. D. Landau, E. M. Lifschitz, Quantum Mechanics. Nonrelativistic Theory (Nauka, Moscow, 1989).

Lifschitz, E. M.

L. D. Landau, E. M. Lifschitz, Quantum Mechanics. Nonrelativistic Theory (Nauka, Moscow, 1989).

Lopatin, V. N.

V. N. Lopatin, F. Ya. Sidko, Introduction to Optics of Cell Suspensions (Nauka, Novosibirsk, 1988).

Ma, Y.

V. K. Varadan, Y. Ma, V. V. Varadan, “Scattering and attenuation of elastic waves in random media,” Pure Appl. Geophys. 131, 577–603 (1989).
[CrossRef]

Y. Ma, V. V. Varadan, V. K. Varadan, “Scattered intensity of a wave propagating in a discrete random medium,” Appl. Opt. 27, 2469–2477 (1988).
[CrossRef] [PubMed]

V. V. Varadan, V. K. Varadan, Y. Ma, W. A. Steele, “Effects of nonspherical statistics on EM wave propagation in discrete random media,” Radio Sci. 22, 491–498 (1987).
[CrossRef]

Ma, Y.Ma

V. K. Varadan, Y.Ma Ma, V. V. Varadan, “Coherent electromagnetic wave propagation through randomly distributed and oriented pair-correlated dielectric scatterers,” Radio Sci. 19, 1445–1449 (1984).
[CrossRef]

McClain, W. M.

W. M. McClain, W. A. Ghoul, “Elastic light scattering by randomly oriented macromolecules: computation of the complete set of observables,” J. Chem. Phys. 84, 6609–6622 (1986).
[CrossRef]

Melnikov, A. G.

N. G. Khlebtsov, A. G. Melnikov, V. A. Bogatyrev, D. A. Borovsky, “The optical effects in disperse systems induced by external field: light scattering, linear dichroism, and birefringence,” in Optics of Sea and Atmosphere, F. Ya. Sid’ko, ed. (Academy of Sciences of the USSR, Krasnoyarsk, 1990), p. 168.

Mishchenko, M. I.

M. I. Mishchenko, “Light scattering by randomly oriented nonspherical particles,” J. Opt. Soc. Am. A 8, 871–882 (1991).
[CrossRef]

M. I. Mishchenko, “Calculation of Integral Characteristics of Light Scattering for Ensemble of Randomly Oriented Non-spherical Particles,” Kinem. Fiz. Nebes. Tel’ 6, 95–96 (1990).

M. I. Mishchenko, “The interstellar absorption of light by randomly oriented nonspherical grains,” Pis’ma Astron. Zh. 15, 694–700 (1989); “Extinction of light by randomly-oriented non-spherical grains,” Astrophys. Space Sci. 164, 1–13 (1990).

Moskalev, A. N.

D. A. Varshalovich, A. N. Moskalev, V. K. Khersonsky, Quantum Theory of Angular Momentum (Nauka, Leningrad, 1975).

Newton, R.

R. Newton, Scattering theory of waves and particles (McGraw-Hill, New York, 1969).

Pennypacker, C. R.

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

Peterson, B.

B. Peterson, S. Ström, “T-matrix for electromagnetic scattering from an arbitrary number of scatterers and representation of E (3),” Phys. Rev. D 8, 3661–3678 (1973).
[CrossRef]

Purcell, E. M.

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

Salzman, G.

M. K.Singham Singham, S. B.Singham Singham, G. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986).
[CrossRef]

Saxon, D. S.

D. S. Saxon, “Tensor scattering matrix for the electromagnetic fields,” Phys. Rev. 100, 1771–1775 (1955).
[CrossRef]

Sidko, F. Ya.

V. N. Lopatin, F. Ya. Sidko, Introduction to Optics of Cell Suspensions (Nauka, Novosibirsk, 1988).

Singham, M. K.Singham

M. K.Singham Singham, S. B.Singham Singham, G. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986).
[CrossRef]

Singham, S. B.

Singham, S. B.Singham

M. K.Singham Singham, S. B.Singham Singham, G. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986).
[CrossRef]

Steele, W. A.

V. V. Varadan, V. K. Varadan, Y. Ma, W. A. Steele, “Effects of nonspherical statistics on EM wave propagation in discrete random media,” Radio Sci. 22, 491–498 (1987).
[CrossRef]

Stratton, J. A.

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

Ström, S.

B. Peterson, S. Ström, “T-matrix for electromagnetic scattering from an arbitrary number of scatterers and representation of E (3),” Phys. Rev. D 8, 3661–3678 (1973).
[CrossRef]

Tsuei, T. G.

Twersky, V.Twersky

V.Twersky Twersky, “Coherent electromagnetic waves in pair-correlated random distributions of aligned scatterers,” J. Math. Phys. 19, 215–230 (1978).
[CrossRef]

Varadan, V. K.

V. K. Varadan, Y. Ma, V. V. Varadan, “Scattering and attenuation of elastic waves in random media,” Pure Appl. Geophys. 131, 577–603 (1989).
[CrossRef]

Y. Ma, V. V. Varadan, V. K. Varadan, “Scattered intensity of a wave propagating in a discrete random medium,” Appl. Opt. 27, 2469–2477 (1988).
[CrossRef] [PubMed]

V. V. Varadan, V. K. Varadan, Y. Ma, W. A. Steele, “Effects of nonspherical statistics on EM wave propagation in discrete random media,” Radio Sci. 22, 491–498 (1987).
[CrossRef]

V. K. Varadan, Y.Ma Ma, V. V. Varadan, “Coherent electromagnetic wave propagation through randomly distributed and oriented pair-correlated dielectric scatterers,” Radio Sci. 19, 1445–1449 (1984).
[CrossRef]

V. V. Varadan, V. K. Varadan, “Multiple scattering of electromagnetic waves by randomly distributed and oriented dielectric scatterers,” Phys. Rev. D 21, 388–394 (1980).
[CrossRef]

Varadan, V. V.

V. K. Varadan, Y. Ma, V. V. Varadan, “Scattering and attenuation of elastic waves in random media,” Pure Appl. Geophys. 131, 577–603 (1989).
[CrossRef]

Y. Ma, V. V. Varadan, V. K. Varadan, “Scattered intensity of a wave propagating in a discrete random medium,” Appl. Opt. 27, 2469–2477 (1988).
[CrossRef] [PubMed]

V. V. Varadan, V. K. Varadan, Y. Ma, W. A. Steele, “Effects of nonspherical statistics on EM wave propagation in discrete random media,” Radio Sci. 22, 491–498 (1987).
[CrossRef]

V. K. Varadan, Y.Ma Ma, V. V. Varadan, “Coherent electromagnetic wave propagation through randomly distributed and oriented pair-correlated dielectric scatterers,” Radio Sci. 19, 1445–1449 (1984).
[CrossRef]

V. V. Varadan, V. K. Varadan, “Multiple scattering of electromagnetic waves by randomly distributed and oriented dielectric scatterers,” Phys. Rev. D 21, 388–394 (1980).
[CrossRef]

Varshalovich, D. A.

D. A. Varshalovich, A. N. Moskalev, V. K. Khersonsky, Quantum Theory of Angular Momentum (Nauka, Leningrad, 1975).

Waterman, P. C.

P. C. Waterman, “Matrix theory of elastic wave scattering,” J. Acoust. Soc. Am. 60, 567–580 (1976).
[CrossRef]

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

P. C. Waterman, “New formulation of acoustic scattering,” J. Acoust. Soc. Am. 45, 1417–1429 (1969).
[CrossRef]

Yeh, C.

Appl. Opt. (5)

Astrophys. J. (1)

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

J. Acoust. Soc. Am. (2)

P. C. Waterman, “New formulation of acoustic scattering,” J. Acoust. Soc. Am. 45, 1417–1429 (1969).
[CrossRef]

P. C. Waterman, “Matrix theory of elastic wave scattering,” J. Acoust. Soc. Am. 60, 567–580 (1976).
[CrossRef]

J. Chem. Phys. (2)

M. K.Singham Singham, S. B.Singham Singham, G. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986).
[CrossRef]

W. M. McClain, W. A. Ghoul, “Elastic light scattering by randomly oriented macromolecules: computation of the complete set of observables,” J. Chem. Phys. 84, 6609–6622 (1986).
[CrossRef]

J. Math. Phys. (1)

V.Twersky Twersky, “Coherent electromagnetic waves in pair-correlated random distributions of aligned scatterers,” J. Math. Phys. 19, 215–230 (1978).
[CrossRef]

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

Kinem. Fiz. Nebes. Tel’ (1)

M. I. Mishchenko, “Calculation of Integral Characteristics of Light Scattering for Ensemble of Randomly Oriented Non-spherical Particles,” Kinem. Fiz. Nebes. Tel’ 6, 95–96 (1990).

Opt. Spektrosk. (1)

N. G. Khlebtsov, “Orientational averaging of the light scattering observables in the T-matrix method,” Opt. Spektrosk. 71, 151–153 (1991).

Phys. Rev. (1)

D. S. Saxon, “Tensor scattering matrix for the electromagnetic fields,” Phys. Rev. 100, 1771–1775 (1955).
[CrossRef]

Phys. Rev. D (3)

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

B. Peterson, S. Ström, “T-matrix for electromagnetic scattering from an arbitrary number of scatterers and representation of E (3),” Phys. Rev. D 8, 3661–3678 (1973).
[CrossRef]

V. V. Varadan, V. K. Varadan, “Multiple scattering of electromagnetic waves by randomly distributed and oriented dielectric scatterers,” Phys. Rev. D 21, 388–394 (1980).
[CrossRef]

Pis’ma Astron. Zh. (1)

M. I. Mishchenko, “The interstellar absorption of light by randomly oriented nonspherical grains,” Pis’ma Astron. Zh. 15, 694–700 (1989); “Extinction of light by randomly-oriented non-spherical grains,” Astrophys. Space Sci. 164, 1–13 (1990).

Pure Appl. Geophys. (1)

V. K. Varadan, Y. Ma, V. V. Varadan, “Scattering and attenuation of elastic waves in random media,” Pure Appl. Geophys. 131, 577–603 (1989).
[CrossRef]

Radio Sci. (2)

V. K. Varadan, Y.Ma Ma, V. V. Varadan, “Coherent electromagnetic wave propagation through randomly distributed and oriented pair-correlated dielectric scatterers,” Radio Sci. 19, 1445–1449 (1984).
[CrossRef]

V. V. Varadan, V. K. Varadan, Y. Ma, W. A. Steele, “Effects of nonspherical statistics on EM wave propagation in discrete random media,” Radio Sci. 22, 491–498 (1987).
[CrossRef]

Other (10)

V. K. Varadan, V. V. Varadan, eds., Acoustic, Electromagnetic, and Elastic Wave Scattering: Focus on the T-matrix Approach (Pergamon, New York, 1980).

V. N. Lopatin, F. Ya. Sidko, Introduction to Optics of Cell Suspensions (Nauka, Novosibirsk, 1988).

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. Press, Princeton, N.J., 1957).

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

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

N. G. Khlebtsov, A. G. Melnikov, V. A. Bogatyrev, D. A. Borovsky, “The optical effects in disperse systems induced by external field: light scattering, linear dichroism, and birefringence,” in Optics of Sea and Atmosphere, F. Ya. Sid’ko, ed. (Academy of Sciences of the USSR, Krasnoyarsk, 1990), p. 168.

D. A. Varshalovich, A. N. Moskalev, V. K. Khersonsky, Quantum Theory of Angular Momentum (Nauka, Leningrad, 1975).

L. D. Landau, E. M. Lifschitz, Quantum Mechanics. Nonrelativistic Theory (Nauka, Moscow, 1989).

A. R. Edmonds, Angular Momentum in Quantum Mechanics (CERN, Geneva, 1955).

R. Newton, Scattering theory of waves and particles (McGraw-Hill, New York, 1969).

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Equations (59)

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T n m , n m = 1 2 n + 1 δ n n T ^ n m , n m ,
T n m , n m = δ n n δ m m T ^ n m , n m .
Ψ τ ν = 1 [ n ( n + 1 ) ] 1 / 2 ( k - 1 curl ) τ [ k r h n ( k r ) Y n m ( θ , φ ) ] ,
Y n m = c n m P n m ( cos θ ) exp ( i m φ ) ,
c n m = [ 2 n + 1 4 π ( n - m ) ! ( n + m ) ! ] 1 / 2 .
Ψ τ ν = 1 ( m π ) 1 / 2 ( Ψ τ e v + i Ψ τ o ν ) = γ n m { M , τ = 1 N , τ = 2 ,
γ n m = c n m / [ n ( n + 1 ) ] 1 / 2 .
Ψ τ ν - i τ - n exp ( i k r ) k r A τ ν ( r ¯ ) ,             r ¯ = r / r .
E 0 = e 0 exp ( i kr ) = τ ν a τ ν Re Ψ τ ν ,
E = τ ν p τ ν Ψ τ ν .
p τ ν = τ ν T τ ν , τ ν a τ ν .
a ν = 4 π i n - τ + 1 ( e 0 · A ν * ) .
A 2 n m = ( 2 n + 1 8 π ) 1 / 2 e m ,             m = ± 1 ,
a ν = [ π ( 2 n + 1 ) ] 1 / 2 i n + 1 [ δ m 1 + ( - 1 ) τ - 1 δ m , - 1 ] .
E = exp ( i k r ) r F e 0 ,
F ( k ¯ s , k ¯ ) = 1 4 π k i a + ( k ¯ s ) T a ( k ¯ ) ,
a ν ( k ¯ ) = 4 π i n - τ + 1 A ν * ( k ¯ ) .
C e = 4 π k Im ( e 0 * F e 0 ) = - 1 k 2 Re ( a + T a ) ,
C s = 1 k 2 ( p + p ) = 1 k 2 a + T + T a ,
Ψ I M ( ϑ , φ ) Ψ ^ I M = M = - I I Ψ I M ( ϑ , φ ) D M M I ,
Ψ I M ( ϑ , φ ) = M ( D M M I ) * Ψ ^ I M ( ϑ , φ ) .
E = ν p ν Ψ ν = ν m p ν D m m n * Ψ ^ n m = ν p ^ ν Ψ ^ ν .
p ^ ν = p ^ n m = m = - n n D m m n * p n m ,
p ^ = D + p = D - 1 p ,             p = D p ^ ,
T ^ = D + T D ,             T = D T ^ D + ,
T n 1 m 1 , n 2 m 2 = m 1 m 2 D m 1 m 1 n 1 T ^ n 1 m 1 , n 2 m 2 D m 2 m 2 n 2 * .
D m 1 m 1 n 1 D m 2 m 2 n 2 * = 1 2 n 1 + 1 δ n 1 n 2 δ m 1 m 2 δ m 1 m 2 .
T n 1 m 1 , n 2 m 2 T ν μ = δ ν μ 2 n 1 + 1 S p m ( T ^ n 1 m , n 1 m ) = 1 2 n 1 + 1 δ n 1 n 2 δ m 1 m 2 m T ^ n 1 m , n 1 m .
R = T + T = D T ^ + T ^ D + = D R ^ D + .
R ν μ = δ ν μ 1 2 n 1 + 1 S p m ( R ^ n 1 m , n 1 m ) ,
R τ 1 n 1 m 1 , τ 2 n 2 m 2 = δ n 1 n 2 δ m 1 m 2 1 2 n 1 + 1 × m ν T ^ τ 1 n 1 m , ν * T ^ τ 2 n 1 m , ν ,
T ν ν = U ν * W ν = I M C ν ν I M t I M ,
T ν ν * T μ μ = I I 1 M M 1 C ν ν I M C μ μ I 1 M 1 t I M * t I 1 M 1 .
t I M * t I 1 M 1 = δ I I 1 δ M M 1 1 2 I + 1 M t ^ I M * t ^ I M ,
t ^ I M τ τ = t ^ I M = m , m C n m , n m I M T ^ τ n m , τ n m .
T ν ν * T μ μ = I C I T ^ I ,
C I C I ( ν , ν , μ , μ ) = M C ν ν I M C μ μ I M ,
T ^ I = 1 2 I + 1 S p M 1 [ ( t ^ I M 1 τ 1 τ 1 ) * ( t ^ I M 1 τ 2 τ 2 ) ] ,
max ( n 1 - n 1 n 2 - n 2 ) I min ( n 1 + n 1 n 2 + n 2 ) .
m 1 m 1 T ^ τ 1 ν , τ 1 ν * T ^ τ 2 ν , τ 2 ν = I ( 2 I + 1 ) T ^ I ,
1 4 π a ν * ( k ¯ ) a ν ( k ¯ ) d Ω ( k ¯ ) = 2 π δ τ τ δ n n δ m m .
C e = - 2 π k 2 Re ν T ^ ν ν = - 2 π k 2 Re [ S p ( T ^ ) ] ,
C e = - 1 k 2 n m τ τ ( a τ n m * a τ n m ) 1 2 n + 1 m 1 T ^ τ n m 1 , τ n m 1 .
m a τ n m * a τ n m = 2 π ( 2 n + 1 ) δ τ τ .
C s = 2 π k 2 ν ν τ τ T ^ τ ν , τ ν 2 .
C s = 1 k 2 n m τ τ a τ n m * a τ n m 1 2 n + 1 S p m 1 ( R ^ τ n m 1 , τ n m 1 ) ,
C s = 2 π k 2 S p ( R ^ τ ν , τ ν ) = Eq . ( 45 ) .
E α ( k ¯ s ) = exp ( i k r ) k r β S α β e 0 β ( k ¯ ) ,
e β = e ± 1 = ( e x ± i e y ) 1 2 .
e α = e ± 1 = ( e θ ± i e φ ) 1 2 .
S α β = k [ e α ( k ¯ s ) ] * F e β ( k ¯ ) .
A ν * ( k ¯ ) e β = - ( β i ) τ ( 2 n + 1 8 π ) 1 / 2 δ m β ,             β = ± 1 ,
A ν * ( k s ) e α = - ( α i ) τ ( 2 n + 1 8 π ) 1 / 2 d m α n ( θ ) ,             α = ± 1 ,
S α β = 1 2 i ν ν i n - n α τ β τ d m α n ( θ ) δ m β × [ ( 2 n + 1 ) ( 2 n + 1 ) ] 1 / 2 T ν ν ,
S α 1 β 1 S α 2 β 2 * = ν μ n 1 n 2 τ 1 τ 2 C d m 1 α 1 n 1 ( θ ) d m 2 α 2 n 2 ( θ ) T ν ν ¯ * T μ μ ¯ ,
C = 1 4 i n 1 - n 1 i n 2 - n 2 j = 1 2 α j τ j β j τ j [ ( 2 n j + 1 ) ( 2 n j + 1 ) ] 1 / 2 ,
M = m 1 + β 1 = m 2 + β 2 ,
C I = C n 1 m 1 , n 1 β 1 I ( m 1 + β 1 ) C n 2 m 2 , n 2 β 2 I ( m 1 + β 1 ) .
S α β = δ α β 2 i τ τ α τ + τ S p n m ( T ^ ) ,

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