Abstract

The Rayleigh approximation is known to be designed only for small ellipsoidal scatterers. We suggest an approach that allows one to find a simple, often analytical, long-wavelength approximation for nonellipsoidal particles. We apply the approach to axisymmetric scatterers and utilize Chebyshev particles to study the main properties of the obtained approximation. To a certain degree, it can be considered as an extension of the Rayleigh approximation to nonspheroidal scatterers.

© 2011 Optical Society of America

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References

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  1. Lord Rayleigh, Philos. Mag. 44, 28 (1897).
  2. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  3. R. E. Kleinman and T. B. A. Senior, in Low and High Frequency Asymptotics, V.K.Varadan and V.V.Varadan, eds. (Elsevier, 1986), pp. 1–70.
  4. B. Posselt, V. G. Farafonov, V. B. Il’in, and M. S. Prokopjeva, Meas. Sci. Technol. 13, 256 (2002).
    [CrossRef]
  5. A. R. Jones, Proc. Royal. Soc. London A 366, 111 (1979).
    [CrossRef]
  6. D. W. Mackowski, Appl. Opt. 34, 3535 (1995).
    [CrossRef] [PubMed]
  7. A. Moroz, J. Opt. Soc. Am. B 26, 517 (2009).
    [CrossRef]
  8. A. Sihvola, J. Venermo, and P. Ylä-Oijala, Microw. Opt. Technol. Lett. 41, 245 (2004).
    [CrossRef]
  9. A. G. Ramm, Wave Scattering by Small Bodies of Arbitrary Shapes (World Scientific, 2005).
    [CrossRef]
  10. V. G. Farafonov, V. B. Il’in, and M. S. Prokopjeva, J. Quant. Spectrosc. Radiat. Transf. 79–80, 599 (2003).
    [CrossRef]
  11. H. Kang and G. W. Milton, Arch. Ration. Mech. Anal. 188, 93 (2008).
    [CrossRef]
  12. W. J. Wiscombe and A. Mugnai, in Light Scattering by Irregularly Shaped Particles, D.W.Schuerman, ed. (Plenum, 1980), pp. 141–152.
  13. W. J. Wiscombe and A. Mugnai, NASA Ref. Publ. 1157, Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1986.
  14. M. I. Mishchenko and L. D. Travis, J. Quant. Spectrosc. Radiat. Transf. 51, 759 (1994).
    [CrossRef]
  15. T. Rother, K. Schmidt, J. Wauer, V. Shcherbakov, and J.-F. Gayet, Appl. Opt. 45, 6030 (2006).
    [CrossRef] [PubMed]
  16. D. Petrov, Y. Shkuratov, and G. Videen, J. Opt. Soc. Am. A 24, 1103 (2007).
    [CrossRef]
  17. A. A. Vinokurov, V. B. Il’in, and V. G. Farafonov, J. Quant. Spectrosc. Radiat. Transf. 112, 1733 (2011).
    [CrossRef]
  18. A. Moroz, Appl. Opt. 44, 3604 (2005).
    [CrossRef] [PubMed]
  19. M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, J. Quant. Spectrosc. Radiat. Transf. 106, 546 (2007).
    [CrossRef]

2011 (1)

A. A. Vinokurov, V. B. Il’in, and V. G. Farafonov, J. Quant. Spectrosc. Radiat. Transf. 112, 1733 (2011).
[CrossRef]

2009 (1)

2008 (1)

H. Kang and G. W. Milton, Arch. Ration. Mech. Anal. 188, 93 (2008).
[CrossRef]

2007 (2)

D. Petrov, Y. Shkuratov, and G. Videen, J. Opt. Soc. Am. A 24, 1103 (2007).
[CrossRef]

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, J. Quant. Spectrosc. Radiat. Transf. 106, 546 (2007).
[CrossRef]

2006 (1)

2005 (1)

2004 (1)

A. Sihvola, J. Venermo, and P. Ylä-Oijala, Microw. Opt. Technol. Lett. 41, 245 (2004).
[CrossRef]

2003 (1)

V. G. Farafonov, V. B. Il’in, and M. S. Prokopjeva, J. Quant. Spectrosc. Radiat. Transf. 79–80, 599 (2003).
[CrossRef]

2002 (1)

B. Posselt, V. G. Farafonov, V. B. Il’in, and M. S. Prokopjeva, Meas. Sci. Technol. 13, 256 (2002).
[CrossRef]

1995 (1)

1994 (1)

M. I. Mishchenko and L. D. Travis, J. Quant. Spectrosc. Radiat. Transf. 51, 759 (1994).
[CrossRef]

1979 (1)

A. R. Jones, Proc. Royal. Soc. London A 366, 111 (1979).
[CrossRef]

1897 (1)

Lord Rayleigh, Philos. Mag. 44, 28 (1897).

Bohren, C. F.

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

Farafonov, V. G.

A. A. Vinokurov, V. B. Il’in, and V. G. Farafonov, J. Quant. Spectrosc. Radiat. Transf. 112, 1733 (2011).
[CrossRef]

V. G. Farafonov, V. B. Il’in, and M. S. Prokopjeva, J. Quant. Spectrosc. Radiat. Transf. 79–80, 599 (2003).
[CrossRef]

B. Posselt, V. G. Farafonov, V. B. Il’in, and M. S. Prokopjeva, Meas. Sci. Technol. 13, 256 (2002).
[CrossRef]

Gayet, J.-F.

Hoekstra, A. G.

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, J. Quant. Spectrosc. Radiat. Transf. 106, 546 (2007).
[CrossRef]

Huffman, D. R.

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

Il’in, V. B.

A. A. Vinokurov, V. B. Il’in, and V. G. Farafonov, J. Quant. Spectrosc. Radiat. Transf. 112, 1733 (2011).
[CrossRef]

V. G. Farafonov, V. B. Il’in, and M. S. Prokopjeva, J. Quant. Spectrosc. Radiat. Transf. 79–80, 599 (2003).
[CrossRef]

B. Posselt, V. G. Farafonov, V. B. Il’in, and M. S. Prokopjeva, Meas. Sci. Technol. 13, 256 (2002).
[CrossRef]

Jones, A. R.

A. R. Jones, Proc. Royal. Soc. London A 366, 111 (1979).
[CrossRef]

Kang, H.

H. Kang and G. W. Milton, Arch. Ration. Mech. Anal. 188, 93 (2008).
[CrossRef]

Kleinman, R. E.

R. E. Kleinman and T. B. A. Senior, in Low and High Frequency Asymptotics, V.K.Varadan and V.V.Varadan, eds. (Elsevier, 1986), pp. 1–70.

Mackowski, D. W.

Maltsev, V. P.

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, J. Quant. Spectrosc. Radiat. Transf. 106, 546 (2007).
[CrossRef]

Milton, G. W.

H. Kang and G. W. Milton, Arch. Ration. Mech. Anal. 188, 93 (2008).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko and L. D. Travis, J. Quant. Spectrosc. Radiat. Transf. 51, 759 (1994).
[CrossRef]

Moroz, A.

Mugnai, A.

W. J. Wiscombe and A. Mugnai, NASA Ref. Publ. 1157, Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1986.

W. J. Wiscombe and A. Mugnai, in Light Scattering by Irregularly Shaped Particles, D.W.Schuerman, ed. (Plenum, 1980), pp. 141–152.

Petrov, D.

Posselt, B.

B. Posselt, V. G. Farafonov, V. B. Il’in, and M. S. Prokopjeva, Meas. Sci. Technol. 13, 256 (2002).
[CrossRef]

Prokopjeva, M. S.

V. G. Farafonov, V. B. Il’in, and M. S. Prokopjeva, J. Quant. Spectrosc. Radiat. Transf. 79–80, 599 (2003).
[CrossRef]

B. Posselt, V. G. Farafonov, V. B. Il’in, and M. S. Prokopjeva, Meas. Sci. Technol. 13, 256 (2002).
[CrossRef]

Ramm, A. G.

A. G. Ramm, Wave Scattering by Small Bodies of Arbitrary Shapes (World Scientific, 2005).
[CrossRef]

Rayleigh, Lord

Lord Rayleigh, Philos. Mag. 44, 28 (1897).

Rother, T.

Schmidt, K.

Senior, T. B. A.

R. E. Kleinman and T. B. A. Senior, in Low and High Frequency Asymptotics, V.K.Varadan and V.V.Varadan, eds. (Elsevier, 1986), pp. 1–70.

Shcherbakov, V.

Shkuratov, Y.

Sihvola, A.

A. Sihvola, J. Venermo, and P. Ylä-Oijala, Microw. Opt. Technol. Lett. 41, 245 (2004).
[CrossRef]

Travis, L. D.

M. I. Mishchenko and L. D. Travis, J. Quant. Spectrosc. Radiat. Transf. 51, 759 (1994).
[CrossRef]

Venermo, J.

A. Sihvola, J. Venermo, and P. Ylä-Oijala, Microw. Opt. Technol. Lett. 41, 245 (2004).
[CrossRef]

Videen, G.

Vinokurov, A. A.

A. A. Vinokurov, V. B. Il’in, and V. G. Farafonov, J. Quant. Spectrosc. Radiat. Transf. 112, 1733 (2011).
[CrossRef]

Wauer, J.

Wiscombe, W. J.

W. J. Wiscombe and A. Mugnai, NASA Ref. Publ. 1157, Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1986.

W. J. Wiscombe and A. Mugnai, in Light Scattering by Irregularly Shaped Particles, D.W.Schuerman, ed. (Plenum, 1980), pp. 141–152.

Ylä-Oijala, P.

A. Sihvola, J. Venermo, and P. Ylä-Oijala, Microw. Opt. Technol. Lett. 41, 245 (2004).
[CrossRef]

Yurkin, M. A.

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, J. Quant. Spectrosc. Radiat. Transf. 106, 546 (2007).
[CrossRef]

Appl. Opt. (3)

Arch. Ration. Mech. Anal. (1)

H. Kang and G. W. Milton, Arch. Ration. Mech. Anal. 188, 93 (2008).
[CrossRef]

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

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

J. Quant. Spectrosc. Radiat. Transf. (4)

A. A. Vinokurov, V. B. Il’in, and V. G. Farafonov, J. Quant. Spectrosc. Radiat. Transf. 112, 1733 (2011).
[CrossRef]

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, J. Quant. Spectrosc. Radiat. Transf. 106, 546 (2007).
[CrossRef]

V. G. Farafonov, V. B. Il’in, and M. S. Prokopjeva, J. Quant. Spectrosc. Radiat. Transf. 79–80, 599 (2003).
[CrossRef]

M. I. Mishchenko and L. D. Travis, J. Quant. Spectrosc. Radiat. Transf. 51, 759 (1994).
[CrossRef]

Meas. Sci. Technol. (1)

B. Posselt, V. G. Farafonov, V. B. Il’in, and M. S. Prokopjeva, Meas. Sci. Technol. 13, 256 (2002).
[CrossRef]

Microw. Opt. Technol. Lett. (1)

A. Sihvola, J. Venermo, and P. Ylä-Oijala, Microw. Opt. Technol. Lett. 41, 245 (2004).
[CrossRef]

Philos. Mag. (1)

Lord Rayleigh, Philos. Mag. 44, 28 (1897).

Proc. Royal. Soc. London A (1)

A. R. Jones, Proc. Royal. Soc. London A 366, 111 (1979).
[CrossRef]

Other (5)

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

R. E. Kleinman and T. B. A. Senior, in Low and High Frequency Asymptotics, V.K.Varadan and V.V.Varadan, eds. (Elsevier, 1986), pp. 1–70.

A. G. Ramm, Wave Scattering by Small Bodies of Arbitrary Shapes (World Scientific, 2005).
[CrossRef]

W. J. Wiscombe and A. Mugnai, in Light Scattering by Irregularly Shaped Particles, D.W.Schuerman, ed. (Plenum, 1980), pp. 141–152.

W. J. Wiscombe and A. Mugnai, NASA Ref. Publ. 1157, Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1986.

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Figures (3)

Fig. 1
Fig. 1

Geometrical cross sections of the Chebyshev particles with (a)  n = 2 , e = 0.1 and (b)  n = 4 , e = 0.1 . The symmetry axes given by the dashed lines are parallel to the z axis. The shading intensity indicates the strength of the z component of the internal field caused by the applied field E in i z (TM mode).

Fig. 2
Fig. 2

The accuracy of polarizability approximation for the Chebyshev particles shown in Fig. 1 as a function of the permittivity ratio ε / ε 0 . The crosses correspond to the approximation based on Eq. (6), and the pluses correspond to the analytical approximation using Eq. (10).

Fig. 3
Fig. 3

The accuracy of polarizability approximation for Chebyshev particles with the parameters n = 1 16 and e = 0.9 ÷ 0.07 . The refractive index is m = 1.3 + 0.01 i .

Equations (12)

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

d λ and | m | d λ ,
α x = V ε ε 0 ε 0 + ( ε ε 0 ) L x ,
L x = a b c 2 0 d t ( t + a 2 ) ( t + a 2 ) ( t + b 2 ) ( t + c 2 ) ,
α ˜ x = α ˜ y = V ε ε 0 ε 0 + ( ε ε 0 ) ( 1 3 I ) ,
α ˜ z = V ε ε 0 ε 0 + ( ε ε 0 ) ( 1 3 + 2 I ) .
I = 1 4 0 π r ( θ ) r ( θ ) cos θ sin 2 θ d θ ,
r ( θ ) = r 0 ( 1 + e cos n θ ) ,
I ( 1 , e ) = 1 6 + 1 e 2 2 e 2 ( 1 1 2 e ln 1 + e 1 e ) ,
I ( 2 , e ) = 1 3 e + 1 2 e ( 1 1 e 2 e arctan 2 e 1 e ) .
I ( n , e ) I 1 ( n , e ) = { e F ( n ) , n   is even , e 2 F ( 2 n ) / 4 , n   is odd ,
F ( n ) = n 2 ( n 2 1 ) ( n 2 9 ) .
C abs = k Im α ˜ , C sca = k 4 6 π | α ˜ | 2 ,

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