Abstract

The backscattering reciprocity theorem is considered for large particles as compared with the incident wavelength particles of arbitrary shape. It is shown that, in the specific case of faceted particles, this theorem is provided by the appearance of pairs of conjugate backscattered beams. A parameter characterizing a deviation of any approximation from the reciprocity theorem is proposed, and it is used for estimation of reliability for the physical-optics approximation.

© 2013 Optical Society of America

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References

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  1. M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000).
  2. P. Yang and K. N. Liou, Light Scattering Reviews, A. A. Kokhanovsky, ed. Vol. 1 (Springer-Praxis, 2006), pp. 31–72.
  3. M. Hayman, S. Spuler, B. Morley, and J. VanAndel, Opt. Express 20, 29553 (2012).
    [CrossRef]
  4. K. Sassen, V. K. Kayetha, and J. Zhu, Geophys. Res. Lett. 39, L20805 (2012).
    [CrossRef]
  5. H. C. van de Hulst, Light Scattering by Small Particles(Wiley, 1957).
  6. A. G. Borovoi and I. A. Grishin, J. Opt. Soc. Am. A 20, 2071 (2003).
    [CrossRef]
  7. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).
  8. Y. Takano and K. Jayaweera, Appl. Opt. 24, 3254 (1985).
    [CrossRef]
  9. L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 163 (2011).
    [CrossRef]
  10. L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 1492 (2011).
    [CrossRef]
  11. M. I. Mishchenko, J. Opt. Soc. Am. A 9, 978 (1992).
    [CrossRef]

2012 (2)

K. Sassen, V. K. Kayetha, and J. Zhu, Geophys. Res. Lett. 39, L20805 (2012).
[CrossRef]

M. Hayman, S. Spuler, B. Morley, and J. VanAndel, Opt. Express 20, 29553 (2012).
[CrossRef]

2011 (2)

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 163 (2011).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 1492 (2011).
[CrossRef]

2003 (1)

1992 (1)

1985 (1)

Baum, B. A.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 163 (2011).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 1492 (2011).
[CrossRef]

Bi, L.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 1492 (2011).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 163 (2011).
[CrossRef]

Borovoi, A. G.

Grishin, I. A.

Hayman, M.

Hovenier, J. W.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000).

Hu, Y.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 163 (2011).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 1492 (2011).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

Jayaweera, K.

Kattawar, G. W.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 1492 (2011).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 163 (2011).
[CrossRef]

Kayetha, V. K.

K. Sassen, V. K. Kayetha, and J. Zhu, Geophys. Res. Lett. 39, L20805 (2012).
[CrossRef]

Liou, K. N.

P. Yang and K. N. Liou, Light Scattering Reviews, A. A. Kokhanovsky, ed. Vol. 1 (Springer-Praxis, 2006), pp. 31–72.

Mishchenko, M. I.

M. I. Mishchenko, J. Opt. Soc. Am. A 9, 978 (1992).
[CrossRef]

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000).

Morley, B.

Sassen, K.

K. Sassen, V. K. Kayetha, and J. Zhu, Geophys. Res. Lett. 39, L20805 (2012).
[CrossRef]

Spuler, S.

Takano, Y.

Travis, L. D.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000).

van de Hulst, H. C.

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

VanAndel, J.

Yang, P.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 163 (2011).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 1492 (2011).
[CrossRef]

P. Yang and K. N. Liou, Light Scattering Reviews, A. A. Kokhanovsky, ed. Vol. 1 (Springer-Praxis, 2006), pp. 31–72.

Zhu, J.

K. Sassen, V. K. Kayetha, and J. Zhu, Geophys. Res. Lett. 39, L20805 (2012).
[CrossRef]

Appl. Opt. (1)

Geophys. Res. Lett. (1)

K. Sassen, V. K. Kayetha, and J. Zhu, Geophys. Res. Lett. 39, L20805 (2012).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Quant. Spectrosc. Radiat. Transfer (2)

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 163 (2011).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 1492 (2011).
[CrossRef]

Opt. Express (1)

Other (4)

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

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

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000).

P. Yang and K. N. Liou, Light Scattering Reviews, A. A. Kokhanovsky, ed. Vol. 1 (Springer-Praxis, 2006), pp. 31–72.

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Figures (3)

Fig. 1.
Fig. 1.

Pair of the direct 4321 and conjugate 1234 plane-parallel beams. The left figures [(a), (b), and (d)] correspond to a back-reflecting crystal orientation (γ=0°) while the right figures [(c) and (e)] are depicted for a nearby-reflecting orientation (γ=20°) where γ is the rotation angle about the hexagon cylinder axis. Lower figures illustrate the phase differences [(b) and (c)] and shapes [(d) and (e)] of the beams for these two particle orientations.

Fig. 2.
Fig. 2.

Reciprocity error δ for the pair of beams of Fig. 1 (lower curves, right scale) and backscattering cross section M11 of the sum (upper curves, left scale) versus the rotation angle γ. Solid and dashed curves correspond to hexagon diameters 100 and 30 μm, respectively, at the incident wavelength of 0.532 μm, the refractive index of 1.31, and the crystal tilt of β=40°.

Fig. 3.
Fig. 3.

Same as in Fig. 2 after averaging over the rotation angle γ versus the crystal tilt β.

Equations (8)

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

J=(abbc).
Jj(nj,n0)=Ln+1FnLnL2F1L1.
JjPO(n,n0)=(i/λ)T(n,nj)Jj(nj,n0)×eiϕj+ik(n0rj0nrj)ηj(ρrj)eik(njn)ρdρ.
T(n,nj)=(Nj·(eθj×eφ)Nj·(eφj×eφ)Nj·(eθ×eθj)Nj·(eθ×eφj)),
Jj+(n0,n0)=L1F1L2LnFnLn+1=UJjTU,
Jj(n0,n0)=(abdc),Jj+(n0,n0)=(adbc).
M11M22+M33M44=|b+d|2.
δ=(M11M22+M33M44)/(4M11),

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