Abstract

The extinction efficiency factor associated with the scattering of a plane electromagnetic wave impinging on a basal face of a dielectric disk or a cylindrical particle is investigated by employing the physical- geometric optics hybrid (PGOH) method and the discrete-dipole approximation (DDA) method. It is found that the derived extinction efficiency factor from the PGOH is a function of the thickness of the disk, or the length of the cylinder, and the refractive index, but is independent of the diameter and shape of the cross section of the basal face of the particle. Furthermore, the oscillations of the extinction efficiency factor versus the thickness or length of the particle do not diminish if the particle is not absorptive. The values of the extinction efficiency factor simulated from the DDA method are quite different from those computed from the PGOH, although the size parameter of the particle is in the commonly recognized geometric optics regime. To explain the difference, the concept of the edge effect associated with the tunneling rays in the semiclassical scattering theory is generalized from the case of spherical particles to that of nonspherical particles based on the localization principle. Accordingly, the edge-effect contribution can be distinguished and removed from the extinction cross section calculation by the DDA method. The remaining part of the extinction cross section, associated with the interference between the transmitted rays and incident rays, agrees well with the results computed from the PGOH, and the agreement illustrates the presence of the edge effect in the case of nonspherical particles with surfaces that have no curvature along the incident direction. It is found that the asymptotic extinction efficiency factor may not necessarily converge to 2, but it depends on the specific physical processes of the interference between diffracted and transmitted light and of the edge effect.

© 2010 Optical Society of America

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References

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  1. P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
    [CrossRef]
  2. M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
    [CrossRef]
  3. A. Doicu, Y. Eremin, and T. Wriedt, Acoustic and Electromagnetic Scattering Analysis Using Discrete Sources (Academic, 2000).
  4. S. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
    [CrossRef]
  5. P. Yang and K. N. Liou, “Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space,” J. Opt. Soc. Am. A 13, 2072–2085(1996).
    [CrossRef]
  6. W. Sun, Q. Fu, and Z. Chen, “Finite-difference time-domain solution of light scattering by dielectric particles with perfectly matched layer absorbing boundary conditions,” Appl. Opt. 38, 3141–3151 (1999).
    [CrossRef]
  7. E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
    [CrossRef]
  8. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
    [CrossRef]
  9. G. H. Goedecke and S. G. O’Brien, “Scattering by irregular inhomogeneous particles via the digitized Green’s function algorithm,” Appl. Opt. 27, 2431–2438 (1988).
    [CrossRef] [PubMed]
  10. M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength,” J. Quant. Spectrosc. Radiat. Transfer 106, 546–557 (2007).
    [CrossRef]
  11. P. Yang and K. N. Liou, “Geometric-optics-integral-equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
    [CrossRef] [PubMed]
  12. P. Yang and K. N. Liou, “Light scattering by hexagonal ice crystals: Solution by ray-by-ray integration algorithm,” J. Opt. Soc. Am. A 14, 2278–2289 (1997).
    [CrossRef]
  13. L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Single-scattering properties of tri-axial ellipsoidal particles for a size parameter range from the Rayleigh to geometric-optics regimes,” Appl. Opt. 48, 114–126 (2009).
    [CrossRef]
  14. L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, “Simulation of the color ratio associated with the backscattering of radiation by ice particles at the wavelengths of 0.532 and 1.064μm,” J. Geophys. Res. 114, D00H08 (2009).
    [CrossRef]
  15. L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Modeling optical properties of mineral aerosol particles by using nonsymmetric hexahedra,” Appl. Opt. 49, 334–342 (2010).
    [CrossRef] [PubMed]
  16. H. C. van de Hulst, Light Scattering by Small Particles(Dover, 1981).
  17. H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge University, 1992).
    [CrossRef]
  18. D. S. Jones, “Approximate methods in high-frequency scattering,” Proc. R. Soc. A 239, 338–348 (1957).
    [CrossRef]
  19. D. S. Jones, “High-frequency scattering of electromagnetic waves,” Proc. R. Soc. Lond. A 240, 206–213 (1957).
    [CrossRef]
  20. G. R. Fournier and B. T. Evans, “Approximations to extinction efficiency for randomly oriented spheroids,” Appl. Opt. 30, 2042–2048 (1991).
    [CrossRef] [PubMed]
  21. G. R. Fournier and B. T. Evans, “Approximations to extinction from randomly oriented circular and elliptical cylinders,” Appl. Opt. 35, 4271–4282 (1996).
    [CrossRef] [PubMed]
  22. J. Q. Zhao and Y. Q. Hu, “Bridging technique for calculating the extinction efficiency of arbitrary shaped particles,” Appl. Opt. 42, 4937–4945 (2003).
    [CrossRef] [PubMed]
  23. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  24. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles(Cambridge University, 2002).
  25. R. E. Langer, “On the connection formulas and the solutions of the wave equation,” Phys. Rev. 51, 669–676 (1937).
    [CrossRef]

2010 (1)

2009 (2)

L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Single-scattering properties of tri-axial ellipsoidal particles for a size parameter range from the Rayleigh to geometric-optics regimes,” Appl. Opt. 48, 114–126 (2009).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, “Simulation of the color ratio associated with the backscattering of radiation by ice particles at the wavelengths of 0.532 and 1.064μm,” J. Geophys. Res. 114, D00H08 (2009).
[CrossRef]

2007 (1)

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength,” J. Quant. Spectrosc. Radiat. Transfer 106, 546–557 (2007).
[CrossRef]

2003 (1)

1999 (1)

1997 (1)

1996 (4)

1991 (1)

1988 (2)

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

G. H. Goedecke and S. G. O’Brien, “Scattering by irregular inhomogeneous particles via the digitized Green’s function algorithm,” Appl. Opt. 27, 2431–2438 (1988).
[CrossRef] [PubMed]

1973 (1)

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

1966 (1)

S. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

1965 (1)

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
[CrossRef]

1957 (2)

D. S. Jones, “Approximate methods in high-frequency scattering,” Proc. R. Soc. A 239, 338–348 (1957).
[CrossRef]

D. S. Jones, “High-frequency scattering of electromagnetic waves,” Proc. R. Soc. Lond. A 240, 206–213 (1957).
[CrossRef]

1937 (1)

R. E. Langer, “On the connection formulas and the solutions of the wave equation,” Phys. Rev. 51, 669–676 (1937).
[CrossRef]

Baum, B. A.

L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, “Simulation of the color ratio associated with the backscattering of radiation by ice particles at the wavelengths of 0.532 and 1.064μm,” J. Geophys. Res. 114, D00H08 (2009).
[CrossRef]

Bi, L.

Bohren, C. F.

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

Brock, R. S.

L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, “Simulation of the color ratio associated with the backscattering of radiation by ice particles at the wavelengths of 0.532 and 1.064μm,” J. Geophys. Res. 114, D00H08 (2009).
[CrossRef]

Chen, Z.

Doicu, A.

A. Doicu, Y. Eremin, and T. Wriedt, Acoustic and Electromagnetic Scattering Analysis Using Discrete Sources (Academic, 2000).

Draine, B. T.

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

Eremin, Y.

A. Doicu, Y. Eremin, and T. Wriedt, Acoustic and Electromagnetic Scattering Analysis Using Discrete Sources (Academic, 2000).

Evans, B. T.

Fournier, G. R.

Fu, Q.

Goedecke, G. H.

Hoekstra, A. G.

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength,” J. Quant. Spectrosc. Radiat. Transfer 106, 546–557 (2007).
[CrossRef]

Hu, Y. Q.

Hu, Y. X.

L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, “Simulation of the color ratio associated with the backscattering of radiation by ice particles at the wavelengths of 0.532 and 1.064μm,” J. Geophys. Res. 114, D00H08 (2009).
[CrossRef]

Huffman, D. R.

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

Jones, D. S.

D. S. Jones, “Approximate methods in high-frequency scattering,” Proc. R. Soc. A 239, 338–348 (1957).
[CrossRef]

D. S. Jones, “High-frequency scattering of electromagnetic waves,” Proc. R. Soc. Lond. A 240, 206–213 (1957).
[CrossRef]

Kahn, R.

Kattawar, G. W.

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles(Cambridge University, 2002).

Langer, R. E.

R. E. Langer, “On the connection formulas and the solutions of the wave equation,” Phys. Rev. 51, 669–676 (1937).
[CrossRef]

Liou, K. N.

Lu, J. Q.

L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, “Simulation of the color ratio associated with the backscattering of radiation by ice particles at the wavelengths of 0.532 and 1.064μm,” J. Geophys. Res. 114, D00H08 (2009).
[CrossRef]

Mackowski, D. W.

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

Maltsev, V. P.

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength,” J. Quant. Spectrosc. Radiat. Transfer 106, 546–557 (2007).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles(Cambridge University, 2002).

Nussenzveig, H. M.

H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge University, 1992).
[CrossRef]

O’Brien, S. G.

Pennypacker, C. R.

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

Purcell, E. M.

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

Sun, W.

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles(Cambridge University, 2002).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles(Dover, 1981).

Waterman, P. C.

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
[CrossRef]

Winker, D. M.

L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, “Simulation of the color ratio associated with the backscattering of radiation by ice particles at the wavelengths of 0.532 and 1.064μm,” J. Geophys. Res. 114, D00H08 (2009).
[CrossRef]

Yang, P.

Yee, S. K.

S. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

Yurkin, M. A.

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength,” J. Quant. Spectrosc. Radiat. Transfer 106, 546–557 (2007).
[CrossRef]

Zhao, J. Q.

Appl. Opt. (8)

W. Sun, Q. Fu, and Z. Chen, “Finite-difference time-domain solution of light scattering by dielectric particles with perfectly matched layer absorbing boundary conditions,” Appl. Opt. 38, 3141–3151 (1999).
[CrossRef]

G. H. Goedecke and S. G. O’Brien, “Scattering by irregular inhomogeneous particles via the digitized Green’s function algorithm,” Appl. Opt. 27, 2431–2438 (1988).
[CrossRef] [PubMed]

P. Yang and K. N. Liou, “Geometric-optics-integral-equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
[CrossRef] [PubMed]

L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Single-scattering properties of tri-axial ellipsoidal particles for a size parameter range from the Rayleigh to geometric-optics regimes,” Appl. Opt. 48, 114–126 (2009).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Modeling optical properties of mineral aerosol particles by using nonsymmetric hexahedra,” Appl. Opt. 49, 334–342 (2010).
[CrossRef] [PubMed]

G. R. Fournier and B. T. Evans, “Approximations to extinction efficiency for randomly oriented spheroids,” Appl. Opt. 30, 2042–2048 (1991).
[CrossRef] [PubMed]

G. R. Fournier and B. T. Evans, “Approximations to extinction from randomly oriented circular and elliptical cylinders,” Appl. Opt. 35, 4271–4282 (1996).
[CrossRef] [PubMed]

J. Q. Zhao and Y. Q. Hu, “Bridging technique for calculating the extinction efficiency of arbitrary shaped particles,” Appl. Opt. 42, 4937–4945 (2003).
[CrossRef] [PubMed]

Astrophys. J. (2)

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

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

S. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

J. Geophys. Res. (1)

L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, “Simulation of the color ratio associated with the backscattering of radiation by ice particles at the wavelengths of 0.532 and 1.064μm,” J. Geophys. Res. 114, D00H08 (2009).
[CrossRef]

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

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

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength,” J. Quant. Spectrosc. Radiat. Transfer 106, 546–557 (2007).
[CrossRef]

Phys. Rev. (1)

R. E. Langer, “On the connection formulas and the solutions of the wave equation,” Phys. Rev. 51, 669–676 (1937).
[CrossRef]

Proc. IEEE (1)

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
[CrossRef]

Proc. R. Soc. A (1)

D. S. Jones, “Approximate methods in high-frequency scattering,” Proc. R. Soc. A 239, 338–348 (1957).
[CrossRef]

Proc. R. Soc. Lond. A (1)

D. S. Jones, “High-frequency scattering of electromagnetic waves,” Proc. R. Soc. Lond. A 240, 206–213 (1957).
[CrossRef]

Other (5)

H. C. van de Hulst, Light Scattering by Small Particles(Dover, 1981).

H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge University, 1992).
[CrossRef]

A. Doicu, Y. Eremin, and T. Wriedt, Acoustic and Electromagnetic Scattering Analysis Using Discrete Sources (Academic, 2000).

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

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles(Cambridge University, 2002).

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Figures (5)

Fig. 1
Fig. 1

Plane wave impinging on the basal face of a cylinder. λ is the wavelength.

Fig. 2
Fig. 2

Extinction efficiency factor of cylinders simulated from the ADDA with the edge effect, the ADDA without the edge effect, and the PGOH. The size parameter defined in terms of the diameter is 50.

Fig. 3
Fig. 3

Extinction efficiency factor of disks simulated with the ADDA with the edge effect, the ADDA without the edge effect, and the PGOH. The size parameter defined in terms of the length is 10.

Fig. 4
Fig. 4

Scattering coefficients a n for a sphere (a) and a cylinder (b) in the complex plane. The size parameter in terms of the radius of both the sphere and the cylinder is 25. The aspect ratio of the cylinder is 1.

Fig. 5
Fig. 5

Difference between the real part of x component of a plane wave and the summation of the multipole fields truncated at n = 24 .

Equations (17)

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Q ext = Im [ k | E inc | 2 G ( m 2 1 ) v E ( r ) · E inc * ( r ) d 3 r ] ,
Q ext = 2 Re { 1 4 m exp { i ( m 1 ) k L } ( m + 1 ) 2 ( m 1 ) 2 exp ( i 2 m k L ) } ,
Q edge = c S p R 1 / 3 d s ,
Q edge = c ( k x sin ϑ ) 2 / 3 ,
S 2 = n = 1 2 n + 1 n ( n + 1 ) [ a n τ n ( cos θ ) + b n π n ( cos θ ) ] ,
S 1 = n = 1 2 n + 1 n ( n + 1 ) [ a n π n ( cos θ ) + b n τ n ( cos θ ) ] ,
a n = n ' = 1 2 n + 1 2 n + 1 i n n [ T 1 n 1 n 21 + T 1 n 1 n 22 ] ,
b n = n ' = 1 2 n + 1 2 n + 1 i n n [ T 1 n 1 n 11 + T 1 n 1 n 12 ] .
a n = T 1 n 1 n 22 ,
b n = T 1 n 1 n 11 .
E i inc = α i 1 P i j i G i j P j ,
E inc = e x exp ( i k z ) ,
E r inc = 1 k 2 r 2 cos φ n = 1 ( 2 n + 1 ) i n i sin θ π n ( cos θ ) ψ n ( k r ) ,
E θ inc = 1 k r cos φ n = 1 2 n + 1 n ( n + 1 ) i n [ i τ n ( cos θ ) ψ n ( k r ) + π n ( cos θ ) ψ n ( k r ) ] ,
E φ inc = 1 k r sin φ n = 1 2 n + 1 n ( n + 1 ) i n [ i π n ( cos θ ) ψ n ' ( k r ) + τ n ( cos θ ) ψ n ( k r ) ] ,
E i , n < [ k a 1 / 2 ] inc = α i 1 P i j i G i j P j ,
E i inc E i , n < [ k a 1 / 2 ] inc = α i 1 P i j i G i j P j .

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