Abstract

The finite-difference time-domain (FDTD) technique is examined for its suitability for studying light scattering by highly refractive dielectric particles. It is found that, for particles with large complex refractive indices, the FDTD solution of light scattering is sensitive to the numerical treatments associated with the particle boundaries. Herein, appropriate treatments of the particle boundaries and related electric fields in the frequency domain are introduced and examined to improve the accuracy of the FDTD solutions. As a result, it is shown that, for a large complex refractive index of 7.1499 + 2.914i for particles with size parameters smaller than 6, the errors in extinction and absorption efficiencies from the FDTD method are generally less than ∼4%. The errors in the scattering phase function are less than ∼5%. We conclude that the present FDTD scheme with appropriate boundary treatments can provide a reliable solution for light scattering by nonspherical particles with large complex refractive indices.

© 2000 Optical Society of America

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References

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  1. L. J. Battan, Radar Observation of the Atmosphere (University of Chicago, Chicago, Ill., 1973).
  2. J. Nadobny, D. Sullivan, P. Wust, M. Seebass, P. Deuflhard, R. Felix, “A high-resolution interpolation at arbitrary interfaces for the fdtd method,” IEEE Trans. Microwave Theory Tech. 46, 1759–1766 (1998).
    [CrossRef]
  3. G. Mie, “Beigrade zur optik truber medien, speziell kolloidaler metallosungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
    [CrossRef]
  4. S. Asano, G. Yamamoto, “Light scattering by a spheroidal particle,” Appl. Opt. 14, 29–49 (1975).
    [CrossRef] [PubMed]
  5. J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
    [CrossRef]
  6. Lord Rayleigh, “The dispersal of light by a dielectric cylinder,” Philos. Mag. 36, 365–376 (1918).
    [CrossRef]
  7. K. A. Fuller, “Scattering and absorption cross sections of compounded spheres. I. Theory for external aggregation,” J. Opt. Soc. Am. A 11, 3251–3260 (1994).
    [CrossRef]
  8. M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer. 55, 535–575 (1996).
    [CrossRef]
  9. E. M. Purcell, C. P. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 196, 705–714 (1973).
    [CrossRef]
  10. S. B. Singham, C. F. Bohren, “Light scattering by an arbitrary particle: a physical reformation of the coupled dipole method,” Opt. Lett. 12, 10–12 (1987).
    [CrossRef] [PubMed]
  11. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
    [CrossRef]
  12. P. J. Flatau, G. L. Stephens, B. T. Draine, “Light scattering by rectangular solids in the discrete-dipole approximation: a new algorithm exploiting the block-toeplitz structure,” J. Opt. Soc. Am. A 7, 593–600 (1990).
    [CrossRef]
  13. B. T. Draine, “The discrete dipole approximation for studying light scattering by irregular targets,” in Proceedings of the Conference on Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (American Meteorological Society, Boston, Mass., 1998).
  14. B. T. Draine, J. Goodman, “Beyond Clausius–Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685–697 (1993).
    [CrossRef]
  15. B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
    [CrossRef]
  16. A. Hoekstra, J. Rahola, P. Sloot, “Accuracy of internal fields in volume integral equation simulations of light scattering,” Appl. Opt. 37, 8482–8497 (1998).
    [CrossRef]
  17. N. B. Piller, “Coupled-dipole approximation for high permittivity materials,” Opt. Commun. 160, 10–14 (1999).
    [CrossRef]
  18. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equation in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).
  19. P. Yang, 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]
  20. W. B. Sun, Q. Fu, Z. Z. Chen, “Finite-difference time-domain solution of light scattering by dielectric particles with a perfectly matched layer absorbing boundary condition,” Appl. Opt. 38, 3141–3151 (1999).
    [CrossRef]
  21. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
    [CrossRef]
  22. J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363–379 (1996).
    [CrossRef]
  23. D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microwave Guided Wave Lett. 4, 268–270 (1994).
    [CrossRef]
  24. Q. Fu, P. Yang, W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Climate 11, 2223–2237 (1998).
    [CrossRef]
  25. Q. Fu, W. B. Sun, P. Yang, “Modeling of scattering and absorption by nonspherical cirrus ice particles at thermal infrared wavelengths,” J. Atmos. Sci. 56, 2937–2947 (1999).
    [CrossRef]
  26. G. Videen, W. B. Sun, Q. Fu, “Light scattering from irregular tetrahedral aggregates,” Opt. Commun. 156, 5–9 (1998).
    [CrossRef]
  27. P. Yang, K. N. Liou, “Application of finite-difference time domain technique to light scattering by irregular and inhomogeneous particles,” in Proceedings of the Conference on Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (American Meteorological Society, Boston, Mass., 1998).
  28. P. Chýlek, V. Srivastava, “Dielectric constant of a composite inhomogeneous medium,” Phys. Rev. B 27, 5098–5106 (1983).
    [CrossRef]
  29. J. S. Dobbie, P. Chýlek, “Evaluation of effective medium theory for large inclusions using DDA,” in Proceedings of the Conference on Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (American Meteorological Society, Boston, Mass., 1998).
  30. G. H. Goedecke, S. G. O’Brien, “Scattering by irregular inhomogeneous particles via the digitized Green’s function algorithm,” Appl. Opt. 15, 2431–2437 (1988).
    [CrossRef]
  31. P. J. Flatau, G. L. Stephens, B. T. Draine, “Light scattering by rectangular solids in the discrete-dipole approximation: a new algorithm exploiting the block-toeplitz structure,” J. Opt. Soc. Am. A 7, 593–600 (1990).
    [CrossRef]
  32. M. I. Mishchenko, S. W. Hovenier, L. D. Travis, eds., Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, San Diego, Calif., 1999).

1999 (3)

Q. Fu, W. B. Sun, P. Yang, “Modeling of scattering and absorption by nonspherical cirrus ice particles at thermal infrared wavelengths,” J. Atmos. Sci. 56, 2937–2947 (1999).
[CrossRef]

N. B. Piller, “Coupled-dipole approximation for high permittivity materials,” Opt. Commun. 160, 10–14 (1999).
[CrossRef]

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

1998 (4)

A. Hoekstra, J. Rahola, P. Sloot, “Accuracy of internal fields in volume integral equation simulations of light scattering,” Appl. Opt. 37, 8482–8497 (1998).
[CrossRef]

Q. Fu, P. Yang, W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Climate 11, 2223–2237 (1998).
[CrossRef]

G. Videen, W. B. Sun, Q. Fu, “Light scattering from irregular tetrahedral aggregates,” Opt. Commun. 156, 5–9 (1998).
[CrossRef]

J. Nadobny, D. Sullivan, P. Wust, M. Seebass, P. Deuflhard, R. Felix, “A high-resolution interpolation at arbitrary interfaces for the fdtd method,” IEEE Trans. Microwave Theory Tech. 46, 1759–1766 (1998).
[CrossRef]

1996 (3)

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

J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363–379 (1996).
[CrossRef]

P. Yang, 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]

1994 (4)

B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
[CrossRef]

K. A. Fuller, “Scattering and absorption cross sections of compounded spheres. I. Theory for external aggregation,” J. Opt. Soc. Am. A 11, 3251–3260 (1994).
[CrossRef]

D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microwave Guided Wave Lett. 4, 268–270 (1994).
[CrossRef]

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

1993 (1)

B. T. Draine, J. Goodman, “Beyond Clausius–Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685–697 (1993).
[CrossRef]

1990 (2)

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, S. G. O’Brien, “Scattering by irregular inhomogeneous particles via the digitized Green’s function algorithm,” Appl. Opt. 15, 2431–2437 (1988).
[CrossRef]

1987 (1)

1983 (1)

P. Chýlek, V. Srivastava, “Dielectric constant of a composite inhomogeneous medium,” Phys. Rev. B 27, 5098–5106 (1983).
[CrossRef]

1975 (1)

1973 (1)

E. M. Purcell, C. P. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 196, 705–714 (1973).
[CrossRef]

1966 (1)

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

1955 (1)

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
[CrossRef]

1918 (1)

Lord Rayleigh, “The dispersal of light by a dielectric cylinder,” Philos. Mag. 36, 365–376 (1918).
[CrossRef]

1908 (1)

G. Mie, “Beigrade zur optik truber medien, speziell kolloidaler metallosungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
[CrossRef]

Asano, S.

Battan, L. J.

L. J. Battan, Radar Observation of the Atmosphere (University of Chicago, Chicago, Ill., 1973).

Berenger, J. P.

J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363–379 (1996).
[CrossRef]

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

Bohren, C. F.

Chen, Z. Z.

Chýlek, P.

P. Chýlek, V. Srivastava, “Dielectric constant of a composite inhomogeneous medium,” Phys. Rev. B 27, 5098–5106 (1983).
[CrossRef]

J. S. Dobbie, P. Chýlek, “Evaluation of effective medium theory for large inclusions using DDA,” in Proceedings of the Conference on Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (American Meteorological Society, Boston, Mass., 1998).

Deuflhard, P.

J. Nadobny, D. Sullivan, P. Wust, M. Seebass, P. Deuflhard, R. Felix, “A high-resolution interpolation at arbitrary interfaces for the fdtd method,” IEEE Trans. Microwave Theory Tech. 46, 1759–1766 (1998).
[CrossRef]

Dobbie, J. S.

J. S. Dobbie, P. Chýlek, “Evaluation of effective medium theory for large inclusions using DDA,” in Proceedings of the Conference on Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (American Meteorological Society, Boston, Mass., 1998).

Draine, B. T.

B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
[CrossRef]

B. T. Draine, J. Goodman, “Beyond Clausius–Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685–697 (1993).
[CrossRef]

P. J. Flatau, G. L. Stephens, B. T. Draine, “Light scattering by rectangular solids in the discrete-dipole approximation: a new algorithm exploiting the block-toeplitz structure,” J. Opt. Soc. Am. A 7, 593–600 (1990).
[CrossRef]

P. J. Flatau, G. L. Stephens, B. T. Draine, “Light scattering by rectangular solids in the discrete-dipole approximation: a new algorithm exploiting the block-toeplitz structure,” J. Opt. Soc. Am. A 7, 593–600 (1990).
[CrossRef]

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

B. T. Draine, “The discrete dipole approximation for studying light scattering by irregular targets,” in Proceedings of the Conference on Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (American Meteorological Society, Boston, Mass., 1998).

Felix, R.

J. Nadobny, D. Sullivan, P. Wust, M. Seebass, P. Deuflhard, R. Felix, “A high-resolution interpolation at arbitrary interfaces for the fdtd method,” IEEE Trans. Microwave Theory Tech. 46, 1759–1766 (1998).
[CrossRef]

Flatau, P. J.

Fu, Q.

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

Q. Fu, W. B. Sun, P. Yang, “Modeling of scattering and absorption by nonspherical cirrus ice particles at thermal infrared wavelengths,” J. Atmos. Sci. 56, 2937–2947 (1999).
[CrossRef]

Q. Fu, P. Yang, W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Climate 11, 2223–2237 (1998).
[CrossRef]

G. Videen, W. B. Sun, Q. Fu, “Light scattering from irregular tetrahedral aggregates,” Opt. Commun. 156, 5–9 (1998).
[CrossRef]

Fuller, K. A.

Goedecke, G. H.

G. H. Goedecke, S. G. O’Brien, “Scattering by irregular inhomogeneous particles via the digitized Green’s function algorithm,” Appl. Opt. 15, 2431–2437 (1988).
[CrossRef]

Goodman, J.

B. T. Draine, J. Goodman, “Beyond Clausius–Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685–697 (1993).
[CrossRef]

Hoekstra, A.

Katz, D. S.

D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microwave Guided Wave Lett. 4, 268–270 (1994).
[CrossRef]

Liou, K. N.

P. Yang, 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]

P. Yang, K. N. Liou, “Application of finite-difference time domain technique to light scattering by irregular and inhomogeneous particles,” in Proceedings of the Conference on Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (American Meteorological Society, Boston, Mass., 1998).

Mackowski, D. W.

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

Mie, G.

G. Mie, “Beigrade zur optik truber medien, speziell kolloidaler metallosungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
[CrossRef]

Mishchenko, M. I.

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

Nadobny, J.

J. Nadobny, D. Sullivan, P. Wust, M. Seebass, P. Deuflhard, R. Felix, “A high-resolution interpolation at arbitrary interfaces for the fdtd method,” IEEE Trans. Microwave Theory Tech. 46, 1759–1766 (1998).
[CrossRef]

O’Brien, S. G.

G. H. Goedecke, S. G. O’Brien, “Scattering by irregular inhomogeneous particles via the digitized Green’s function algorithm,” Appl. Opt. 15, 2431–2437 (1988).
[CrossRef]

Pennypacker, C. P.

E. M. Purcell, C. P. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 196, 705–714 (1973).
[CrossRef]

Piller, N. B.

N. B. Piller, “Coupled-dipole approximation for high permittivity materials,” Opt. Commun. 160, 10–14 (1999).
[CrossRef]

Purcell, E. M.

E. M. Purcell, C. P. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 196, 705–714 (1973).
[CrossRef]

Rahola, J.

Rayleigh, Lord

Lord Rayleigh, “The dispersal of light by a dielectric cylinder,” Philos. Mag. 36, 365–376 (1918).
[CrossRef]

Seebass, M.

J. Nadobny, D. Sullivan, P. Wust, M. Seebass, P. Deuflhard, R. Felix, “A high-resolution interpolation at arbitrary interfaces for the fdtd method,” IEEE Trans. Microwave Theory Tech. 46, 1759–1766 (1998).
[CrossRef]

Singham, S. B.

Sloot, P.

Srivastava, V.

P. Chýlek, V. Srivastava, “Dielectric constant of a composite inhomogeneous medium,” Phys. Rev. B 27, 5098–5106 (1983).
[CrossRef]

Stephens, G. L.

Sullivan, D.

J. Nadobny, D. Sullivan, P. Wust, M. Seebass, P. Deuflhard, R. Felix, “A high-resolution interpolation at arbitrary interfaces for the fdtd method,” IEEE Trans. Microwave Theory Tech. 46, 1759–1766 (1998).
[CrossRef]

Sun, W. B.

Q. Fu, W. B. Sun, P. Yang, “Modeling of scattering and absorption by nonspherical cirrus ice particles at thermal infrared wavelengths,” J. Atmos. Sci. 56, 2937–2947 (1999).
[CrossRef]

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

G. Videen, W. B. Sun, Q. Fu, “Light scattering from irregular tetrahedral aggregates,” Opt. Commun. 156, 5–9 (1998).
[CrossRef]

Q. Fu, P. Yang, W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Climate 11, 2223–2237 (1998).
[CrossRef]

Taflove, A.

D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microwave Guided Wave Lett. 4, 268–270 (1994).
[CrossRef]

Thiele, E. T.

D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microwave Guided Wave Lett. 4, 268–270 (1994).
[CrossRef]

Travis, L. D.

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

Videen, G.

G. Videen, W. B. Sun, Q. Fu, “Light scattering from irregular tetrahedral aggregates,” Opt. Commun. 156, 5–9 (1998).
[CrossRef]

Wait, J. R.

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
[CrossRef]

Wust, P.

J. Nadobny, D. Sullivan, P. Wust, M. Seebass, P. Deuflhard, R. Felix, “A high-resolution interpolation at arbitrary interfaces for the fdtd method,” IEEE Trans. Microwave Theory Tech. 46, 1759–1766 (1998).
[CrossRef]

Yamamoto, G.

Yang, P.

Q. Fu, W. B. Sun, P. Yang, “Modeling of scattering and absorption by nonspherical cirrus ice particles at thermal infrared wavelengths,” J. Atmos. Sci. 56, 2937–2947 (1999).
[CrossRef]

Q. Fu, P. Yang, W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Climate 11, 2223–2237 (1998).
[CrossRef]

P. Yang, 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]

P. Yang, K. N. Liou, “Application of finite-difference time domain technique to light scattering by irregular and inhomogeneous particles,” in Proceedings of the Conference on Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (American Meteorological Society, Boston, Mass., 1998).

Yee, K. S.

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

Ann. Phys. (Leipzig) (1)

G. Mie, “Beigrade zur optik truber medien, speziell kolloidaler metallosungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
[CrossRef]

Appl. Opt. (4)

Astrophys. J. (3)

E. M. Purcell, C. P. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 196, 705–714 (1973).
[CrossRef]

B. T. Draine, J. Goodman, “Beyond Clausius–Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685–697 (1993).
[CrossRef]

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

Can. J. Phys. (1)

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
[CrossRef]

IEEE Microwave Guided Wave Lett. (1)

D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microwave Guided Wave Lett. 4, 268–270 (1994).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

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

IEEE Trans. Microwave Theory Tech. (1)

J. Nadobny, D. Sullivan, P. Wust, M. Seebass, P. Deuflhard, R. Felix, “A high-resolution interpolation at arbitrary interfaces for the fdtd method,” IEEE Trans. Microwave Theory Tech. 46, 1759–1766 (1998).
[CrossRef]

J. Atmos. Sci. (1)

Q. Fu, W. B. Sun, P. Yang, “Modeling of scattering and absorption by nonspherical cirrus ice particles at thermal infrared wavelengths,” J. Atmos. Sci. 56, 2937–2947 (1999).
[CrossRef]

J. Climate (1)

Q. Fu, P. Yang, W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Climate 11, 2223–2237 (1998).
[CrossRef]

J. Comput. Phys. (2)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363–379 (1996).
[CrossRef]

J. Opt. Soc. Am. A (5)

J. Quant. Spectrosc. Radiat. Transfer. (1)

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

Opt. Commun. (2)

G. Videen, W. B. Sun, Q. Fu, “Light scattering from irregular tetrahedral aggregates,” Opt. Commun. 156, 5–9 (1998).
[CrossRef]

N. B. Piller, “Coupled-dipole approximation for high permittivity materials,” Opt. Commun. 160, 10–14 (1999).
[CrossRef]

Opt. Lett. (1)

Philos. Mag. (1)

Lord Rayleigh, “The dispersal of light by a dielectric cylinder,” Philos. Mag. 36, 365–376 (1918).
[CrossRef]

Phys. Rev. B (1)

P. Chýlek, V. Srivastava, “Dielectric constant of a composite inhomogeneous medium,” Phys. Rev. B 27, 5098–5106 (1983).
[CrossRef]

Other (5)

J. S. Dobbie, P. Chýlek, “Evaluation of effective medium theory for large inclusions using DDA,” in Proceedings of the Conference on Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (American Meteorological Society, Boston, Mass., 1998).

P. Yang, K. N. Liou, “Application of finite-difference time domain technique to light scattering by irregular and inhomogeneous particles,” in Proceedings of the Conference on Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (American Meteorological Society, Boston, Mass., 1998).

L. J. Battan, Radar Observation of the Atmosphere (University of Chicago, Chicago, Ill., 1973).

B. T. Draine, “The discrete dipole approximation for studying light scattering by irregular targets,” in Proceedings of the Conference on Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (American Meteorological Society, Boston, Mass., 1998).

M. I. Mishchenko, S. W. Hovenier, L. D. Travis, eds., Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, San Diego, Calif., 1999).

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Figures (9)

Fig. 1
Fig. 1

Positions of the electric and magnetic field components in an elementary cubic cell of the FDTD lattice.

Fig. 2
Fig. 2

Comparison of the scattering phase functions for dielectric spheres with different refractive indices from Mie theory and those from the FDTD scheme by use of different dielectric property treatments. For the FDTD calculations, the dielectric constant at each position of the electric field components for a cell (see Fig. 1) is either the averaged value (average) or just the local value at that point (no average). The grid cell size is λ d /20, where λ d is the wavelength inside the particle. The size parameter is defined as 2πa/λ, where a is the radius of the sphere and λ is the wavelength in air.

Fig. 3
Fig. 3

Comparison of the scattering phase functions of dielectric spheres with different refractive indices from Mie theory and those from the FDTD scheme by use of different field-interpolation methods. Here BC denotes the interpolation obtained with the exact boundary condition, D uses electric displacement, and E makes direct use of the electric field.

Fig. 4
Fig. 4

Comparison of the scattering phase functions of dielectric spheres with different refractive indices from Mie theory and those from the FDTD method by use of different field-interpolation positions. In the FDTD calculations, the field components are interpolated either at the cell center or at the gravity center.

Fig. 5
Fig. 5

Extinction efficiency, absorption efficiency, and asymmetry factor for water spheres as functions of size parameters 2πa/λ, where a is the radius of the sphere and λ is the wavelength in air. These results were calculated by use of Mie theory and the FDTD scheme at 3.2-cm wavelength (m = 7.1499 + 2.914i). Also shown are the absolute and relative errors of the FDTD results. A grid cell size of λ d /20 was used for the FDTD calculation, where λ d is the wavelength inside the particle. For size parameters smaller than 3, the FDTD results (FDTD*) are also shown by use of the cell size so that the number of cells is the same as that for the particle with a size parameter of 3.

Fig. 6
Fig. 6

Comparison of scattering phase functions for water spheres from Mie theory and those from the FDTD scheme at 3.2-cm wavelength (m = 7.1499 + 2.914i) for size parameters of 1, 2, and 3.

Fig. 7
Fig. 7

Same as Fig. 6, but for size parameters of 4, 5, and 6.

Fig. 8
Fig. 8

Comparison of the scattering phase functions from Mie theory and those from the FDTD scheme at the wavelengths of 10.8 µm for ice spheres (m = 1.0891 + 0.18216i) and 3.2 cm for water spheres (m = 7.1499 + 2.914i) with size parameters of 20 and 3, respectively. A cell size of λ d /20 was used, where λ d is the wavelength inside the particle. For the FDTD simulation, we employed the interpolation using electric displacement to the cell center.

Fig. 9
Fig. 9

Schematic diagram of a particle surface element within a FDTD grid cell and its normal vector.

Tables (1)

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Table 1 Extinction and Absorption Efficiencies for the Cases in Figs. 2 4

Equations (15)

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Hxn+1/2i, j+1/2, k+1/2=Hxn-1/2i, j+1/2, k+1/2+Δtμi, j+1/2, k+1/2Δs×Eyni, j+1/2, k+1-Eyni, j+1/2, k +Ezni, j, k+1/2-Ezni, j+ 1, k+1/2,
Exn+1i+1/2, j, k=exp-τi+1/2, j, kΔtExni+1/2, j, k+exp-τi+1/2, j, k Δt/2Δtri+1/2, j, kΔsHzn+1/2i+1/2, j+1/2, k-Hzn+1/2i+1/2, j-1/2, k+Hyn+1/2i+1/2, j, k-1/2-Hyn+1/2i+1/2, j, k+1/2,
Cabs=2πiλ|E0|2 v |Er|2d3r=2πiΔs3λ|E0|2×i,j,k |Ei+ΔiΔs, j+ΔjΔs, k+ΔkΔs|2δi,j,k,
Exr=Ex sin θ cos ϕ,
Exθ=Ex cos θ cos ϕ,
Exϕ=-Ex sin ϕ,
Eyr=Ey sin θ sin ϕ,
Eyθ=Ey cos θ sin ϕ,
Eyϕ=Ey cos ϕ,
Ezr=Ez cos θ,
Ezθ=-Ez sin θ,
Ezϕ=0,
Ex=Drsin θ cos ϕ+Eθ cos θ cos ϕ-Eϕ sin ϕ,
Ey=Drsin θ sin ϕ+Eθ cos θ sin ϕ+Eϕ cos ϕ,
Ez=Drcos θ-Eθ sin θ,

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