Abstract

A three-dimensional finite-difference time-domain (FDTD) program has been developed to provide a numerical solution for light scattering by nonspherical dielectric particles. The perfectly matched layer (PML) absorbing boundary condition (ABC) is used to truncate the computational domain. As a result of using the PML ABC, the present FDTD program requires much less computer memory and CPU time than those that use traditional truncation techniques. For spheres with particle-size parameters as large as 40, the extinction and absorption efficiencies from the present FDTD program match the Mie results closely, with differences of less than ∼1%. The difference in the scattering phase function is typically smaller than ∼5%. The FDTD program has also been checked by use of the exact solution for light scattering by a pair of spheres in contact. Finally, applications of the PML FDTD to hexagonal particles and to spheres aggregated into tetrahedral structures are presented.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
    [CrossRef]
  2. D. O. Starr, “A cirrus cloud experiment: intensive field observations planned for FIRE,” Bull. Am. Meteorol. Soc. 68, 119–124 (1987).
    [CrossRef]
  3. L. M. Miloshevich, A. J. Heymsfield, P. M. Norris, “Microphysical measurements in cirrus clouds from ice crystal replicator sonders launched during FIRE II,” in Proceedings of the 11th International Conference on Clouds and Precipitation (Elsevier, New York, 1992), pp. 525–528.
  4. G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
    [CrossRef]
  5. Y. Takano, K. N. Liou, P. Minnis, “The effects of small ice crystals on cirrus infrared radiative properties,” J. Atmos. Sci. 49, 1487–1493 (1992).
    [CrossRef]
  6. Q. Fu, W. B. Sun, P. Yang, “On modeling of scattering and absorption by nonspherical cirrus ice particles at thermal infrared wavelengths,” J. Atmos. Sci. (to be published).
  7. 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]
  8. G. Mie, “Beigrade zur optik truber medien, speziell kolloidaler metallosungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
    [CrossRef]
  9. G. Videen, D. Ngo, M. B. Hart, “Light scattering from a pair of conducting, osculating spheres,” Opt. Commun. 125, 275–287 (1996).
    [CrossRef]
  10. S. Asano, G. Yamamoto, “Light scattering by a spheroidal particle,” Appl. Opt. 14, 29–49 (1975).
    [CrossRef] [PubMed]
  11. J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
    [CrossRef]
  12. Lord Rayleigh, “The dispersal of light by a dielectric cylinder,” Philos. Mag. 36, 365–376 (1918).
    [CrossRef]
  13. A. Mugnai, W. J. Wiscombe, “Scattering from nonspherical Chebyshev particles,” Appl. Opt. 25, 1235–1244 (1986).
    [CrossRef]
  14. M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
    [CrossRef] [PubMed]
  15. H. Laitinen, K. Lumme, “T-matrix method for general star-shaped particles: first results,” J. Quant. Spectrosc. Radiat. Transfer 60, 325–334 (1998).
    [CrossRef]
  16. Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
    [CrossRef]
  17. P. Yang, K. N. Liou, “Geometric-optics integral-equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
    [CrossRef] [PubMed]
  18. A. Macke, J. Muller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
    [CrossRef]
  19. P. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
    [CrossRef] [PubMed]
  20. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  21. D. L. Mitchell, “How appropriate is Mie theory for predicting the radiative properties of atmospheric particles?” GEWEX News 7–11 (February1995).
  22. W. B. Sun, “An investigation of infrared radiative properties of cirrus clouds,” M.S. thesis (Dalhousie University, Halifax, N.S., 1997).
  23. Q. Fu, P. Yang, W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Climate 11, 2223–2236 (1998).
    [CrossRef]
  24. E. M. Purcell, C. P. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 196, 705–714 (1973).
    [CrossRef]
  25. 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]
  26. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
    [CrossRef]
  27. 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]
  28. K. N. Liou, Y. Takano, “Light scattering by nonspherical particles: remote sensing and climatic implications,” Atmos. Res. 31, 271–298 (1994).
    [CrossRef]
  29. B. T. Draine, “The discrete dipole approximation for studying light scattering by irregular targets,” in Proceedings of Conference on Light Scattering by Nonspherical Particles (American Meteorological Society, Boston, 1998).
  30. 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).
  31. J. Xu, Z. Chen, J. Chuang, “Numerical implementation of PML in the TLM-based finite-difference time-domain grids,” IEEE Trans. Microwave Theory Tech. 45, 1263–1266 (1997).
  32. J. Xu, J. G. Ma, Z. Chen, “Numerical validations of a nonlinear PML scheme for absorption of nonlinear electromagnetic waves,” IEEE Trans. Microwave Theory Tech. 46, 1752–1758 (1998).
    [CrossRef]
  33. C. E. Reuter, R. M. Joseph, E. T. Thiele, D. S. Katz, T. Tflove, “Ultrawide-band absorbing boundary condition for termination of wave guide structures in FD-TD simulations,” IEEE Microwave Guided Wave Lett. 4, 344–346 (1994).
    [CrossRef]
  34. R. Holland, “Finite-difference time domain (FDTD) analysis of magnetic diffusion,” IEEE Trans. Electromagn. Compat. 36, 32–39 (1994).
    [CrossRef]
  35. 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]
  36. Z. Liao, H. L. Wong, B. Yang, Y. Yuan, “A transmitting boundary for transient wave analyses,” Sci. Sin. 27, 1063–1076 (1984).
  37. P. Yang, K. N. Liou, “An efficient algorithm for truncating spatial domain in modeling lighting scattering by finite-difference technique,” J. Comput. Phys. 140, 346–369 (1998).
    [CrossRef]
  38. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
    [CrossRef]
  39. J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363–379 (1996).
    [CrossRef]
  40. 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]
  41. A. Taflove, M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. MTT-23, 623–630 (1975).
    [CrossRef]
  42. D. M. Sullivan, “A simplified PML for use with the FDTD method,” IEEE Microwave Guided Wave Lett. 6, 97–99 (1996).
    [CrossRef]
  43. B. Engquist, A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comput. 31, 629–651 (1971).
    [CrossRef]
  44. G. Mur, “Absorbing boundary condition for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
    [CrossRef]
  45. A. Bayliss, E. Turkel, “Radiation boundary conditions for wavelike equations,” Commun. Pure Appl. Math. 33, 707–725 (1980).
    [CrossRef]
  46. R. L. Higdon, “Absorbing boundary conditions for difference approximations to the multidimensional wave equation,” Math. Comput. 47, 437–459 (1986).
  47. S. A. Schelkunoff, Electromagnetic Waves (Van Nostrand, New York, 1943).
  48. D. E. Merewether, R. Fisher, F. W. Smith, “On implementing a numeric Huygen’s source in a finite difference program to illustrate scattering bodies,” IEEE Trans. Nucl. Sci. NS-27, 1829–1833 (1980).
    [CrossRef]
  49. P. S. Tuminello, E. T. Arakawa, B. N. Khare, J. M. Wrobel, M. R. Querry, M. E. Milham, “Optical properties of Bacillus subtilis spores from 0.2 to 2.5 µm,” Appl. Opt. 36, 2818–2824 (1997).
    [CrossRef] [PubMed]
  50. A. J. Heymsfield, C. M. R. Platt, “A parameterization of the particle size spectrum of ice clouds in terms of the ambient temperature and the ice water content,” J. Atmos. Sci. 41, 846–855 (1984).
    [CrossRef]
  51. G. N. Plass, G. W. Kattawa, “Radiative transfer in water and ice clouds in the visible and infrared region,” Appl. Opt. 10, 738–749 (1968).
    [CrossRef]
  52. W. P. Arnott, Y. Liu, J. Hallet, “Unreasonable effectiveness of mimicking measured infrared extinction by hexagonal ice crystals with Mie ice spheres,” in Optical Remote Sensing of the Atmosphere, Vol. 5 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 216–218.
  53. D. L. Mitchell, A. Macke, Y. G. Liu, “Modeling cirrus clouds. Part II: Treatment of radiative properties,” J. Atmos. Sci. 53, 2967–2988 (1996).
    [CrossRef]
  54. Z. Sun, K. P. Shine, “Parameterization of ice cloud radiative properties and its application to the potential climatic importance of mixed phase clouds,” J. Climate 8, 1874–1888 (1995).
    [CrossRef]
  55. A. Ono, “The shape and riming properties of ice crystals in natural clouds,” J. Atmos. Sci. 26, 138–147 (1969).
    [CrossRef]
  56. A. H. Auer, D. L. Veal, “The dimension of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
    [CrossRef]
  57. R. G. Pinnick, S. C. Hill, P. Nachman, G. Videen, G. Chen, R. K. Chang, “Aerosol fluorescence spectrum analyzer for measurement of single micrometer-sized airborne biological particles,” Aerosol. Sci. Technol. 28, 95–104 (1998).
    [CrossRef]
  58. G. Videen, W. B. Sun, Q. Fu, “Light scattering from irregular tetrahedral aggregates,” Opt. Commun. 156, 5–9 (1998).
    [CrossRef]

1998

H. Laitinen, K. Lumme, “T-matrix method for general star-shaped particles: first results,” J. Quant. Spectrosc. Radiat. Transfer 60, 325–334 (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, 2223–2236 (1998).
[CrossRef]

J. Xu, J. G. Ma, Z. Chen, “Numerical validations of a nonlinear PML scheme for absorption of nonlinear electromagnetic waves,” IEEE Trans. Microwave Theory Tech. 46, 1752–1758 (1998).
[CrossRef]

P. Yang, K. N. Liou, “An efficient algorithm for truncating spatial domain in modeling lighting scattering by finite-difference technique,” J. Comput. Phys. 140, 346–369 (1998).
[CrossRef]

R. G. Pinnick, S. C. Hill, P. Nachman, G. Videen, G. Chen, R. K. Chang, “Aerosol fluorescence spectrum analyzer for measurement of single micrometer-sized airborne biological particles,” Aerosol. Sci. Technol. 28, 95–104 (1998).
[CrossRef]

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

1997

J. Xu, Z. Chen, J. Chuang, “Numerical implementation of PML in the TLM-based finite-difference time-domain grids,” IEEE Trans. Microwave Theory Tech. 45, 1263–1266 (1997).

P. S. Tuminello, E. T. Arakawa, B. N. Khare, J. M. Wrobel, M. R. Querry, M. E. Milham, “Optical properties of Bacillus subtilis spores from 0.2 to 2.5 µm,” Appl. Opt. 36, 2818–2824 (1997).
[CrossRef] [PubMed]

1996

D. M. Sullivan, “A simplified PML for use with the FDTD method,” IEEE Microwave Guided Wave Lett. 6, 97–99 (1996).
[CrossRef]

D. L. Mitchell, A. Macke, Y. G. Liu, “Modeling cirrus clouds. Part II: Treatment of radiative properties,” J. Atmos. Sci. 53, 2967–2988 (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]

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

A. Macke, J. Muller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

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]

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

G. Videen, D. Ngo, M. B. Hart, “Light scattering from a pair of conducting, osculating spheres,” Opt. Commun. 125, 275–287 (1996).
[CrossRef]

1995

D. L. Mitchell, “How appropriate is Mie theory for predicting the radiative properties of atmospheric particles?” GEWEX News 7–11 (February1995).

Z. Sun, K. P. Shine, “Parameterization of ice cloud radiative properties and its application to the potential climatic importance of mixed phase clouds,” J. Climate 8, 1874–1888 (1995).
[CrossRef]

1994

K. N. Liou, Y. Takano, “Light scattering by nonspherical particles: remote sensing and climatic implications,” Atmos. Res. 31, 271–298 (1994).
[CrossRef]

C. E. Reuter, R. M. Joseph, E. T. Thiele, D. S. Katz, T. Tflove, “Ultrawide-band absorbing boundary condition for termination of wave guide structures in FD-TD simulations,” IEEE Microwave Guided Wave Lett. 4, 344–346 (1994).
[CrossRef]

R. Holland, “Finite-difference time domain (FDTD) analysis of magnetic diffusion,” IEEE Trans. Electromagn. Compat. 36, 32–39 (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]

1992

Y. Takano, K. N. Liou, P. Minnis, “The effects of small ice crystals on cirrus infrared radiative properties,” J. Atmos. Sci. 49, 1487–1493 (1992).
[CrossRef]

1990

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback,” J. Atmos. Sci. 47, 1742–1753 (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]

1989

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

1988

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

1987

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]

D. O. Starr, “A cirrus cloud experiment: intensive field observations planned for FIRE,” Bull. Am. Meteorol. Soc. 68, 119–124 (1987).
[CrossRef]

1986

K. N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[CrossRef]

A. Mugnai, W. J. Wiscombe, “Scattering from nonspherical Chebyshev particles,” Appl. Opt. 25, 1235–1244 (1986).
[CrossRef]

R. L. Higdon, “Absorbing boundary conditions for difference approximations to the multidimensional wave equation,” Math. Comput. 47, 437–459 (1986).

1984

A. J. Heymsfield, C. M. R. Platt, “A parameterization of the particle size spectrum of ice clouds in terms of the ambient temperature and the ice water content,” J. Atmos. Sci. 41, 846–855 (1984).
[CrossRef]

Z. Liao, H. L. Wong, B. Yang, Y. Yuan, “A transmitting boundary for transient wave analyses,” Sci. Sin. 27, 1063–1076 (1984).

1981

G. Mur, “Absorbing boundary condition for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
[CrossRef]

1980

A. Bayliss, E. Turkel, “Radiation boundary conditions for wavelike equations,” Commun. Pure Appl. Math. 33, 707–725 (1980).
[CrossRef]

D. E. Merewether, R. Fisher, F. W. Smith, “On implementing a numeric Huygen’s source in a finite difference program to illustrate scattering bodies,” IEEE Trans. Nucl. Sci. NS-27, 1829–1833 (1980).
[CrossRef]

1975

A. Taflove, M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. MTT-23, 623–630 (1975).
[CrossRef]

P. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
[CrossRef] [PubMed]

S. Asano, G. Yamamoto, “Light scattering by a spheroidal particle,” Appl. Opt. 14, 29–49 (1975).
[CrossRef] [PubMed]

1973

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

1971

B. Engquist, A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comput. 31, 629–651 (1971).
[CrossRef]

1970

A. H. Auer, D. L. Veal, “The dimension of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

1969

A. Ono, “The shape and riming properties of ice crystals in natural clouds,” J. Atmos. Sci. 26, 138–147 (1969).
[CrossRef]

1968

1966

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

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

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

1908

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

Arakawa, E. T.

Arnott, W. P.

W. P. Arnott, Y. Liu, J. Hallet, “Unreasonable effectiveness of mimicking measured infrared extinction by hexagonal ice crystals with Mie ice spheres,” in Optical Remote Sensing of the Atmosphere, Vol. 5 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 216–218.

Asano, S.

Auer, A. H.

A. H. Auer, D. L. Veal, “The dimension of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

Barber, P.

Bayliss, A.

A. Bayliss, E. Turkel, “Radiation boundary conditions for wavelike equations,” Commun. Pure Appl. Math. 33, 707–725 (1980).
[CrossRef]

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.

Brodwin, M. E.

A. Taflove, M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. MTT-23, 623–630 (1975).
[CrossRef]

Chang, R. K.

R. G. Pinnick, S. C. Hill, P. Nachman, G. Videen, G. Chen, R. K. Chang, “Aerosol fluorescence spectrum analyzer for measurement of single micrometer-sized airborne biological particles,” Aerosol. Sci. Technol. 28, 95–104 (1998).
[CrossRef]

Chen, G.

R. G. Pinnick, S. C. Hill, P. Nachman, G. Videen, G. Chen, R. K. Chang, “Aerosol fluorescence spectrum analyzer for measurement of single micrometer-sized airborne biological particles,” Aerosol. Sci. Technol. 28, 95–104 (1998).
[CrossRef]

Chen, Z.

J. Xu, J. G. Ma, Z. Chen, “Numerical validations of a nonlinear PML scheme for absorption of nonlinear electromagnetic waves,” IEEE Trans. Microwave Theory Tech. 46, 1752–1758 (1998).
[CrossRef]

J. Xu, Z. Chen, J. Chuang, “Numerical implementation of PML in the TLM-based finite-difference time-domain grids,” IEEE Trans. Microwave Theory Tech. 45, 1263–1266 (1997).

Chuang, J.

J. Xu, Z. Chen, J. Chuang, “Numerical implementation of PML in the TLM-based finite-difference time-domain grids,” IEEE Trans. Microwave Theory Tech. 45, 1263–1266 (1997).

Draine, B. T.

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 Conference on Light Scattering by Nonspherical Particles (American Meteorological Society, Boston, 1998).

Engquist, B.

B. Engquist, A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comput. 31, 629–651 (1971).
[CrossRef]

Fisher, R.

D. E. Merewether, R. Fisher, F. W. Smith, “On implementing a numeric Huygen’s source in a finite difference program to illustrate scattering bodies,” IEEE Trans. Nucl. Sci. NS-27, 1829–1833 (1980).
[CrossRef]

Flatau, P. J.

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]

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Fu, Q.

Q. Fu, P. Yang, W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Climate 11, 2223–2236 (1998).
[CrossRef]

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

Q. Fu, W. B. Sun, P. Yang, “On modeling of scattering and absorption by nonspherical cirrus ice particles at thermal infrared wavelengths,” J. Atmos. Sci. (to be published).

Hallet, J.

W. P. Arnott, Y. Liu, J. Hallet, “Unreasonable effectiveness of mimicking measured infrared extinction by hexagonal ice crystals with Mie ice spheres,” in Optical Remote Sensing of the Atmosphere, Vol. 5 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 216–218.

Hart, M. B.

G. Videen, D. Ngo, M. B. Hart, “Light scattering from a pair of conducting, osculating spheres,” Opt. Commun. 125, 275–287 (1996).
[CrossRef]

Heymsfield, A. J.

A. J. Heymsfield, C. M. R. Platt, “A parameterization of the particle size spectrum of ice clouds in terms of the ambient temperature and the ice water content,” J. Atmos. Sci. 41, 846–855 (1984).
[CrossRef]

L. M. Miloshevich, A. J. Heymsfield, P. M. Norris, “Microphysical measurements in cirrus clouds from ice crystal replicator sonders launched during FIRE II,” in Proceedings of the 11th International Conference on Clouds and Precipitation (Elsevier, New York, 1992), pp. 525–528.

Higdon, R. L.

R. L. Higdon, “Absorbing boundary conditions for difference approximations to the multidimensional wave equation,” Math. Comput. 47, 437–459 (1986).

Hill, S. C.

R. G. Pinnick, S. C. Hill, P. Nachman, G. Videen, G. Chen, R. K. Chang, “Aerosol fluorescence spectrum analyzer for measurement of single micrometer-sized airborne biological particles,” Aerosol. Sci. Technol. 28, 95–104 (1998).
[CrossRef]

Holland, R.

R. Holland, “Finite-difference time domain (FDTD) analysis of magnetic diffusion,” IEEE Trans. Electromagn. Compat. 36, 32–39 (1994).
[CrossRef]

Joseph, R. M.

C. E. Reuter, R. M. Joseph, E. T. Thiele, D. S. Katz, T. Tflove, “Ultrawide-band absorbing boundary condition for termination of wave guide structures in FD-TD simulations,” IEEE Microwave Guided Wave Lett. 4, 344–346 (1994).
[CrossRef]

Kattawa, G. W.

Katz, D. S.

C. E. Reuter, R. M. Joseph, E. T. Thiele, D. S. Katz, T. Tflove, “Ultrawide-band absorbing boundary condition for termination of wave guide structures in FD-TD simulations,” IEEE Microwave Guided Wave Lett. 4, 344–346 (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]

Khare, B. N.

Laitinen, H.

H. Laitinen, K. Lumme, “T-matrix method for general star-shaped particles: first results,” J. Quant. Spectrosc. Radiat. Transfer 60, 325–334 (1998).
[CrossRef]

Liao, Z.

Z. Liao, H. L. Wong, B. Yang, Y. Yuan, “A transmitting boundary for transient wave analyses,” Sci. Sin. 27, 1063–1076 (1984).

Liou, K. N.

P. Yang, K. N. Liou, “An efficient algorithm for truncating spatial domain in modeling lighting scattering by finite-difference technique,” J. Comput. Phys. 140, 346–369 (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, “Geometric-optics integral-equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
[CrossRef] [PubMed]

K. N. Liou, Y. Takano, “Light scattering by nonspherical particles: remote sensing and climatic implications,” Atmos. Res. 31, 271–298 (1994).
[CrossRef]

Y. Takano, K. N. Liou, P. Minnis, “The effects of small ice crystals on cirrus infrared radiative properties,” J. Atmos. Sci. 49, 1487–1493 (1992).
[CrossRef]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

K. N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[CrossRef]

Liu, Y.

W. P. Arnott, Y. Liu, J. Hallet, “Unreasonable effectiveness of mimicking measured infrared extinction by hexagonal ice crystals with Mie ice spheres,” in Optical Remote Sensing of the Atmosphere, Vol. 5 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 216–218.

Liu, Y. G.

D. L. Mitchell, A. Macke, Y. G. Liu, “Modeling cirrus clouds. Part II: Treatment of radiative properties,” J. Atmos. Sci. 53, 2967–2988 (1996).
[CrossRef]

Lumme, K.

H. Laitinen, K. Lumme, “T-matrix method for general star-shaped particles: first results,” J. Quant. Spectrosc. Radiat. Transfer 60, 325–334 (1998).
[CrossRef]

Ma, J. G.

J. Xu, J. G. Ma, Z. Chen, “Numerical validations of a nonlinear PML scheme for absorption of nonlinear electromagnetic waves,” IEEE Trans. Microwave Theory Tech. 46, 1752–1758 (1998).
[CrossRef]

Macke, A.

A. Macke, J. Muller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

D. L. Mitchell, A. Macke, Y. G. Liu, “Modeling cirrus clouds. Part II: Treatment of radiative properties,” J. Atmos. Sci. 53, 2967–2988 (1996).
[CrossRef]

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]

Majda, A.

B. Engquist, A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comput. 31, 629–651 (1971).
[CrossRef]

Merewether, D. E.

D. E. Merewether, R. Fisher, F. W. Smith, “On implementing a numeric Huygen’s source in a finite difference program to illustrate scattering bodies,” IEEE Trans. Nucl. Sci. NS-27, 1829–1833 (1980).
[CrossRef]

Mie, G.

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

Milham, M. E.

Miloshevich, L. M.

L. M. Miloshevich, A. J. Heymsfield, P. M. Norris, “Microphysical measurements in cirrus clouds from ice crystal replicator sonders launched during FIRE II,” in Proceedings of the 11th International Conference on Clouds and Precipitation (Elsevier, New York, 1992), pp. 525–528.

Minnis, P.

Y. Takano, K. N. Liou, P. Minnis, “The effects of small ice crystals on cirrus infrared radiative properties,” J. Atmos. Sci. 49, 1487–1493 (1992).
[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]

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

Mitchell, D. L.

D. L. Mitchell, A. Macke, Y. G. Liu, “Modeling cirrus clouds. Part II: Treatment of radiative properties,” J. Atmos. Sci. 53, 2967–2988 (1996).
[CrossRef]

D. L. Mitchell, “How appropriate is Mie theory for predicting the radiative properties of atmospheric particles?” GEWEX News 7–11 (February1995).

Mugnai, A.

Muller, J.

A. Macke, J. Muller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

Mur, G.

G. Mur, “Absorbing boundary condition for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
[CrossRef]

Nachman, P.

R. G. Pinnick, S. C. Hill, P. Nachman, G. Videen, G. Chen, R. K. Chang, “Aerosol fluorescence spectrum analyzer for measurement of single micrometer-sized airborne biological particles,” Aerosol. Sci. Technol. 28, 95–104 (1998).
[CrossRef]

Ngo, D.

G. Videen, D. Ngo, M. B. Hart, “Light scattering from a pair of conducting, osculating spheres,” Opt. Commun. 125, 275–287 (1996).
[CrossRef]

Norris, P. M.

L. M. Miloshevich, A. J. Heymsfield, P. M. Norris, “Microphysical measurements in cirrus clouds from ice crystal replicator sonders launched during FIRE II,” in Proceedings of the 11th International Conference on Clouds and Precipitation (Elsevier, New York, 1992), pp. 525–528.

Ono, A.

A. Ono, “The shape and riming properties of ice crystals in natural clouds,” J. Atmos. Sci. 26, 138–147 (1969).
[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]

Pinnick, R. G.

R. G. Pinnick, S. C. Hill, P. Nachman, G. Videen, G. Chen, R. K. Chang, “Aerosol fluorescence spectrum analyzer for measurement of single micrometer-sized airborne biological particles,” Aerosol. Sci. Technol. 28, 95–104 (1998).
[CrossRef]

Plass, G. N.

Platt, C. M. R.

A. J. Heymsfield, C. M. R. Platt, “A parameterization of the particle size spectrum of ice clouds in terms of the ambient temperature and the ice water content,” J. Atmos. Sci. 41, 846–855 (1984).
[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]

Querry, M. R.

Raschke, E.

A. Macke, J. Muller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

Rayleigh, Lord

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

Reuter, C. E.

C. E. Reuter, R. M. Joseph, E. T. Thiele, D. S. Katz, T. Tflove, “Ultrawide-band absorbing boundary condition for termination of wave guide structures in FD-TD simulations,” IEEE Microwave Guided Wave Lett. 4, 344–346 (1994).
[CrossRef]

Schelkunoff, S. A.

S. A. Schelkunoff, Electromagnetic Waves (Van Nostrand, New York, 1943).

Shine, K. P.

Z. Sun, K. P. Shine, “Parameterization of ice cloud radiative properties and its application to the potential climatic importance of mixed phase clouds,” J. Climate 8, 1874–1888 (1995).
[CrossRef]

Singham, S. B.

Smith, F. W.

D. E. Merewether, R. Fisher, F. W. Smith, “On implementing a numeric Huygen’s source in a finite difference program to illustrate scattering bodies,” IEEE Trans. Nucl. Sci. NS-27, 1829–1833 (1980).
[CrossRef]

Stackhouse, P. W.

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Starr, D. O.

D. O. Starr, “A cirrus cloud experiment: intensive field observations planned for FIRE,” Bull. Am. Meteorol. Soc. 68, 119–124 (1987).
[CrossRef]

Stephens, G. L.

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback,” J. Atmos. Sci. 47, 1742–1753 (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]

Sullivan, D. M.

D. M. Sullivan, “A simplified PML for use with the FDTD method,” IEEE Microwave Guided Wave Lett. 6, 97–99 (1996).
[CrossRef]

Sun, W. B.

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, 2223–2236 (1998).
[CrossRef]

W. B. Sun, “An investigation of infrared radiative properties of cirrus clouds,” M.S. thesis (Dalhousie University, Halifax, N.S., 1997).

Q. Fu, W. B. Sun, P. Yang, “On modeling of scattering and absorption by nonspherical cirrus ice particles at thermal infrared wavelengths,” J. Atmos. Sci. (to be published).

Sun, Z.

Z. Sun, K. P. Shine, “Parameterization of ice cloud radiative properties and its application to the potential climatic importance of mixed phase clouds,” J. Climate 8, 1874–1888 (1995).
[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]

A. Taflove, M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. MTT-23, 623–630 (1975).
[CrossRef]

Takano, Y.

K. N. Liou, Y. Takano, “Light scattering by nonspherical particles: remote sensing and climatic implications,” Atmos. Res. 31, 271–298 (1994).
[CrossRef]

Y. Takano, K. N. Liou, P. Minnis, “The effects of small ice crystals on cirrus infrared radiative properties,” J. Atmos. Sci. 49, 1487–1493 (1992).
[CrossRef]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

Tflove, T.

C. E. Reuter, R. M. Joseph, E. T. Thiele, D. S. Katz, T. Tflove, “Ultrawide-band absorbing boundary condition for termination of wave guide structures in FD-TD simulations,” IEEE Microwave Guided Wave Lett. 4, 344–346 (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]

C. E. Reuter, R. M. Joseph, E. T. Thiele, D. S. Katz, T. Tflove, “Ultrawide-band absorbing boundary condition for termination of wave guide structures in FD-TD simulations,” IEEE Microwave Guided Wave Lett. 4, 344–346 (1994).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

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]

Tsay, S. C.

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Tuminello, P. S.

Turkel, E.

A. Bayliss, E. Turkel, “Radiation boundary conditions for wavelike equations,” Commun. Pure Appl. Math. 33, 707–725 (1980).
[CrossRef]

van de Hulst, H. C.

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

Veal, D. L.

A. H. Auer, D. L. Veal, “The dimension of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

Videen, G.

R. G. Pinnick, S. C. Hill, P. Nachman, G. Videen, G. Chen, R. K. Chang, “Aerosol fluorescence spectrum analyzer for measurement of single micrometer-sized airborne biological particles,” Aerosol. Sci. Technol. 28, 95–104 (1998).
[CrossRef]

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

G. Videen, D. Ngo, M. B. Hart, “Light scattering from a pair of conducting, osculating spheres,” Opt. Commun. 125, 275–287 (1996).
[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]

Wiscombe, W. J.

Wong, H. L.

Z. Liao, H. L. Wong, B. Yang, Y. Yuan, “A transmitting boundary for transient wave analyses,” Sci. Sin. 27, 1063–1076 (1984).

Wrobel, J. M.

Xu, J.

J. Xu, J. G. Ma, Z. Chen, “Numerical validations of a nonlinear PML scheme for absorption of nonlinear electromagnetic waves,” IEEE Trans. Microwave Theory Tech. 46, 1752–1758 (1998).
[CrossRef]

J. Xu, Z. Chen, J. Chuang, “Numerical implementation of PML in the TLM-based finite-difference time-domain grids,” IEEE Trans. Microwave Theory Tech. 45, 1263–1266 (1997).

Yamamoto, G.

Yang, B.

Z. Liao, H. L. Wong, B. Yang, Y. Yuan, “A transmitting boundary for transient wave analyses,” Sci. Sin. 27, 1063–1076 (1984).

Yang, P.

P. Yang, K. N. Liou, “An efficient algorithm for truncating spatial domain in modeling lighting scattering by finite-difference technique,” J. Comput. Phys. 140, 346–369 (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, 2223–2236 (1998).
[CrossRef]

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

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]

Q. Fu, W. B. Sun, P. Yang, “On modeling of scattering and absorption by nonspherical cirrus ice particles at thermal infrared wavelengths,” J. Atmos. Sci. (to be published).

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).

Yeh, C.

Yuan, Y.

Z. Liao, H. L. Wong, B. Yang, Y. Yuan, “A transmitting boundary for transient wave analyses,” Sci. Sin. 27, 1063–1076 (1984).

Aerosol. Sci. Technol.

R. G. Pinnick, S. C. Hill, P. Nachman, G. Videen, G. Chen, R. K. Chang, “Aerosol fluorescence spectrum analyzer for measurement of single micrometer-sized airborne biological particles,” Aerosol. Sci. Technol. 28, 95–104 (1998).
[CrossRef]

Ann. Phys. (Leipzig)

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

Appl. Opt.

Astrophys. J.

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

Atmos. Res.

K. N. Liou, Y. Takano, “Light scattering by nonspherical particles: remote sensing and climatic implications,” Atmos. Res. 31, 271–298 (1994).
[CrossRef]

Bull. Am. Meteorol. Soc.

D. O. Starr, “A cirrus cloud experiment: intensive field observations planned for FIRE,” Bull. Am. Meteorol. Soc. 68, 119–124 (1987).
[CrossRef]

Can. J. Phys.

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

Commun. Pure Appl. Math.

A. Bayliss, E. Turkel, “Radiation boundary conditions for wavelike equations,” Commun. Pure Appl. Math. 33, 707–725 (1980).
[CrossRef]

GEWEX News

D. L. Mitchell, “How appropriate is Mie theory for predicting the radiative properties of atmospheric particles?” GEWEX News 7–11 (February1995).

IEEE Microwave Guided Wave Lett.

C. E. Reuter, R. M. Joseph, E. T. Thiele, D. S. Katz, T. Tflove, “Ultrawide-band absorbing boundary condition for termination of wave guide structures in FD-TD simulations,” IEEE Microwave Guided Wave Lett. 4, 344–346 (1994).
[CrossRef]

D. M. Sullivan, “A simplified PML for use with the FDTD method,” IEEE Microwave Guided Wave Lett. 6, 97–99 (1996).
[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]

IEEE Trans. Antennas Propag.

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. Electromagn. Compat.

R. Holland, “Finite-difference time domain (FDTD) analysis of magnetic diffusion,” IEEE Trans. Electromagn. Compat. 36, 32–39 (1994).
[CrossRef]

G. Mur, “Absorbing boundary condition for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

A. Taflove, M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. MTT-23, 623–630 (1975).
[CrossRef]

J. Xu, Z. Chen, J. Chuang, “Numerical implementation of PML in the TLM-based finite-difference time-domain grids,” IEEE Trans. Microwave Theory Tech. 45, 1263–1266 (1997).

J. Xu, J. G. Ma, Z. Chen, “Numerical validations of a nonlinear PML scheme for absorption of nonlinear electromagnetic waves,” IEEE Trans. Microwave Theory Tech. 46, 1752–1758 (1998).
[CrossRef]

IEEE Trans. Nucl. Sci.

D. E. Merewether, R. Fisher, F. W. Smith, “On implementing a numeric Huygen’s source in a finite difference program to illustrate scattering bodies,” IEEE Trans. Nucl. Sci. NS-27, 1829–1833 (1980).
[CrossRef]

J. Atmos. Sci.

A. J. Heymsfield, C. M. R. Platt, “A parameterization of the particle size spectrum of ice clouds in terms of the ambient temperature and the ice water content,” J. Atmos. Sci. 41, 846–855 (1984).
[CrossRef]

D. L. Mitchell, A. Macke, Y. G. Liu, “Modeling cirrus clouds. Part II: Treatment of radiative properties,” J. Atmos. Sci. 53, 2967–2988 (1996).
[CrossRef]

A. Ono, “The shape and riming properties of ice crystals in natural clouds,” J. Atmos. Sci. 26, 138–147 (1969).
[CrossRef]

A. H. Auer, D. L. Veal, “The dimension of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

A. Macke, J. Muller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Y. Takano, K. N. Liou, P. Minnis, “The effects of small ice crystals on cirrus infrared radiative properties,” J. Atmos. Sci. 49, 1487–1493 (1992).
[CrossRef]

J. Climate

Q. Fu, P. Yang, W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Climate 11, 2223–2236 (1998).
[CrossRef]

Z. Sun, K. P. Shine, “Parameterization of ice cloud radiative properties and its application to the potential climatic importance of mixed phase clouds,” J. Climate 8, 1874–1888 (1995).
[CrossRef]

J. Comput. Phys.

P. Yang, K. N. Liou, “An efficient algorithm for truncating spatial domain in modeling lighting scattering by finite-difference technique,” J. Comput. Phys. 140, 346–369 (1998).
[CrossRef]

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

J. Quant. Spectrosc. Radiat. Transfer

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]

H. Laitinen, K. Lumme, “T-matrix method for general star-shaped particles: first results,” J. Quant. Spectrosc. Radiat. Transfer 60, 325–334 (1998).
[CrossRef]

Math. Comput.

B. Engquist, A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comput. 31, 629–651 (1971).
[CrossRef]

R. L. Higdon, “Absorbing boundary conditions for difference approximations to the multidimensional wave equation,” Math. Comput. 47, 437–459 (1986).

Mon. Weather Rev.

K. N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[CrossRef]

Opt. Commun.

G. Videen, D. Ngo, M. B. Hart, “Light scattering from a pair of conducting, osculating spheres,” Opt. Commun. 125, 275–287 (1996).
[CrossRef]

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

Opt. Lett.

Philos. Mag.

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

Sci. Sin.

Z. Liao, H. L. Wong, B. Yang, Y. Yuan, “A transmitting boundary for transient wave analyses,” Sci. Sin. 27, 1063–1076 (1984).

Other

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

W. B. Sun, “An investigation of infrared radiative properties of cirrus clouds,” M.S. thesis (Dalhousie University, Halifax, N.S., 1997).

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

Q. Fu, W. B. Sun, P. Yang, “On modeling of scattering and absorption by nonspherical cirrus ice particles at thermal infrared wavelengths,” J. Atmos. Sci. (to be published).

L. M. Miloshevich, A. J. Heymsfield, P. M. Norris, “Microphysical measurements in cirrus clouds from ice crystal replicator sonders launched during FIRE II,” in Proceedings of the 11th International Conference on Clouds and Precipitation (Elsevier, New York, 1992), pp. 525–528.

S. A. Schelkunoff, Electromagnetic Waves (Van Nostrand, New York, 1943).

W. P. Arnott, Y. Liu, J. Hallet, “Unreasonable effectiveness of mimicking measured infrared extinction by hexagonal ice crystals with Mie ice spheres,” in Optical Remote Sensing of the Atmosphere, Vol. 5 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 216–218.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

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

Fig. 2
Fig. 2

Computational domain terminated by the PML. The arrangement of the fictitious electric conductivity (σ) and magnetic conductivity (σ*) in the PML walls is also shown.

Fig. 3
Fig. 3

Extinction efficiency, absorption efficiency, and asymmetry factor for spherical ice crystals as functions of the size parameter, 2πa/λ, where a is the radius of the sphere and λ is the wavelength. These results are computed by Mie theory and the PML FDTD method at a wavelength of 10.8 µm (m = 1.0891 + 0.18216i). Also shown are the absolute and the relative errors of the FDTD results. A grid size of Δs = λ/20 is used in the FDTD calculation.

Fig. 4
Fig. 4

Scattering phase functions for spherical ice crystals computed by Mie theory and the PML FDTD method at a wavelength of 10.8 µm (m = 1.0891 + 0.18216i) for different size parameters. Also shown are the absolute and the relative errors of the FDTD results. In the FDTD calculations a cell size of Δs = λ/20 is used.

Fig. 5
Fig. 5

Same as Fig. 4 but for size parameters of 15, 20, and 25.

Fig. 6
Fig. 6

Same as Fig. 4 but for size parameters of 30, 35, and 40.

Fig. 7
Fig. 7

Scattering phase functions for spherical ice crystals computed by Mie theory and the PML FDTD method at wavelengths of 0.55 µm (m = 1.311), 10.8 µm (m = 1.0891 + 0.18216i), and 12.99 µm (m = 1.4717 + 0.3890i) for a size parameter of 6. Also shown are the absolute and the relative errors of the FDTD results. Different cell sizes of Δs = λ/20, λ/30, and λ/60 are used in the FDTD calculations.

Fig. 8
Fig. 8

Scattering phase function for a pair of spheres (r = λ/2) in contact, illuminated end-on. The results are calculated using the multipole method and the PML FDTD program with a cell size of Δs = λ/30; m = 1.53 + 0.001i is used to represent the refractive index of biological spores at a wavelength of 0.55 µm. Also shown are the absolute and the relative errors of the FDTD results.

Fig. 9
Fig. 9

Comparison of absorption efficiency for randomly oriented hexagonal ice crystals derived from a different scattering program: Mie theory for spheres with an equal projected area, ADT, a GOM, and a FDTD technique. The results are shown as functions of size parameter, 2πr p /λ, where r p is the radius for a projected area equivalent sphere.

Fig. 10
Fig. 10

Diagram of the tetrahedral scattering system. Four r = λ/2, m = 1.53 + 0.001i spheres are in contact.

Fig. 11
Fig. 11

Angular dependence of the scattering intensity of the system illustrated in Fig. 10 when the light is incident in the positive z direction.

Equations (26)

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

×E=-μ Ht,
×H= Et,
Ex, y, z, t=Ex, y, zexp-iωt,
Hx, y, z, t=Hx, y, zexp-iωt,
=r+ii.
r=mr2-mi2,  i=2mrmi.
×Hx, y, z=ωi-irEx, y, z.
×Hx, y, z, t=ωiEx, y, z, t+rEx, y, z, tt.
expτtEx, y, z, tt=expτtr ×Hx, y, z, t,
En+1x, y, z=exp-τΔtEnx, y, z+exp-τΔt/2Δtr ×Hn+1/2x, y, z,
Hn+1/2x, y, z=Hn-1/2x, y, z-Δtμ ×Enx, y, z.
Hxn+1/2i, j+1/2, k+1/2=Hxn-1/2i, j+1/2, k+1/2+Δtμi, j+1/2, k+1/2δ×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, kΔt×Exni+1/2, j, k+exp-τi+1/2, j, kΔt/2×Δtri+1/2, j, kδ×Hzn+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.
cΔt1Δx2+1Δy2+1Δz2-1/2,
μ0Hxyt+σy*Hxy=-Ezx+Ezyy,
μ0Hxzt+σz*Hxz=Eyx+Eyzz,
0Exyt+σyExy=Hzx+Hzyy,
0Exzt+σzExz=-Hyx+Hyzz,
σ0=σ*μ0.
Rθ=exp-2 cos θ0c0d σρdρ,
σρ=σmρdn,
Rθ=R0cosθ,
R0=exp-2n+1σmd0c.
HH-Δtμ0ΔsEin×n,
EE-Δt0Δsn×Hin,
Et=exp-t30Δt-52.

Metrics