Abstract

In this paper, we introduce an efficient numerical method to characterize the multiple scattering by random discrete particles illuminated by Bessel beams with arbitrary incidence. Specifically, the vector expressions of Bessel beams that perfectly satisfy Maxwell’s equations in combination with rotation Euler angles are used to represent the arbitrarily incident Bessel beams. A hybrid vector finite element–boundary integral–characteristic-basis function method is utilized to formulate the scattering problems involving multiple discrete particles with a random distribution. Due to the flexibility of the finite element method, the adopted method can conveniently deal with the problems of multiple scattering by randomly distributed homogeneous particles, inhomogeneous particles, and anisotropic particles. Some numerical results are included to illustrate the validity and capability of the proposed method and to show the scattering behaviors of random discrete particles when they are illuminated by Bessel beams.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. L. Foldy, “The multiple scattering of waves. I. General theory of isotropic scattering by randomly distributed scatterers,” Phys. Rev. 67, 107–119 (1945).
    [CrossRef]
  2. M. Lax, “Multiple scattering of waves,” Rev. Mod. Phys. 23, 287–310 (1951).
    [CrossRef]
  3. V. V. Varadan and V. K. Varadan, “Multiple scattering of electromagnetic waves by randomly distributed and oriented dielectric scatters,” Phys. Rev. D 21, 388–394 (1980).
    [CrossRef]
  4. V. K. Varadan, V. N. Bringi, V. V. Varadan, and A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
    [CrossRef]
  5. K. Furutsu, “Multiple scattering of waves in a medium of randomly distributed particles and derivation of the transport equation,” Radio Sci. 10, 29–44 (1975).
    [CrossRef]
  6. V. P. Tishkovets and K. Jockers, “Multiple scattering of light by densely packed random media of spherical particles: dense media vector radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 101, 54–72 (2006).
    [CrossRef]
  7. C. C. Lu, W. C. Chew, and L. Tsang, “The application of recursive aggregate T-matrix algorithm in the Monte Carlo simulations of the extinction rate of random distribution of particles,” Radio Sci. 30, 25–28 (1995).
    [CrossRef]
  8. W. C. Chew, J. H. Lin, and X. G. Yang, “An FFT T-matrix method for 3D microwave scattering solution from random discrete scatterers,” Microw. Opt. Technol. Lett. 9, 194–196 (1995).
    [CrossRef]
  9. P. R. Siqueira and K. Sarabandi, “T-matrix determination of effective permittivity for three-dimensional dense random media,” IEEE Trans. Antennas Propag. 48, 317–327 (2000).
    [CrossRef]
  10. M. I. Mishchenko, L. Liu, D. W. Mackowski, B. Cairns, and G. Videen, “Multiple scattering by random particulate media: exact 3D results,” Opt. Express 15, 2822–2836 (2007).
    [CrossRef]
  11. C. H. Chart and L. Tsang, “A sparse-matrix canonical-grid method for scattering by many scatterers,” Microw. Opt. Technol. Lett. 8, 114–118 (1995).
    [CrossRef]
  12. B. E. Barrowes, C. O. Ao, F. L. Teixeira, and J. A. Kong, “Sparse matrix/canonical grid method applied to 3-D dense medium simulations,” IEEE Trans. Antennas Propag. 51, 48–58 (2003).
    [CrossRef]
  13. Y. F. Sun, C. H. Chan, R. Mittra, and L. Tsang, “Characteristic basis function method for solving large problem arising in dense medium scattering,” in IEEE Antennas and Propagation Society International Symposium (IEEE, 2003), pp. 1068–1071.
  14. Z. W. Cui, Y. P. Han, and Q. Xu, “Numerical simulation of multiple scattering by random discrete particles illuminated by Gaussian beams,” J. Opt. Soc. Am. A 28, 2200–2208 (2011).
    [CrossRef]
  15. Z. W. Cui, Y. P. Han, and C. Y. Li, “Simulation of electromagnetic scattering by random discrete particles using a hybrid FE-BI-CBFM technique,” Waves Random Complex Media 22, 234–248 (2012).
    [CrossRef]
  16. D. W. Mackowski and M. I. Mishchenko, “Direct simulation of multiple scattering by discrete random media illuminated by Gaussian beams,” Phys. Rev. A 83, 013804 (2011).
    [CrossRef]
  17. J. Durnin, “Exact solution for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
    [CrossRef]
  18. S. R. Mishra, “A vector wave analysis of a Bessel beam,” Opt. Commun. 85, 159–161 (1991).
    [CrossRef]
  19. F. G. Mitri, “Arbitrary scattering of an electromagnetic zero-order Bessel beam by a dielectric sphere,” Opt. Lett. 36, 766–768 (2011).
    [CrossRef]
  20. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University, 1957).
  21. X. Q. Sheng, J. M. Jin, J. M. Song, C. C. Lu, and W. C. Chew, “On the formulation of hybrid finite-element and boundary-integral methods for 3-D scattering,” IEEE Trans. Antennas Propag. 46, 303–311 (1998).
    [CrossRef]
  22. J. Liu and J. M. Jin, “A novel hybridization of higher order finite element and boundary integral methods for electromagnetic scattering and radiation problems,” IEEE Trans. Antennas Propag. 49, 1794–1806 (2001).
    [CrossRef]
  23. X. Q. Sheng and Z. Peng, “Analysis of scattering by large objects with off-diagonally anisotropic material using finite element-boundary integral-multilevel fast multipole algorithm,” IET Microw. Antennas Propag. 4, 492–500 (2010).
    [CrossRef]
  24. Z. W. Cui, Y. P. Han, X. Ai, and W. J. Zhao, “A domain decomposition of the finite element–boundary integral method for scattering by multiple objects,” Electromagnetics 31, 469–482 (2011).
    [CrossRef]
  25. L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves, Numerical Simulations (Wiley, 2001).
  26. J. M. Jin, The Finite Element Method in Electromagnetics (Wiley, 2002).
  27. S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 30, 409–418 (1982).
    [CrossRef]

2012

Z. W. Cui, Y. P. Han, and C. Y. Li, “Simulation of electromagnetic scattering by random discrete particles using a hybrid FE-BI-CBFM technique,” Waves Random Complex Media 22, 234–248 (2012).
[CrossRef]

2011

D. W. Mackowski and M. I. Mishchenko, “Direct simulation of multiple scattering by discrete random media illuminated by Gaussian beams,” Phys. Rev. A 83, 013804 (2011).
[CrossRef]

Z. W. Cui, Y. P. Han, X. Ai, and W. J. Zhao, “A domain decomposition of the finite element–boundary integral method for scattering by multiple objects,” Electromagnetics 31, 469–482 (2011).
[CrossRef]

F. G. Mitri, “Arbitrary scattering of an electromagnetic zero-order Bessel beam by a dielectric sphere,” Opt. Lett. 36, 766–768 (2011).
[CrossRef]

Z. W. Cui, Y. P. Han, and Q. Xu, “Numerical simulation of multiple scattering by random discrete particles illuminated by Gaussian beams,” J. Opt. Soc. Am. A 28, 2200–2208 (2011).
[CrossRef]

2010

X. Q. Sheng and Z. Peng, “Analysis of scattering by large objects with off-diagonally anisotropic material using finite element-boundary integral-multilevel fast multipole algorithm,” IET Microw. Antennas Propag. 4, 492–500 (2010).
[CrossRef]

2007

2006

V. P. Tishkovets and K. Jockers, “Multiple scattering of light by densely packed random media of spherical particles: dense media vector radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 101, 54–72 (2006).
[CrossRef]

2003

B. E. Barrowes, C. O. Ao, F. L. Teixeira, and J. A. Kong, “Sparse matrix/canonical grid method applied to 3-D dense medium simulations,” IEEE Trans. Antennas Propag. 51, 48–58 (2003).
[CrossRef]

2001

J. Liu and J. M. Jin, “A novel hybridization of higher order finite element and boundary integral methods for electromagnetic scattering and radiation problems,” IEEE Trans. Antennas Propag. 49, 1794–1806 (2001).
[CrossRef]

2000

P. R. Siqueira and K. Sarabandi, “T-matrix determination of effective permittivity for three-dimensional dense random media,” IEEE Trans. Antennas Propag. 48, 317–327 (2000).
[CrossRef]

1998

X. Q. Sheng, J. M. Jin, J. M. Song, C. C. Lu, and W. C. Chew, “On the formulation of hybrid finite-element and boundary-integral methods for 3-D scattering,” IEEE Trans. Antennas Propag. 46, 303–311 (1998).
[CrossRef]

1995

C. H. Chart and L. Tsang, “A sparse-matrix canonical-grid method for scattering by many scatterers,” Microw. Opt. Technol. Lett. 8, 114–118 (1995).
[CrossRef]

C. C. Lu, W. C. Chew, and L. Tsang, “The application of recursive aggregate T-matrix algorithm in the Monte Carlo simulations of the extinction rate of random distribution of particles,” Radio Sci. 30, 25–28 (1995).
[CrossRef]

W. C. Chew, J. H. Lin, and X. G. Yang, “An FFT T-matrix method for 3D microwave scattering solution from random discrete scatterers,” Microw. Opt. Technol. Lett. 9, 194–196 (1995).
[CrossRef]

1991

S. R. Mishra, “A vector wave analysis of a Bessel beam,” Opt. Commun. 85, 159–161 (1991).
[CrossRef]

1987

1983

V. K. Varadan, V. N. Bringi, V. V. Varadan, and A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

1982

S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 30, 409–418 (1982).
[CrossRef]

1980

V. V. Varadan and V. K. Varadan, “Multiple scattering of electromagnetic waves by randomly distributed and oriented dielectric scatters,” Phys. Rev. D 21, 388–394 (1980).
[CrossRef]

1975

K. Furutsu, “Multiple scattering of waves in a medium of randomly distributed particles and derivation of the transport equation,” Radio Sci. 10, 29–44 (1975).
[CrossRef]

1951

M. Lax, “Multiple scattering of waves,” Rev. Mod. Phys. 23, 287–310 (1951).
[CrossRef]

1945

L. L. Foldy, “The multiple scattering of waves. I. General theory of isotropic scattering by randomly distributed scatterers,” Phys. Rev. 67, 107–119 (1945).
[CrossRef]

Ai, X.

Z. W. Cui, Y. P. Han, X. Ai, and W. J. Zhao, “A domain decomposition of the finite element–boundary integral method for scattering by multiple objects,” Electromagnetics 31, 469–482 (2011).
[CrossRef]

Ao, C. O.

B. E. Barrowes, C. O. Ao, F. L. Teixeira, and J. A. Kong, “Sparse matrix/canonical grid method applied to 3-D dense medium simulations,” IEEE Trans. Antennas Propag. 51, 48–58 (2003).
[CrossRef]

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves, Numerical Simulations (Wiley, 2001).

Barrowes, B. E.

B. E. Barrowes, C. O. Ao, F. L. Teixeira, and J. A. Kong, “Sparse matrix/canonical grid method applied to 3-D dense medium simulations,” IEEE Trans. Antennas Propag. 51, 48–58 (2003).
[CrossRef]

Bringi, V. N.

V. K. Varadan, V. N. Bringi, V. V. Varadan, and A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

Cairns, B.

Chan, C. H.

Y. F. Sun, C. H. Chan, R. Mittra, and L. Tsang, “Characteristic basis function method for solving large problem arising in dense medium scattering,” in IEEE Antennas and Propagation Society International Symposium (IEEE, 2003), pp. 1068–1071.

Chart, C. H.

C. H. Chart and L. Tsang, “A sparse-matrix canonical-grid method for scattering by many scatterers,” Microw. Opt. Technol. Lett. 8, 114–118 (1995).
[CrossRef]

Chew, W. C.

X. Q. Sheng, J. M. Jin, J. M. Song, C. C. Lu, and W. C. Chew, “On the formulation of hybrid finite-element and boundary-integral methods for 3-D scattering,” IEEE Trans. Antennas Propag. 46, 303–311 (1998).
[CrossRef]

W. C. Chew, J. H. Lin, and X. G. Yang, “An FFT T-matrix method for 3D microwave scattering solution from random discrete scatterers,” Microw. Opt. Technol. Lett. 9, 194–196 (1995).
[CrossRef]

C. C. Lu, W. C. Chew, and L. Tsang, “The application of recursive aggregate T-matrix algorithm in the Monte Carlo simulations of the extinction rate of random distribution of particles,” Radio Sci. 30, 25–28 (1995).
[CrossRef]

Cui, Z. W.

Z. W. Cui, Y. P. Han, and C. Y. Li, “Simulation of electromagnetic scattering by random discrete particles using a hybrid FE-BI-CBFM technique,” Waves Random Complex Media 22, 234–248 (2012).
[CrossRef]

Z. W. Cui, Y. P. Han, and Q. Xu, “Numerical simulation of multiple scattering by random discrete particles illuminated by Gaussian beams,” J. Opt. Soc. Am. A 28, 2200–2208 (2011).
[CrossRef]

Z. W. Cui, Y. P. Han, X. Ai, and W. J. Zhao, “A domain decomposition of the finite element–boundary integral method for scattering by multiple objects,” Electromagnetics 31, 469–482 (2011).
[CrossRef]

Ding, K. H.

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves, Numerical Simulations (Wiley, 2001).

Durnin, J.

Edmonds, A. R.

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University, 1957).

Foldy, L. L.

L. L. Foldy, “The multiple scattering of waves. I. General theory of isotropic scattering by randomly distributed scatterers,” Phys. Rev. 67, 107–119 (1945).
[CrossRef]

Furutsu, K.

K. Furutsu, “Multiple scattering of waves in a medium of randomly distributed particles and derivation of the transport equation,” Radio Sci. 10, 29–44 (1975).
[CrossRef]

Glisson, A. W.

S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 30, 409–418 (1982).
[CrossRef]

Han, Y. P.

Z. W. Cui, Y. P. Han, and C. Y. Li, “Simulation of electromagnetic scattering by random discrete particles using a hybrid FE-BI-CBFM technique,” Waves Random Complex Media 22, 234–248 (2012).
[CrossRef]

Z. W. Cui, Y. P. Han, and Q. Xu, “Numerical simulation of multiple scattering by random discrete particles illuminated by Gaussian beams,” J. Opt. Soc. Am. A 28, 2200–2208 (2011).
[CrossRef]

Z. W. Cui, Y. P. Han, X. Ai, and W. J. Zhao, “A domain decomposition of the finite element–boundary integral method for scattering by multiple objects,” Electromagnetics 31, 469–482 (2011).
[CrossRef]

Ishimaru, A.

V. K. Varadan, V. N. Bringi, V. V. Varadan, and A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

Jin, J. M.

J. Liu and J. M. Jin, “A novel hybridization of higher order finite element and boundary integral methods for electromagnetic scattering and radiation problems,” IEEE Trans. Antennas Propag. 49, 1794–1806 (2001).
[CrossRef]

X. Q. Sheng, J. M. Jin, J. M. Song, C. C. Lu, and W. C. Chew, “On the formulation of hybrid finite-element and boundary-integral methods for 3-D scattering,” IEEE Trans. Antennas Propag. 46, 303–311 (1998).
[CrossRef]

J. M. Jin, The Finite Element Method in Electromagnetics (Wiley, 2002).

Jockers, K.

V. P. Tishkovets and K. Jockers, “Multiple scattering of light by densely packed random media of spherical particles: dense media vector radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 101, 54–72 (2006).
[CrossRef]

Kong, J. A.

B. E. Barrowes, C. O. Ao, F. L. Teixeira, and J. A. Kong, “Sparse matrix/canonical grid method applied to 3-D dense medium simulations,” IEEE Trans. Antennas Propag. 51, 48–58 (2003).
[CrossRef]

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves, Numerical Simulations (Wiley, 2001).

Lax, M.

M. Lax, “Multiple scattering of waves,” Rev. Mod. Phys. 23, 287–310 (1951).
[CrossRef]

Li, C. Y.

Z. W. Cui, Y. P. Han, and C. Y. Li, “Simulation of electromagnetic scattering by random discrete particles using a hybrid FE-BI-CBFM technique,” Waves Random Complex Media 22, 234–248 (2012).
[CrossRef]

Lin, J. H.

W. C. Chew, J. H. Lin, and X. G. Yang, “An FFT T-matrix method for 3D microwave scattering solution from random discrete scatterers,” Microw. Opt. Technol. Lett. 9, 194–196 (1995).
[CrossRef]

Liu, J.

J. Liu and J. M. Jin, “A novel hybridization of higher order finite element and boundary integral methods for electromagnetic scattering and radiation problems,” IEEE Trans. Antennas Propag. 49, 1794–1806 (2001).
[CrossRef]

Liu, L.

Lu, C. C.

X. Q. Sheng, J. M. Jin, J. M. Song, C. C. Lu, and W. C. Chew, “On the formulation of hybrid finite-element and boundary-integral methods for 3-D scattering,” IEEE Trans. Antennas Propag. 46, 303–311 (1998).
[CrossRef]

C. C. Lu, W. C. Chew, and L. Tsang, “The application of recursive aggregate T-matrix algorithm in the Monte Carlo simulations of the extinction rate of random distribution of particles,” Radio Sci. 30, 25–28 (1995).
[CrossRef]

Mackowski, D. W.

D. W. Mackowski and M. I. Mishchenko, “Direct simulation of multiple scattering by discrete random media illuminated by Gaussian beams,” Phys. Rev. A 83, 013804 (2011).
[CrossRef]

M. I. Mishchenko, L. Liu, D. W. Mackowski, B. Cairns, and G. Videen, “Multiple scattering by random particulate media: exact 3D results,” Opt. Express 15, 2822–2836 (2007).
[CrossRef]

Mishchenko, M. I.

D. W. Mackowski and M. I. Mishchenko, “Direct simulation of multiple scattering by discrete random media illuminated by Gaussian beams,” Phys. Rev. A 83, 013804 (2011).
[CrossRef]

M. I. Mishchenko, L. Liu, D. W. Mackowski, B. Cairns, and G. Videen, “Multiple scattering by random particulate media: exact 3D results,” Opt. Express 15, 2822–2836 (2007).
[CrossRef]

Mishra, S. R.

S. R. Mishra, “A vector wave analysis of a Bessel beam,” Opt. Commun. 85, 159–161 (1991).
[CrossRef]

Mitri, F. G.

Mittra, R.

Y. F. Sun, C. H. Chan, R. Mittra, and L. Tsang, “Characteristic basis function method for solving large problem arising in dense medium scattering,” in IEEE Antennas and Propagation Society International Symposium (IEEE, 2003), pp. 1068–1071.

Peng, Z.

X. Q. Sheng and Z. Peng, “Analysis of scattering by large objects with off-diagonally anisotropic material using finite element-boundary integral-multilevel fast multipole algorithm,” IET Microw. Antennas Propag. 4, 492–500 (2010).
[CrossRef]

Rao, S. M.

S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 30, 409–418 (1982).
[CrossRef]

Sarabandi, K.

P. R. Siqueira and K. Sarabandi, “T-matrix determination of effective permittivity for three-dimensional dense random media,” IEEE Trans. Antennas Propag. 48, 317–327 (2000).
[CrossRef]

Sheng, X. Q.

X. Q. Sheng and Z. Peng, “Analysis of scattering by large objects with off-diagonally anisotropic material using finite element-boundary integral-multilevel fast multipole algorithm,” IET Microw. Antennas Propag. 4, 492–500 (2010).
[CrossRef]

X. Q. Sheng, J. M. Jin, J. M. Song, C. C. Lu, and W. C. Chew, “On the formulation of hybrid finite-element and boundary-integral methods for 3-D scattering,” IEEE Trans. Antennas Propag. 46, 303–311 (1998).
[CrossRef]

Siqueira, P. R.

P. R. Siqueira and K. Sarabandi, “T-matrix determination of effective permittivity for three-dimensional dense random media,” IEEE Trans. Antennas Propag. 48, 317–327 (2000).
[CrossRef]

Song, J. M.

X. Q. Sheng, J. M. Jin, J. M. Song, C. C. Lu, and W. C. Chew, “On the formulation of hybrid finite-element and boundary-integral methods for 3-D scattering,” IEEE Trans. Antennas Propag. 46, 303–311 (1998).
[CrossRef]

Sun, Y. F.

Y. F. Sun, C. H. Chan, R. Mittra, and L. Tsang, “Characteristic basis function method for solving large problem arising in dense medium scattering,” in IEEE Antennas and Propagation Society International Symposium (IEEE, 2003), pp. 1068–1071.

Teixeira, F. L.

B. E. Barrowes, C. O. Ao, F. L. Teixeira, and J. A. Kong, “Sparse matrix/canonical grid method applied to 3-D dense medium simulations,” IEEE Trans. Antennas Propag. 51, 48–58 (2003).
[CrossRef]

Tishkovets, V. P.

V. P. Tishkovets and K. Jockers, “Multiple scattering of light by densely packed random media of spherical particles: dense media vector radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 101, 54–72 (2006).
[CrossRef]

Tsang, L.

C. H. Chart and L. Tsang, “A sparse-matrix canonical-grid method for scattering by many scatterers,” Microw. Opt. Technol. Lett. 8, 114–118 (1995).
[CrossRef]

C. C. Lu, W. C. Chew, and L. Tsang, “The application of recursive aggregate T-matrix algorithm in the Monte Carlo simulations of the extinction rate of random distribution of particles,” Radio Sci. 30, 25–28 (1995).
[CrossRef]

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves, Numerical Simulations (Wiley, 2001).

Y. F. Sun, C. H. Chan, R. Mittra, and L. Tsang, “Characteristic basis function method for solving large problem arising in dense medium scattering,” in IEEE Antennas and Propagation Society International Symposium (IEEE, 2003), pp. 1068–1071.

Varadan, V. K.

V. K. Varadan, V. N. Bringi, V. V. Varadan, and A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

V. V. Varadan and V. K. Varadan, “Multiple scattering of electromagnetic waves by randomly distributed and oriented dielectric scatters,” Phys. Rev. D 21, 388–394 (1980).
[CrossRef]

Varadan, V. V.

V. K. Varadan, V. N. Bringi, V. V. Varadan, and A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

V. V. Varadan and V. K. Varadan, “Multiple scattering of electromagnetic waves by randomly distributed and oriented dielectric scatters,” Phys. Rev. D 21, 388–394 (1980).
[CrossRef]

Videen, G.

Wilton, D. R.

S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 30, 409–418 (1982).
[CrossRef]

Xu, Q.

Yang, X. G.

W. C. Chew, J. H. Lin, and X. G. Yang, “An FFT T-matrix method for 3D microwave scattering solution from random discrete scatterers,” Microw. Opt. Technol. Lett. 9, 194–196 (1995).
[CrossRef]

Zhao, W. J.

Z. W. Cui, Y. P. Han, X. Ai, and W. J. Zhao, “A domain decomposition of the finite element–boundary integral method for scattering by multiple objects,” Electromagnetics 31, 469–482 (2011).
[CrossRef]

Electromagnetics

Z. W. Cui, Y. P. Han, X. Ai, and W. J. Zhao, “A domain decomposition of the finite element–boundary integral method for scattering by multiple objects,” Electromagnetics 31, 469–482 (2011).
[CrossRef]

IEEE Trans. Antennas Propag.

S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 30, 409–418 (1982).
[CrossRef]

P. R. Siqueira and K. Sarabandi, “T-matrix determination of effective permittivity for three-dimensional dense random media,” IEEE Trans. Antennas Propag. 48, 317–327 (2000).
[CrossRef]

B. E. Barrowes, C. O. Ao, F. L. Teixeira, and J. A. Kong, “Sparse matrix/canonical grid method applied to 3-D dense medium simulations,” IEEE Trans. Antennas Propag. 51, 48–58 (2003).
[CrossRef]

X. Q. Sheng, J. M. Jin, J. M. Song, C. C. Lu, and W. C. Chew, “On the formulation of hybrid finite-element and boundary-integral methods for 3-D scattering,” IEEE Trans. Antennas Propag. 46, 303–311 (1998).
[CrossRef]

J. Liu and J. M. Jin, “A novel hybridization of higher order finite element and boundary integral methods for electromagnetic scattering and radiation problems,” IEEE Trans. Antennas Propag. 49, 1794–1806 (2001).
[CrossRef]

IET Microw. Antennas Propag.

X. Q. Sheng and Z. Peng, “Analysis of scattering by large objects with off-diagonally anisotropic material using finite element-boundary integral-multilevel fast multipole algorithm,” IET Microw. Antennas Propag. 4, 492–500 (2010).
[CrossRef]

J. Opt. Soc. Am. A

J. Quant. Spectrosc. Radiat. Transfer

V. P. Tishkovets and K. Jockers, “Multiple scattering of light by densely packed random media of spherical particles: dense media vector radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 101, 54–72 (2006).
[CrossRef]

Microw. Opt. Technol. Lett.

C. H. Chart and L. Tsang, “A sparse-matrix canonical-grid method for scattering by many scatterers,” Microw. Opt. Technol. Lett. 8, 114–118 (1995).
[CrossRef]

W. C. Chew, J. H. Lin, and X. G. Yang, “An FFT T-matrix method for 3D microwave scattering solution from random discrete scatterers,” Microw. Opt. Technol. Lett. 9, 194–196 (1995).
[CrossRef]

Opt. Commun.

S. R. Mishra, “A vector wave analysis of a Bessel beam,” Opt. Commun. 85, 159–161 (1991).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev.

L. L. Foldy, “The multiple scattering of waves. I. General theory of isotropic scattering by randomly distributed scatterers,” Phys. Rev. 67, 107–119 (1945).
[CrossRef]

Phys. Rev. A

D. W. Mackowski and M. I. Mishchenko, “Direct simulation of multiple scattering by discrete random media illuminated by Gaussian beams,” Phys. Rev. A 83, 013804 (2011).
[CrossRef]

Phys. Rev. D

V. V. Varadan and V. K. Varadan, “Multiple scattering of electromagnetic waves by randomly distributed and oriented dielectric scatters,” Phys. Rev. D 21, 388–394 (1980).
[CrossRef]

Radio Sci.

V. K. Varadan, V. N. Bringi, V. V. Varadan, and A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

K. Furutsu, “Multiple scattering of waves in a medium of randomly distributed particles and derivation of the transport equation,” Radio Sci. 10, 29–44 (1975).
[CrossRef]

C. C. Lu, W. C. Chew, and L. Tsang, “The application of recursive aggregate T-matrix algorithm in the Monte Carlo simulations of the extinction rate of random distribution of particles,” Radio Sci. 30, 25–28 (1995).
[CrossRef]

Rev. Mod. Phys.

M. Lax, “Multiple scattering of waves,” Rev. Mod. Phys. 23, 287–310 (1951).
[CrossRef]

Waves Random Complex Media

Z. W. Cui, Y. P. Han, and C. Y. Li, “Simulation of electromagnetic scattering by random discrete particles using a hybrid FE-BI-CBFM technique,” Waves Random Complex Media 22, 234–248 (2012).
[CrossRef]

Other

Y. F. Sun, C. H. Chan, R. Mittra, and L. Tsang, “Characteristic basis function method for solving large problem arising in dense medium scattering,” in IEEE Antennas and Propagation Society International Symposium (IEEE, 2003), pp. 1068–1071.

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University, 1957).

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves, Numerical Simulations (Wiley, 2001).

J. M. Jin, The Finite Element Method in Electromagnetics (Wiley, 2002).

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 (9)

Fig. 1.
Fig. 1.

Illustration of 125 randomly distributed uniform spherical particles generated with the Monte Carlo method.

Fig. 2.
Fig. 2.

Geometry of Cartesian coordinates of the beam and particle.

Fig. 3.
Fig. 3.

Illustration of a 3×3×3 array of spherical particles.

Fig. 4.
Fig. 4.

DSCS for a 3×3×3 array of spherical particles illuminated by a plane wave and a Bessel beam: (a) E-plane and (b) H-plane.

Fig. 5.
Fig. 5.

Comparison of the DSCS for multiple scattering and independent scattering: (a) E-plane and (b) H-plane.

Fig. 6.
Fig. 6.

Illustration of 512 randomly distributed inhomogeneous spherical particles.

Fig. 7.
Fig. 7.

Effects of the beam center position on the DSCS: (a) E-plane and (b) H-plane.

Fig. 8.
Fig. 8.

Illustration of 1000 randomly distributed anisotropic spherical particles.

Fig. 9.
Fig. 9.

Angular distributions of the DSCS for 1000 randomly distributed anisotropic spherical particles in different incident values of angle α, β, and γ: (a) E-plane and (b) H-plane.

Equations (24)

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

f=4πM3l3r3.
[xx0yy0zz0]=A[uvw],
A=[a11a12a13a21a22a23a31a32a33],
a11=cosαcosβcosγsinαsinγ,a12=cosαcosβsinγsinαcosγ,a13=cosαsinβ,a21=sinαcosβcosγ+cosαsinγ,a22=sinαcosβsinγ+cosαcosγ,a23=sinαsinβ,a31=sinβcosγ,a32=sinβsinγ,a33=cosβ.
[ExEyEz]=A[EuEvEw],[HxHyHz]=A[HuHvHw].
Eu=12E0[(1+kwkkr2u2k2r2)J0(krr)kr(v2u2)k2r3J1(krr)]exp(ikww),
Ev=12E0[2kruvk2r3J1(krr)kr2uvk2r2J0(krr)]exp(ikww),
Ew=12E0[iukr(1+kwk)krJ1(krr)]exp(ikww),
Hu=12H0[2kruvk2r3J1(krr)kr2uvk2r2J0(krr)]exp(ikww),
Hv=12H0[(1+kwkkr2v2k2r2)J0(krr)kr(u2v2)k2r3J1(krr)]exp(ikww),
Hw=12H0[ivkr(1+kwk)krJ1(krr)]exp(ikww),
F(Ei)=12Vi[1μr(×Ei)·(×Ei)k02εrEi·Ei]dV+ik0Z0Si(Ei×Hi)·n^idS·
[KiIIKiIS0KiSIKiSSBi]{EiIEiSHiS}={00},
[K˜iSS]{EiS}+[Bi]{HiS}={0},
[K˜iSS]=[KiSS][KiSI][KiII]1[KiIS].
{E1SE2SEMS}=[S1S2SM]{H1SH2SHMS},
[Si]=[K˜iSS]1[Bi](i=1,2,,M).
|n^i×Mi+j=1M[Z0Lj(Jj)Kj(Mj)]=Einc|tan(Si),
|Ji×n^i+j=1M[1Z0Lj(Mj)+Kj(Jj)]=Hinc|tan(Si),
CFIEi=EFIEi+n^i×Z0MFIEi,
[P11P12P1MP21P22P2MPM1PM2PMM]{E1SE2SEMS}+[Q11Q12Q1MQ21Q22Q2MQM1QM2QMM]{H1SH2SHMS}={b1b2bM},
[Z11Z12Z1MZ21Z22Z2MZM1ZM2ZMM]{H1SH2SHMS}={b1b2bM},
σ=limr4πr2|Efarsca|2|E0|2,
εr=[3.02i02i3.00004.0]

Metrics