Abstract

In this paper, we present an efficient numerical method for the simulation of multiple scattering by random discrete particles illuminated by focused Gaussian beams with arbitrary incidence. Specifically, the Davis first-order approximation in combination with rotation Euler angles is used to represent the arbitrarily incident Gaussian beams. The surface integral equations are applied to formulate the scattering problems involving multiple discrete particles with a random distribution and are numerically discretized by the method of moments. The resultant matrix equation is solved by employing the characteristic basis function method based on the use of macrobasis functions constructed according to the Foldy–Lax multiple scattering equations. Since this method only requires the solution of small-size matrix equations associated with isolated particles and it is also readily parallelized, the computational burden can be significantly relieved. Some numerical results are included to illustrate the validity of the present method and to show the scattering behaviors of random discrete particles when they are illuminated by focused Gaussian beams.

© 2011 Optical Society of America

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  1. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).
  2. 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]
  3. M. Lax, “Multiple scattering of waves,” Rev. Mod. Phys. 23, 287–310 (1951).
    [CrossRef]
  4. 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]
  5. 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]
  6. 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]
  7. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000).
  8. 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]
  9. L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2001).
    [CrossRef]
  10. 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]
  11. 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]
  12. 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]
  13. 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] [PubMed]
  14. 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]
  15. 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]
  16. Y. F. Sun, C. H. Chan, R. Mittra, and L. Tsang, “Characteristic basis function method for solving large problem arising in dense medium scattering,” IEEE Antennas Propagation Society International Symposium (IEEE, 2003), pp. 1068–1071.
  17. 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]
  18. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
    [CrossRef]
  19. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University, 1957).
  20. K. Umashankar, A. Taflove, and S. M. Rao, “Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects,” IEEE Trans. Antennas Propag. 34, 758–766 (1986).
    [CrossRef]
  21. X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, “Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies,” IEEE Trans. Antennas Propag. 46, 1718–1726 (1998).
    [CrossRef]
  22. 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]
  23. V. V. S. Prakash and R. Mittra, “Characteristic basis function method: anew technique for efficient solution of method of moments matrix equations,” Microw. Opt. Technol. Lett. 36, 95–100 (2003).
    [CrossRef]
  24. S. J. Kwon, K. Du, and R. Mittra, “Characteristic basis function method a numerically efficient technique for analyzing microwave and RF circuits,” Microw. Opt. Technol. Lett. 38, 444–448(2003).
    [CrossRef]
  25. E. Lucente, A. Monorchio, and R. Mittra, “An iteration-free MoM approach based on excitation independent characteristic basis functions for solving large multiscale electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 56, 999–1007 (2008).
    [CrossRef]
  26. G. D. Han and C. Q. Gu, “A hybrid QR factorization with dual-MGS and adaptively modified characteristic basis function method for electromagnetic scattering analysis,” Microw. Opt. Technol. Lett. 49, 2879–2883 (2007).
    [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]

2008

E. Lucente, A. Monorchio, and R. Mittra, “An iteration-free MoM approach based on excitation independent characteristic basis functions for solving large multiscale electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 56, 999–1007 (2008).
[CrossRef]

2007

G. D. Han and C. Q. Gu, “A hybrid QR factorization with dual-MGS and adaptively modified characteristic basis function method for electromagnetic scattering analysis,” Microw. Opt. Technol. Lett. 49, 2879–2883 (2007).
[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] [PubMed]

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]

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

V. V. S. Prakash and R. Mittra, “Characteristic basis function method: anew technique for efficient solution of method of moments matrix equations,” Microw. Opt. Technol. Lett. 36, 95–100 (2003).
[CrossRef]

S. J. Kwon, K. Du, and R. Mittra, “Characteristic basis function method a numerically efficient technique for analyzing microwave and RF circuits,” Microw. Opt. Technol. Lett. 38, 444–448(2003).
[CrossRef]

2001

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

Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000).

1998

X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, “Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies,” IEEE Trans. Antennas Propag. 46, 1718–1726 (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]

1986

K. Umashankar, A. Taflove, and S. M. Rao, “Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects,” IEEE Trans. Antennas Propag. 34, 758–766 (1986).
[CrossRef]

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]

1979

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[CrossRef]

1978

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

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]

1957

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

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]

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).
[CrossRef]

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,” IEEE Antennas 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, W. C. Chew, and C. C. Lu, “Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies,” IEEE Trans. Antennas Propag. 46, 1718–1726 (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]

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]

Davis, L. W.

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[CrossRef]

Ding, K. H.

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

Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000).

Du, K.

S. J. Kwon, K. Du, and R. Mittra, “Characteristic basis function method a numerically efficient technique for analyzing microwave and RF circuits,” Microw. Opt. Technol. Lett. 38, 444–448(2003).
[CrossRef]

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]

Gu, C. Q.

G. D. Han and C. Q. Gu, “A hybrid QR factorization with dual-MGS and adaptively modified characteristic basis function method for electromagnetic scattering analysis,” Microw. Opt. Technol. Lett. 49, 2879–2883 (2007).
[CrossRef]

Han, G. D.

G. D. Han and C. Q. Gu, “A hybrid QR factorization with dual-MGS and adaptively modified characteristic basis function method for electromagnetic scattering analysis,” Microw. Opt. Technol. Lett. 49, 2879–2883 (2007).
[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]

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

Jin, J. M.

X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, “Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies,” IEEE Trans. Antennas Propag. 46, 1718–1726 (1998).
[CrossRef]

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).
[CrossRef]

Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000).

Kwon, S. J.

S. J. Kwon, K. Du, and R. Mittra, “Characteristic basis function method a numerically efficient technique for analyzing microwave and RF circuits,” Microw. Opt. Technol. Lett. 38, 444–448(2003).
[CrossRef]

Lax, M.

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

Lu, C. C.

X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, “Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies,” IEEE Trans. Antennas Propag. 46, 1718–1726 (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]

Lucente, E.

E. Lucente, A. Monorchio, and R. Mittra, “An iteration-free MoM approach based on excitation independent characteristic basis functions for solving large multiscale electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 56, 999–1007 (2008).
[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] [PubMed]

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] [PubMed]

Mittra, R.

E. Lucente, A. Monorchio, and R. Mittra, “An iteration-free MoM approach based on excitation independent characteristic basis functions for solving large multiscale electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 56, 999–1007 (2008).
[CrossRef]

S. J. Kwon, K. Du, and R. Mittra, “Characteristic basis function method a numerically efficient technique for analyzing microwave and RF circuits,” Microw. Opt. Technol. Lett. 38, 444–448(2003).
[CrossRef]

V. V. S. Prakash and R. Mittra, “Characteristic basis function method: anew technique for efficient solution of method of moments matrix equations,” Microw. Opt. Technol. Lett. 36, 95–100 (2003).
[CrossRef]

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

Monorchio, A.

E. Lucente, A. Monorchio, and R. Mittra, “An iteration-free MoM approach based on excitation independent characteristic basis functions for solving large multiscale electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 56, 999–1007 (2008).
[CrossRef]

Prakash, V. V. S.

V. V. S. Prakash and R. Mittra, “Characteristic basis function method: anew technique for efficient solution of method of moments matrix equations,” Microw. Opt. Technol. Lett. 36, 95–100 (2003).
[CrossRef]

Rao, S. M.

K. Umashankar, A. Taflove, and S. M. Rao, “Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects,” IEEE Trans. Antennas Propag. 34, 758–766 (1986).
[CrossRef]

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, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, “Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies,” IEEE Trans. Antennas Propag. 46, 1718–1726 (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, W. C. Chew, and C. C. Lu, “Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies,” IEEE Trans. Antennas Propag. 46, 1718–1726 (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,” IEEE Antennas Propagation Society International Symposium (IEEE, 2003), pp. 1068–1071.

Taflove, A.

K. Umashankar, A. Taflove, and S. M. Rao, “Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects,” IEEE Trans. Antennas Propag. 34, 758–766 (1986).
[CrossRef]

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.

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

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

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]

Umashankar, K.

K. Umashankar, A. Taflove, and S. M. Rao, “Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects,” IEEE Trans. Antennas Propag. 34, 758–766 (1986).
[CrossRef]

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]

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]

IEEE Trans. Antennas Propag.

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]

K. Umashankar, A. Taflove, and S. M. Rao, “Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects,” IEEE Trans. Antennas Propag. 34, 758–766 (1986).
[CrossRef]

X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, “Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies,” IEEE Trans. Antennas Propag. 46, 1718–1726 (1998).
[CrossRef]

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]

E. Lucente, A. Monorchio, and R. Mittra, “An iteration-free MoM approach based on excitation independent characteristic basis functions for solving large multiscale electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 56, 999–1007 (2008).
[CrossRef]

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]

G. D. Han and C. Q. Gu, “A hybrid QR factorization with dual-MGS and adaptively modified characteristic basis function method for electromagnetic scattering analysis,” Microw. Opt. Technol. Lett. 49, 2879–2883 (2007).
[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]

V. V. S. Prakash and R. Mittra, “Characteristic basis function method: anew technique for efficient solution of method of moments matrix equations,” Microw. Opt. Technol. Lett. 36, 95–100 (2003).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Three examples of random discrete particles generated from the Monte Carlo method: (a)  M = 125 , (b)  M = 512 , (c)  M = 1000 .

Fig. 2
Fig. 2

Illustration of an arbitrarily incident Gaus sian beam impinging on multiple discrete particles with a random distribution.

Fig. 3
Fig. 3

Comparison of the DSCS for a 2 × 2 × 2 array of spherical particles obtained from the CBFM and the T-matrix method: (a) E-plane, (b) H-plane.

Fig. 4
Fig. 4

DSCSs for 125 randomly distributed particles illuminated by a plane wave and a Gaussian beam: (a) E-plane, (b) H-plane.

Fig. 5
Fig. 5

Illustration of the effects of the obliquely incident angle on the DSCS.

Fig. 6
Fig. 6

DSCSs for 1000 randomly distributed particles illuminated by a Gaussian beam with oblique incidence.

Fig. 7
Fig. 7

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

Equations (55)

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f = 4 π M 3 l 3 r 3 ,
[ x y z ] = A α A β A γ [ x y z ] ,
A α = [ cos α sin α 0 sin α cos α 0 0 0 1 ] ,
A β = [ cos β 0 sin β 0 1 0 sin β 0 cos β ] ,
A γ = [ cos γ sin γ 0 sin γ cos γ 0 0 0 1 ] .
E u = E 0 Ψ e i k w , E v = 0 , E w = 2 u l Q E u ,
H u = 0 , H v = H 0 Ψ e i k w , H w = 2 v l Q H v ,
Ψ = i Q exp [ i Q ( ξ 2 + η 2 ) ] ,
Q = 1 i 2 ζ ,
ξ = u ω 0 , η = v ω 0 , ζ = w l ,
[ x 0 y 0 z 0 ] = A 1 [ x 0 y 0 z 0 ] ,
E x = E 0 Ψ e i k 0 ( z z 0 ) , E y = 0 , E z = 2 x x 0 l Q E x ,
H x = 0 , H y = H 0 Ψ e i k 0 ( z z 0 ) , H z = 2 y y 0 l Q H y ,
ξ = x x 0 ω 0 , η = y y 0 ω 0 , ζ = z z 0 l .
[ E x E y E z ] = A [ E x E y E z ] , [ H x H y H z ] = A [ H x H y H z ] ,
[ x y z ] = A 1 [ x y z ] .
E 0 sca = i = 1 M [ Z 0 L 0 ( J i ) K 0 ( M i ) ] ,
H 0 sca = i = 1 M [ K 0 ( J i ) + 1 Z 0 L 0 ( M i ) ] ,
L 0 ( X i ) = i k 0 S i [ X i ( r ) + 1 k 0 2 ( · X i ( r ) ) ] G 0 ( r , r ) d S ,
K 0 ( X i ) = S i X i ( r ) × G 0 ( r , r ) d S ,
G 0 ( r , r ) = e i k 0 | r r | 4 π | r r | ,
E i sca = Z p L p ( J i ) K p ( M i ) ,
H i sca = K p ( J i ) + 1 Z p L p ( M i ) ,
| j = 1 M [ Z 0 L 0 ( J j ) K 0 ( M j ) ] + [ Z p L p ( J i ) K p ( M i ) ] = E i inc | tan ( S i )
| j = 1 M [ K 0 ( J j ) + 1 Z 0 L 0 ( M j ) ] + [ K p ( J i ) + 1 Z p L p ( M i ) ] = H i inc | tan ( S i ) ,
[ A 11 A 12 A 1 M A 21 A 22 A 2 M A M 1 A M 2 A M M ] { J 1 J 2 J M } + [ B 11 B 12 B 1 M B 21 B 22 B 2 M B M 1 B M 2 B M M ] { M 1 M 2 M M } = { V 1 E V 2 E V M E } ,
A i i , m n = S i g i , m · [ Z 0 L 0 ( g i , n ) + Z p L p ( g i , n ) ] d S ,
A i j , m n = S i g i , m · [ Z 0 L 0 ( g j , n ) ] d S ( i j ) ,
B i i , m n = S i g i , m · [ K 0 ( g i , n ) + K p ( g i , n ) ] d S ,
B i j , m n = S i g i , m · [ K 0 ( g j , n ) ] d S ( i j ) ,
V i , m E = S i g i , m · E i inc d S ,
[ C 11 C 12 C 1 M C 21 C 22 C 2 M C M 1 C M 2 C M M ] { J 1 J 2 J M } + [ D 11 D 12 D 1 M D 21 D 22 D 2 M D M 1 D M 2 D M M ] { M 1 M 2 M M } = { V 1 H V 2 H V M H } .
C i i , m n = S i g i , m · [ K 0 ( g i , n ) + K p ( g i , n ) ] d S ,
C i j , m n = S i g i , m · [ K 0 ( g j , n ) ] d S ( i j ) ,
D i i , m n = S i g i , m · [ 1 Z 0 L 0 ( g i , n ) + 1 Z p L p ( g i , n ) ] d S ,
D i j , m n = S i g i , m · [ 1 Z 0 L 0 ( g j , n ) ] d S ( i j ) ,
V i , m H = S i g i , m · H i inc d S .
[ A 11 B 11 A 1 M B 1 M C 11 D 11 C 1 M D 1 M A M 1 B M 1 A M M B M M C M 1 D M 1 C M M D M M ] { J 1 M 1 J M M M } = { V 1 E V 1 H V M E V M H } .
Z i j = [ A i j B i j C i j D i j ] ( i , j = 1 , 2 , , M )
I i = { J i M i } , V i = { V i E V i H } .
[ Z 11 Z 12 Z 1 M Z 21 Z 22 Z 2 M Z M 1 Z M 2 Z M M ] [ I 1 I 2 I M ] = [ V 1 V 2 V M ] .
Z i i · I i + j = 1 ( j i ) M [ Z i j · I j ] = V i ,
Z i i · I i = V i j = 1 ( j i ) M [ Z i j · I j ] .
Z i i · I i CBF s = V i ,
Z i i · I i CBF s = j = 1 ( j i ) M [ Z i j · I j ] .
Z i i · I i P = V i .
Z i i · I i S 1 = j = 1 ( j i ) M [ Z i j · I j P ] .
Z i i · I i S 2 = j = 1 ( j i ) M [ Z i j · I j S 1 ] .
I i = a i I i P + b i I i S 1 + c i I i S 2 ,
[ Z 11 Z 12 Z 1 M Z 21 Z 22 Z 2 M Z M 1 Z M 2 Z M M ] [ a 1 I 1 P + b 1 I 1 S 1 + c 1 I 1 S 2 a 2 I 2 P + b 2 I 2 S 1 + c 2 I 2 S 2 a M I M P + b M I M S 1 + c M I M S 2 ] = [ V 1 V 2 V M ] .
[ Z 11 · I 1 P Z 11 · I 1 S 1 Z 11 · I 1 S 2 Z 1 M · I M P Z 1 M · I M S 1 Z 1 M · I M S 2 Z 21 · I 1 P Z 21 · I 1 S 1 Z 21 · I 1 S 2 Z 2 M · I M P Z 2 M · I M S 1 Z 2 M · I M S 2 Z M 1 · I 1 P Z M 1 · I 1 S 1 Z M 1 · I 1 S 2 Z M M · I M P Z M M · I M S 1 Z M M · I M S 2 ] [ a 1 b 1 c 1 a M b M c M ] = [ V 1 V 2 V M ] .
[ Z ˜ 11 Z ˜ 12 Z ˜ 1 M Z ˜ 21 Z ˜ 22 Z ˜ 2 M Z ˜ M 1 Z ˜ M 2 Z ˜ M M ] [ I ˜ 1 I ˜ 2 I ˜ M ] = [ V ˜ 1 V ˜ 2 V ˜ M ] ,
Z ˜ i j = [ ( I i P ) T · Z i j · I j P ( I i P ) T · Z i j · I j S 1 ( I i P ) T · Z i j · I j S 2 ( I i S 1 ) T · Z i j · I j P ( I i S 1 ) T · Z i j · I j S 1 ( I i S 1 ) T · Z i j · I j S 2 ( I i S 2 ) T · Z i j · I j P ( I i S 2 ) T · Z i j · I j S 1 ( I i S 2 ) T · Z i j · I j S 2 ] ,
I ˜ i = [ a i b i c i ] , V ˜ i = [ ( I i P ) T · V i ( I i S 1 ) T · V i ( I i S 2 ) T · V i ] ,
σ = lim r 4 π r 2 | E far sca | 2 | E 0 | 2 ,

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