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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 30, Iss. 11 — Nov. 1, 2013
  • pp: 2320–2327

Multiple scattering of arbitrarily incident Bessel beams by random discrete particles

Zhiwei Cui, Yiping Han, and Xia Ai  »View Author Affiliations

JOSA A, Vol. 30, Issue 11, pp. 2320-2327 (2013)

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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

OCIS Codes
(140.0140) Lasers and laser optics : Lasers and laser optics
(290.4210) Scattering : Multiple scattering
(290.5850) Scattering : Scattering, particles
(050.1755) Diffraction and gratings : Computational electromagnetic methods

ToC Category:

Original Manuscript: August 29, 2013
Revised Manuscript: September 27, 2013
Manuscript Accepted: September 27, 2013
Published: October 24, 2013

Virtual Issues
Vol. 9, Iss. 1 Virtual Journal for Biomedical Optics

Zhiwei Cui, Yiping Han, and Xia Ai, "Multiple scattering of arbitrarily incident Bessel beams by random discrete particles," J. Opt. Soc. Am. A 30, 2320-2327 (2013)

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  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]

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