## Scattering of Gaussian beam by arbitrarily shaped particles with multiple internal inclusions |

Optics Express, Vol. 20, Issue 2, pp. 718-731 (2012)

http://dx.doi.org/10.1364/OE.20.000718

Acrobat PDF (2220 KB)

### Abstract

In this paper, we introduce an efficient numerical method based on surface integral equations to characterize the scattering of an arbitrarily incident Gaussian beam by arbitrarily shaped particles with multiple internal inclusions. The incident Gaussian beam is described by the Davis–Barton fifth-order approximation in combination with rotation Euler angles. For numerical purposes, the surfaces of the host particle and the inclusions are modeled using small triangular patches and the established surface integral equations are discretized with the method of moments. The resultant matrix equation is solved by using a parallel implementation of conjugate gradient method on distributed-memory architectures. Some numerical results are included to illustrate the validity and capability of the developed method. These results are also expected to provide useful insights into the scattering of Gaussian beam by composite particles.

© 2012 OSA

## 1. Introduction

1. F. Borghese, P. Denti, R. Saija, and O. I. Sindoni, “Optical properties of spheres containing a spherical eccentric inclusion,” J. Opt. Soc. Am. A **9**(8), 1327–1335 (1992). [CrossRef]

24. B. Yan, H. Y. Zhang, and C. H. Liu, “Scattering of Gaussian beam by a spheroidal particle with a spherical inclusion at the center,” Opt. Commun. **284**(16–17), 3811–3815 (2011). [CrossRef]

1. F. Borghese, P. Denti, R. Saija, and O. I. Sindoni, “Optical properties of spheres containing a spherical eccentric inclusion,” J. Opt. Soc. Am. A **9**(8), 1327–1335 (1992). [CrossRef]

15. S. Xian-Ming, W. Hai-Hua, L. Wan-Qiang, and S. Jin, “Light scattering by a spherical particle with multiple densely packed inclusions,” Chin. Phys. B **18**(3), 1040–1044 (2009). [CrossRef]

*et al*. [16

16. E. E. Khaled, S. C. Hill, and P. W. Barber, “Light scattering by a coated sphere illuminated with a Gaussian beam,” Appl. Opt. **33**(15), 3308–3314 (1994). [CrossRef] [PubMed]

*et al.*[19

19. G. X. Han, Y. P. Han, J. Y. Liu, and Y. Zhang, “Scattering of an eccentric sphere arbitrarily located in a shaped beam,” J. Opt. Soc. Am. B **25**(12), 2064–2072 (2008). [CrossRef]

*et al.*[20

20. B. Yan, X. E. Han, and K. F. Ren, “Scattering of a shaped beam by a spherical particle with an eccentric spherical inclusion,” J. Opt. A **11**(1), 015705 (2009). [CrossRef]

*et al.*[21

21. J. J. Wang, G. Gouesbet, Y. P. Han, and G. Gréhan, “Study of scattering from a sphere with an eccentrically located spherical inclusion by generalized Lorenz-Mie theory: internal and external field distribution,” J. Opt. Soc. Am. A **28**(1), 24–39 (2011). [CrossRef] [PubMed]

22. J. J. Wang, G. Gouesbet, G. Gréhan, Y. P. Han, and S. Saengkaew, “Morphology-dependent resonances in an eccentrically layered sphere illuminated by a tightly focused off-axis Gaussian beam: parallel and perpendicular beam incidence,” J. Opt. Soc. Am. A **28**(9), 1849–1859 (2011). [CrossRef]

23. H. Y. Zhang and T. Q. Liao, “Scattering of Gaussian beam by a spherical particle with a spheroidal inclusion,” J. Quant. Spectrosc. Radiat. Transf. **112**(9), 1486–1491 (2011). [CrossRef]

*et al.*[24

24. B. Yan, H. Y. Zhang, and C. H. Liu, “Scattering of Gaussian beam by a spheroidal particle with a spherical inclusion at the center,” Opt. Commun. **284**(16–17), 3811–3815 (2011). [CrossRef]

25. J. P. Barton and D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. **66**(7), 2800–2802 (1989). [CrossRef]

27. G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz-Mie theories through rotations of coordinate systemsIII. Special Euler angles,” Opt. Commun. **283**(17), 3235–3243 (2010). [CrossRef]

28. S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antenn. Propag. **30**(3), 409–418 (1982). [CrossRef]

32. Z. W. Cui, Y. P. Han, and M. L. Li, “Solution of CFIE-JMCFIE using parallel MOM for scattering by dielectrically coated conducting bodies,” J. Electromagn. Waves Appl. **25**(2), 211–222 (2011). [CrossRef]

28. S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antenn. Propag. **30**(3), 409–418 (1982). [CrossRef]

32. Z. W. Cui, Y. P. Han, and M. L. Li, “Solution of CFIE-JMCFIE using parallel MOM for scattering by dielectrically coated conducting bodies,” J. Electromagn. Waves Appl. **25**(2), 211–222 (2011). [CrossRef]

## 2. Description of the incident Gaussian beam

34. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A **19**(3), 1177–1179 (1979). [CrossRef]

*et al*[17]. In this study, we adopt the Davis-Barton fifth-order approximation [25

25. J. P. Barton and D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. **66**(7), 2800–2802 (1989). [CrossRef]

27. G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz-Mie theories through rotations of coordinate systemsIII. Special Euler angles,” Opt. Commun. **283**(17), 3235–3243 (2010). [CrossRef]

25. J. P. Barton and D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. **66**(7), 2800–2802 (1989). [CrossRef]

## 3. Surface integral equation method

## 4. Numerical results and discussion

40. D. W. Mackowski, “A simplified model to predict the effects of aggregation on the absorption properties of soot particles,” J. Quant. Spectrosc. Radiat. Transf. **100**(1–3), 237–249 (2006). [CrossRef]

## 5. Conclusion

## References and links

1. | F. Borghese, P. Denti, R. Saija, and O. I. Sindoni, “Optical properties of spheres containing a spherical eccentric inclusion,” J. Opt. Soc. Am. A |

2. | N. C. Skaropoulos, M. P. Ioannidou, and D. P. Chrissoulidis, “Indirect mode-matching solution to scattering from a dielectric sphere with an eccentric inclusion,” J. Opt. Soc. Am. A |

3. | F. Borghese, P. Denti, and R. Saija, “Optical properties of spheres containing several spherical inclusions,” Appl. Opt. |

4. | G. Videen, D. Ngo, P. Chylek, and R. G. Pinnick, “Light scattering from a sphere with an irregular inclusion,” J. Opt. Soc. Am. A |

5. | D. Ngo, G. Videen, and P. Chýlek, “A FORTRAN code for the scattering of EM waves by a sphere with a nonconcentric spherical inclusion,” Comput. Phys. Commun. |

6. | A. Macke, M. I. Mishchenko, and B. Cairns, “The influence of inclusions on light scattering by large ice particles,” J. Geophys. Res. |

7. | M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, |

8. | D. R. Prabhu, M. Davies, and G. Videen, “Light scattering calculations from oleic-acid droplets with water inclusions,” Opt. Express |

9. | M. P. Ioannidou and D. P. Chrissoulidis, “Electromagnetic-wave scattering by a sphere with multiple spherical inclusions,” J. Opt. Soc. Am. A |

10. | T. Weigel, J. Schulte, and G. Schweiger, “Inelastic scattering on particles with inclusions,” J. Opt. Soc. Am. A |

11. | A. Doicu, T. Wriedt, and Y. A. Eremin, |

12. | A. P. Moneda and D. P. Chrissoulidis, “Dyadic Green’s function of a sphere with an eccentric spherical inclusion,” J. Opt. Soc. Am. A |

13. | D. K. Wu and Y. P. Zhou, “Forward scattering light of droplets containing different size inclusions,” Appl. Opt. |

14. | M. Mikrenska and P. Koulev, “Simulation of light scattering by large particles with randomly distributed spherical or cubic inclusions,” J. Quant. Spectrosc. Radiat. Transf. |

15. | S. Xian-Ming, W. Hai-Hua, L. Wan-Qiang, and S. Jin, “Light scattering by a spherical particle with multiple densely packed inclusions,” Chin. Phys. B |

16. | E. E. Khaled, S. C. Hill, and P. W. Barber, “Light scattering by a coated sphere illuminated with a Gaussian beam,” Appl. Opt. |

17. | G. Gouesbet and G. Gréhan, |

18. | G. Gouesbet and G. Gréhan, “Generalized Lorenz-Mie theory for a sphere with an eccentrically located spherical inclusion,” J. Mod. Opt. |

19. | G. X. Han, Y. P. Han, J. Y. Liu, and Y. Zhang, “Scattering of an eccentric sphere arbitrarily located in a shaped beam,” J. Opt. Soc. Am. B |

20. | B. Yan, X. E. Han, and K. F. Ren, “Scattering of a shaped beam by a spherical particle with an eccentric spherical inclusion,” J. Opt. A |

21. | J. J. Wang, G. Gouesbet, Y. P. Han, and G. Gréhan, “Study of scattering from a sphere with an eccentrically located spherical inclusion by generalized Lorenz-Mie theory: internal and external field distribution,” J. Opt. Soc. Am. A |

22. | J. J. Wang, G. Gouesbet, G. Gréhan, Y. P. Han, and S. Saengkaew, “Morphology-dependent resonances in an eccentrically layered sphere illuminated by a tightly focused off-axis Gaussian beam: parallel and perpendicular beam incidence,” J. Opt. Soc. Am. A |

23. | H. Y. Zhang and T. Q. Liao, “Scattering of Gaussian beam by a spherical particle with a spheroidal inclusion,” J. Quant. Spectrosc. Radiat. Transf. |

24. | B. Yan, H. Y. Zhang, and C. H. Liu, “Scattering of Gaussian beam by a spheroidal particle with a spherical inclusion at the center,” Opt. Commun. |

25. | J. P. Barton and D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. |

26. | A. R. Edmonds, |

27. | G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz-Mie theories through rotations of coordinate systemsIII. Special Euler angles,” Opt. Commun. |

28. | S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antenn. Propag. |

29. | S. M. Rao, C. C. Cha, R. L. Cravey, and D. Wilkes, “Electromagnetic scattering from arbitrary shaped conducting bodies coated with lossy materials of arbitrary thickness,” IEEE Trans. Antenn. Propag. |

30. | P. Ylä-Oijala, M. Taskinen, and J. Sarvas, “Surface integral equation method for general composite metallic and dielectric structures with junctions,” Prog. Electromagn. Res. |

31. | J. Rivero, J. M. Taboada, L. Landesa, F. Obelleiro, and I. García-Tuñón, “Surface integral equation formulation for the analysis of left-handed metamaterials,” Opt. Express |

32. | Z. W. Cui, Y. P. Han, and M. L. Li, “Solution of CFIE-JMCFIE using parallel MOM for scattering by dielectrically coated conducting bodies,” J. Electromagn. Waves Appl. |

33. | R. F. Harrington, |

34. | L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A |

35. | Z. W. Cui, Y. P. Han, and H. Y. Zhang, “Scattering of an arbitrarily incident focused Gaussian beam by arbitrarily shaped dielectric particles,” J. Opt. Soc. Am. B |

36. | 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 |

37. | D. A. Dunavant, “High degree efficient symmetrical Gaussian quadrature rules for the triangle,” Int. J. Numer. Methods Eng. |

38. | R. D. Graglia, “On the numerical integration of the linear shape functions times the 3-D green’s function or its gradient on a plane triangle,” IEEE Trans. Antenn. Propag. |

39. | L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, |

40. | D. W. Mackowski, “A simplified model to predict the effects of aggregation on the absorption properties of soot particles,” J. Quant. Spectrosc. Radiat. Transf. |

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(290.5850) Scattering : Scattering, particles

(140.3295) Lasers and laser optics : Laser beam characterization

**ToC Category:**

Scattering

**History**

Original Manuscript: November 3, 2011

Revised Manuscript: December 8, 2011

Manuscript Accepted: December 18, 2011

Published: January 3, 2012

**Citation**

Yiping Han, Zhiwei Cui, and Wenjuan Zhao, "Scattering of Gaussian beam by arbitrarily shaped particles with multiple internal inclusions," Opt. Express **20**, 718-731 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-2-718

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### References

- F. Borghese, P. Denti, R. Saija, and O. I. Sindoni, “Optical properties of spheres containing a spherical eccentric inclusion,” J. Opt. Soc. Am. A9(8), 1327–1335 (1992). [CrossRef]
- N. C. Skaropoulos, M. P. Ioannidou, and D. P. Chrissoulidis, “Indirect mode-matching solution to scattering from a dielectric sphere with an eccentric inclusion,” J. Opt. Soc. Am. A11(6), 1859–1866 (1994). [CrossRef]
- F. Borghese, P. Denti, and R. Saija, “Optical properties of spheres containing several spherical inclusions,” Appl. Opt.33(3), 484–493 (1994). [CrossRef] [PubMed]
- G. Videen, D. Ngo, P. Chylek, and R. G. Pinnick, “Light scattering from a sphere with an irregular inclusion,” J. Opt. Soc. Am. A12(5), 922–928 (1995). [CrossRef]
- D. Ngo, G. Videen, and P. Chýlek, “A FORTRAN code for the scattering of EM waves by a sphere with a nonconcentric spherical inclusion,” Comput. Phys. Commun.99(1), 94–112 (1996). [CrossRef]
- A. Macke, M. I. Mishchenko, and B. Cairns, “The influence of inclusions on light scattering by large ice particles,” J. Geophys. Res.101(D18), 23311–23316 (1996). [CrossRef]
- M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles:Ttheory, Measurements, and Applications (Academic, San Diego, 2000).
- D. R. Prabhu, M. Davies, and G. Videen, “Light scattering calculations from oleic-acid droplets with water inclusions,” Opt. Express8(6), 308–313 (2001). [CrossRef] [PubMed]
- M. P. Ioannidou and D. P. Chrissoulidis, “Electromagnetic-wave scattering by a sphere with multiple spherical inclusions,” J. Opt. Soc. Am. A19(3), 505–512 (2002). [CrossRef] [PubMed]
- T. Weigel, J. Schulte, and G. Schweiger, “Inelastic scattering on particles with inclusions,” J. Opt. Soc. Am. A22(6), 1048–1052 (2005). [CrossRef] [PubMed]
- A. Doicu, T. Wriedt, and Y. A. Eremin, Light Scattering by Systems of Particles (Springer, Berlin, 2006).
- A. P. Moneda and D. P. Chrissoulidis, “Dyadic Green’s function of a sphere with an eccentric spherical inclusion,” J. Opt. Soc. Am. A24(6), 1695–1703 (2007). [CrossRef] [PubMed]
- D. K. Wu and Y. P. Zhou, “Forward scattering light of droplets containing different size inclusions,” Appl. Opt.48(15), 2957–2965 (2009). [CrossRef] [PubMed]
- M. Mikrenska and P. Koulev, “Simulation of light scattering by large particles with randomly distributed spherical or cubic inclusions,” J. Quant. Spectrosc. Radiat. Transf.110(14–16), 1411–1417 (2009). [CrossRef]
- S. Xian-Ming, W. Hai-Hua, L. Wan-Qiang, and S. Jin, “Light scattering by a spherical particle with multiple densely packed inclusions,” Chin. Phys. B18(3), 1040–1044 (2009). [CrossRef]
- E. E. Khaled, S. C. Hill, and P. W. Barber, “Light scattering by a coated sphere illuminated with a Gaussian beam,” Appl. Opt.33(15), 3308–3314 (1994). [CrossRef] [PubMed]
- G. Gouesbet and G. Gréhan, Generalized Lorenz-Mie Theories (Springer, Berlin, 2011).
- G. Gouesbet and G. Gréhan, “Generalized Lorenz-Mie theory for a sphere with an eccentrically located spherical inclusion,” J. Mod. Opt.47(5), 821–837 (2000).
- G. X. Han, Y. P. Han, J. Y. Liu, and Y. Zhang, “Scattering of an eccentric sphere arbitrarily located in a shaped beam,” J. Opt. Soc. Am. B25(12), 2064–2072 (2008). [CrossRef]
- B. Yan, X. E. Han, and K. F. Ren, “Scattering of a shaped beam by a spherical particle with an eccentric spherical inclusion,” J. Opt. A11(1), 015705 (2009). [CrossRef]
- J. J. Wang, G. Gouesbet, Y. P. Han, and G. Gréhan, “Study of scattering from a sphere with an eccentrically located spherical inclusion by generalized Lorenz-Mie theory: internal and external field distribution,” J. Opt. Soc. Am. A28(1), 24–39 (2011). [CrossRef] [PubMed]
- J. J. Wang, G. Gouesbet, G. Gréhan, Y. P. Han, and S. Saengkaew, “Morphology-dependent resonances in an eccentrically layered sphere illuminated by a tightly focused off-axis Gaussian beam: parallel and perpendicular beam incidence,” J. Opt. Soc. Am. A28(9), 1849–1859 (2011). [CrossRef]
- H. Y. Zhang and T. Q. Liao, “Scattering of Gaussian beam by a spherical particle with a spheroidal inclusion,” J. Quant. Spectrosc. Radiat. Transf.112(9), 1486–1491 (2011). [CrossRef]
- B. Yan, H. Y. Zhang, and C. H. Liu, “Scattering of Gaussian beam by a spheroidal particle with a spherical inclusion at the center,” Opt. Commun.284(16–17), 3811–3815 (2011). [CrossRef]
- J. P. Barton and D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys.66(7), 2800–2802 (1989). [CrossRef]
- A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, 1957).
- G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz-Mie theories through rotations of coordinate systemsIII. Special Euler angles,” Opt. Commun.283(17), 3235–3243 (2010). [CrossRef]
- S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antenn. Propag.30(3), 409–418 (1982). [CrossRef]
- S. M. Rao, C. C. Cha, R. L. Cravey, and D. Wilkes, “Electromagnetic scattering from arbitrary shaped conducting bodies coated with lossy materials of arbitrary thickness,” IEEE Trans. Antenn. Propag.39(5), 627–631 (1991). [CrossRef]
- P. Ylä-Oijala, M. Taskinen, and J. Sarvas, “Surface integral equation method for general composite metallic and dielectric structures with junctions,” Prog. Electromagn. Res.52, 81–108 (2005). [CrossRef]
- J. Rivero, J. M. Taboada, L. Landesa, F. Obelleiro, and I. García-Tuñón, “Surface integral equation formulation for the analysis of left-handed metamaterials,” Opt. Express18(15), 15876–15886 (2010). [CrossRef] [PubMed]
- Z. W. Cui, Y. P. Han, and M. L. Li, “Solution of CFIE-JMCFIE using parallel MOM for scattering by dielectrically coated conducting bodies,” J. Electromagn. Waves Appl.25(2), 211–222 (2011). [CrossRef]
- R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).
- L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A19(3), 1177–1179 (1979). [CrossRef]
- Z. W. Cui, Y. P. Han, and H. Y. Zhang, “Scattering of an arbitrarily incident focused Gaussian beam by arbitrarily shaped dielectric particles,” J. Opt. Soc. Am. B28(11), 2625–2632 (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. A28(11), 2200–2208 (2011). [CrossRef] [PubMed]
- D. A. Dunavant, “High degree efficient symmetrical Gaussian quadrature rules for the triangle,” Int. J. Numer. Methods Eng.21(6), 1129–1148 (1985). [CrossRef]
- R. D. Graglia, “On the numerical integration of the linear shape functions times the 3-D green’s function or its gradient on a plane triangle,” IEEE Trans. Antenn. Propag.41(10), 1448–1455 (1993). [CrossRef]
- L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2001).
- D. W. Mackowski, “A simplified model to predict the effects of aggregation on the absorption properties of soot particles,” J. Quant. Spectrosc. Radiat. Transf.100(1–3), 237–249 (2006). [CrossRef]

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