Abstract

A so-called localized approximation, allowing one to speed up the evaluation of beam shape coefficients in the generalized Lorenz–Mie theory for spheres, has been previously introduced and, in the case of Gaussian beams, rigorously justified. We examine and demonstrate the validity of this approximation for arbitrary shaped beams.

© 1999 Optical Society of America

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  1. G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
    [CrossRef]
  2. B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. (Paris) 19, 59–67 (1988).
    [CrossRef]
  3. G. Gouesbet, G. Gréhan, B. Maheu, “Generalized Lorenz–Mie theory and applications to optical sizing,” in Combustion Measurements, N. Chigier, ed. (Hemisphere, New York, 1991), pp. 339–384.
  4. F. Onofri, G. Gréhan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
    [CrossRef] [PubMed]
  5. Z. S. Wu, L. X. Guo, K. F. Ren, G. Gouesbet, G. Gréhan, “Improved algorithms for electromagnetic scattering of plane waves and shaped beams by multilayered spheres,” Appl. Opt. 36, 5188–5198 (1997).
    [CrossRef] [PubMed]
  6. G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” Part. Part. Syst. Charact. 11, 22–23 (1994).
    [CrossRef]
  7. G. Gouesbet, G. Gréhan, “Diffusion des faisceaux laser par des particules,” (Techniques de l’Ingénieur, 249, rue de Crimée, 75019 Paris, 1998).
  8. W. C. Tsai, R. J. Pogorzelski, “Eigenfunction solution of the scattering of beam radiation fields by spherical objects,” J. Opt. Soc. Am. 65, 1457–1463 (1975).
    [CrossRef]
  9. L. W. Casperson, C. Yeh, “Rayleigh–Debye scattering with focused laser beams,” Appl. Opt. 17, 1637–1643 (1978).
    [CrossRef] [PubMed]
  10. S. Colak, C. Yeh, L. W. Casperson, “Scattering of focused beams by tenuous particles,” Appl. Opt. 18, 294–302 (1979).
    [CrossRef] [PubMed]
  11. J. S. Kim, S. S. Lee, “Scattering of laser beams and the optical potential well for a homogeneous sphere,” J. Opt. Soc. Am. 73, 303–312 (1983).
    [CrossRef]
  12. J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
    [CrossRef]
  13. J. A. Lock, “Contribution of high-order rainbows to the scattering of a Gaussian laser beam by a spherical particle,” J. Opt. Soc. Am. A 10, 693–706 (1993).
    [CrossRef]
  14. G. Gouesbet, C. Letellier, K. F. Ren, G. Gréhan, “Discussion of two quadrature methods of evaluating beam shape coefficients in generalized Lorenz–Mie theory,” Appl. Opt. 35, 1537–1542 (1996).
    [CrossRef] [PubMed]
  15. G. Gouesbet, G. Gréhan, B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz–Mie theory, using finite series,” J. Opt. (Paris) 19, 35–48 (1988).
    [CrossRef]
  16. G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of laser beams by Mie scatter centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986).
    [CrossRef] [PubMed]
  17. G. Gouesbet, G. Gréhan, B. Maheu, “A localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
    [CrossRef]
  18. J. A. Lock, G. Gouesbet, “Rigorous justification of the localized approximation to the beam shape coefficients in generalized Lorenz–Mie theory. I. On-axis beams,” J. Opt. Soc. Am. A 11, 2503–2515 (1994).
    [CrossRef]
  19. G. Gouesbet, J. A. Lock, “Rigorous justification of the localized approximation to the beam shape coefficients in generalized Lorenz–Mie theory. II. Off-axis beams,” J. Opt. Soc. Am. A 11, 2516–2525 (1994).
    [CrossRef]
  20. K. F. Ren, G. Gréhan, G. Gouesbet, “Localized approximation of generalized Lorenz–Mie theory. Faster algorithm for computations of the beam shape coefficients,” Part. Part. Syst. Charact. 9, 144–150 (1992).
    [CrossRef]
  21. J. A. Lock, “An improved Gaussian beam scattering algorithm,” Appl. Opt. 34, 559–570 (1995).
    [CrossRef] [PubMed]
  22. K. F. Ren, G. Gréhan, G. Gouesbet, “Evaluation of laser sheet beam shape coefficients in generalized Lorenz–Mie theory by using a localized approximation,” J. Opt. Soc. Am. A 11, 2072–2079 (1994).
    [CrossRef]
  23. G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representations of laser beams for use in light scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
    [CrossRef] [PubMed]
  24. K. F. Ren, G. Gouesbet, G. Gréhan, “The integral localized approximation in generalized Lorenz–Mie theory,” Appl. Opt. 37, 4218–4225 (1998).
    [CrossRef]
  25. G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz–Mie,” J. Opt. (Paris) 13, 97–103 (1982).
    [CrossRef]
  26. G. Gouesbet, “Partial wave expansions and properties of axisymmetric light beams,” Appl. Opt. 35, 1543–1555 (1996).
    [CrossRef] [PubMed]
  27. G. Gouesbet, “Exact description of arbitrary shaped beams for use in light scattering theories,” J. Opt. Soc. Am. A 13, 2434–2440 (1996).
    [CrossRef]
  28. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
    [CrossRef]
  29. J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
    [CrossRef]
  30. G. Gouesbet, “Higher-order descriptions of Gaussian beams,” J. Opt. (Paris) 27, 35–50 (1996).
    [CrossRef]
  31. H. Polaert, G. Gréhan, G. Gouesbet, “Improved standard beams with applications to reverse radiation pressure,” Appl. Opt. 37, 2435–2440 (1998).
    [CrossRef]
  32. K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder in GLMT—framework, formulation and numerical results,” J. Opt. Soc. Am. A 14, 3014–3025 (1997).
    [CrossRef]
  33. G. Gouesbet, G. Gréhan, K. F. Ren, “Rigorous justification of the cylindrical localized approximation to speed up computations in GLMT for cylinders,” J. Opt. Soc. Am. A 15, 511–523 (1998).
    [CrossRef]
  34. G. Gouesbet, K. F. Ren, L. Mees, G. Gréhan, “The cylindrical localized approximation, to speed up computations for Gaussian beams in the GLMT for cylinders, with arbitrary location and orientation of the scatterer,” Appl. Opt. 38, 2647–2665 (1999).
    [CrossRef]
  35. G. Gouesbet, L. Mees, G. Gréhan, K. F. Ren, “The structure of generalized Lorenz–Mie theory for elliptical infinite cylinders,” Part. Part. Syst. Charact. (to be published).
  36. G. Gouesbet, L. Mees, G. Gréhan, K. F. Ren, “Localized approximation for Gaussian beams in elliptical cylinder coordinates,” submitted to Appl. Opt.

1999 (1)

1998 (3)

1997 (2)

1996 (4)

1995 (3)

1994 (4)

1993 (1)

1992 (1)

K. F. Ren, G. Gréhan, G. Gouesbet, “Localized approximation of generalized Lorenz–Mie theory. Faster algorithm for computations of the beam shape coefficients,” Part. Part. Syst. Charact. 9, 144–150 (1992).
[CrossRef]

1990 (1)

1989 (1)

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

1988 (4)

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. (Paris) 19, 59–67 (1988).
[CrossRef]

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz–Mie theory, using finite series,” J. Opt. (Paris) 19, 35–48 (1988).
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

1986 (1)

1983 (1)

1982 (1)

G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz–Mie,” J. Opt. (Paris) 13, 97–103 (1982).
[CrossRef]

1979 (2)

1978 (1)

1975 (1)

Alexander, D. R.

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

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

Barton, J. P.

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

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

Casperson, L. W.

Colak, S.

Davis, L. W.

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

Gouesbet, G.

G. Gouesbet, K. F. Ren, L. Mees, G. Gréhan, “The cylindrical localized approximation, to speed up computations for Gaussian beams in the GLMT for cylinders, with arbitrary location and orientation of the scatterer,” Appl. Opt. 38, 2647–2665 (1999).
[CrossRef]

G. Gouesbet, G. Gréhan, K. F. Ren, “Rigorous justification of the cylindrical localized approximation to speed up computations in GLMT for cylinders,” J. Opt. Soc. Am. A 15, 511–523 (1998).
[CrossRef]

H. Polaert, G. Gréhan, G. Gouesbet, “Improved standard beams with applications to reverse radiation pressure,” Appl. Opt. 37, 2435–2440 (1998).
[CrossRef]

K. F. Ren, G. Gouesbet, G. Gréhan, “The integral localized approximation in generalized Lorenz–Mie theory,” Appl. Opt. 37, 4218–4225 (1998).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder in GLMT—framework, formulation and numerical results,” J. Opt. Soc. Am. A 14, 3014–3025 (1997).
[CrossRef]

Z. S. Wu, L. X. Guo, K. F. Ren, G. Gouesbet, G. Gréhan, “Improved algorithms for electromagnetic scattering of plane waves and shaped beams by multilayered spheres,” Appl. Opt. 36, 5188–5198 (1997).
[CrossRef] [PubMed]

G. Gouesbet, “Higher-order descriptions of Gaussian beams,” J. Opt. (Paris) 27, 35–50 (1996).
[CrossRef]

G. Gouesbet, “Exact description of arbitrary shaped beams for use in light scattering theories,” J. Opt. Soc. Am. A 13, 2434–2440 (1996).
[CrossRef]

G. Gouesbet, C. Letellier, K. F. Ren, G. Gréhan, “Discussion of two quadrature methods of evaluating beam shape coefficients in generalized Lorenz–Mie theory,” Appl. Opt. 35, 1537–1542 (1996).
[CrossRef] [PubMed]

G. Gouesbet, “Partial wave expansions and properties of axisymmetric light beams,” Appl. Opt. 35, 1543–1555 (1996).
[CrossRef] [PubMed]

F. Onofri, G. Gréhan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
[CrossRef] [PubMed]

G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representations of laser beams for use in light scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
[CrossRef] [PubMed]

G. Gouesbet, J. A. Lock, “Rigorous justification of the localized approximation to the beam shape coefficients in generalized Lorenz–Mie theory. II. Off-axis beams,” J. Opt. Soc. Am. A 11, 2516–2525 (1994).
[CrossRef]

G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” Part. Part. Syst. Charact. 11, 22–23 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Evaluation of laser sheet beam shape coefficients in generalized Lorenz–Mie theory by using a localized approximation,” J. Opt. Soc. Am. A 11, 2072–2079 (1994).
[CrossRef]

J. A. Lock, G. Gouesbet, “Rigorous justification of the localized approximation to the beam shape coefficients in generalized Lorenz–Mie theory. I. On-axis beams,” J. Opt. Soc. Am. A 11, 2503–2515 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Localized approximation of generalized Lorenz–Mie theory. Faster algorithm for computations of the beam shape coefficients,” Part. Part. Syst. Charact. 9, 144–150 (1992).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “A localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz–Mie theory, using finite series,” J. Opt. (Paris) 19, 35–48 (1988).
[CrossRef]

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. (Paris) 19, 59–67 (1988).
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of laser beams by Mie scatter centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986).
[CrossRef] [PubMed]

G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz–Mie,” J. Opt. (Paris) 13, 97–103 (1982).
[CrossRef]

G. Gouesbet, L. Mees, G. Gréhan, K. F. Ren, “The structure of generalized Lorenz–Mie theory for elliptical infinite cylinders,” Part. Part. Syst. Charact. (to be published).

G. Gouesbet, G. Gréhan, B. Maheu, “Generalized Lorenz–Mie theory and applications to optical sizing,” in Combustion Measurements, N. Chigier, ed. (Hemisphere, New York, 1991), pp. 339–384.

G. Gouesbet, L. Mees, G. Gréhan, K. F. Ren, “Localized approximation for Gaussian beams in elliptical cylinder coordinates,” submitted to Appl. Opt.

G. Gouesbet, G. Gréhan, “Diffusion des faisceaux laser par des particules,” (Techniques de l’Ingénieur, 249, rue de Crimée, 75019 Paris, 1998).

Gréhan, G.

G. Gouesbet, K. F. Ren, L. Mees, G. Gréhan, “The cylindrical localized approximation, to speed up computations for Gaussian beams in the GLMT for cylinders, with arbitrary location and orientation of the scatterer,” Appl. Opt. 38, 2647–2665 (1999).
[CrossRef]

G. Gouesbet, G. Gréhan, K. F. Ren, “Rigorous justification of the cylindrical localized approximation to speed up computations in GLMT for cylinders,” J. Opt. Soc. Am. A 15, 511–523 (1998).
[CrossRef]

H. Polaert, G. Gréhan, G. Gouesbet, “Improved standard beams with applications to reverse radiation pressure,” Appl. Opt. 37, 2435–2440 (1998).
[CrossRef]

K. F. Ren, G. Gouesbet, G. Gréhan, “The integral localized approximation in generalized Lorenz–Mie theory,” Appl. Opt. 37, 4218–4225 (1998).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder in GLMT—framework, formulation and numerical results,” J. Opt. Soc. Am. A 14, 3014–3025 (1997).
[CrossRef]

Z. S. Wu, L. X. Guo, K. F. Ren, G. Gouesbet, G. Gréhan, “Improved algorithms for electromagnetic scattering of plane waves and shaped beams by multilayered spheres,” Appl. Opt. 36, 5188–5198 (1997).
[CrossRef] [PubMed]

G. Gouesbet, C. Letellier, K. F. Ren, G. Gréhan, “Discussion of two quadrature methods of evaluating beam shape coefficients in generalized Lorenz–Mie theory,” Appl. Opt. 35, 1537–1542 (1996).
[CrossRef] [PubMed]

G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representations of laser beams for use in light scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
[CrossRef] [PubMed]

F. Onofri, G. Gréhan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
[CrossRef] [PubMed]

K. F. Ren, G. Gréhan, G. Gouesbet, “Evaluation of laser sheet beam shape coefficients in generalized Lorenz–Mie theory by using a localized approximation,” J. Opt. Soc. Am. A 11, 2072–2079 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Localized approximation of generalized Lorenz–Mie theory. Faster algorithm for computations of the beam shape coefficients,” Part. Part. Syst. Charact. 9, 144–150 (1992).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “A localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz–Mie theory, using finite series,” J. Opt. (Paris) 19, 35–48 (1988).
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. (Paris) 19, 59–67 (1988).
[CrossRef]

G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of laser beams by Mie scatter centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986).
[CrossRef] [PubMed]

G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz–Mie,” J. Opt. (Paris) 13, 97–103 (1982).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Generalized Lorenz–Mie theory and applications to optical sizing,” in Combustion Measurements, N. Chigier, ed. (Hemisphere, New York, 1991), pp. 339–384.

G. Gouesbet, L. Mees, G. Gréhan, K. F. Ren, “The structure of generalized Lorenz–Mie theory for elliptical infinite cylinders,” Part. Part. Syst. Charact. (to be published).

G. Gouesbet, L. Mees, G. Gréhan, K. F. Ren, “Localized approximation for Gaussian beams in elliptical cylinder coordinates,” submitted to Appl. Opt.

G. Gouesbet, G. Gréhan, “Diffusion des faisceaux laser par des particules,” (Techniques de l’Ingénieur, 249, rue de Crimée, 75019 Paris, 1998).

Guo, L. X.

Kim, J. S.

Lee, S. S.

Letellier, C.

Lock, J. A.

Maheu, B.

G. Gouesbet, G. Gréhan, B. Maheu, “A localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz–Mie theory, using finite series,” J. Opt. (Paris) 19, 35–48 (1988).
[CrossRef]

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. (Paris) 19, 59–67 (1988).
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of laser beams by Mie scatter centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986).
[CrossRef] [PubMed]

G. Gouesbet, G. Gréhan, B. Maheu, “Generalized Lorenz–Mie theory and applications to optical sizing,” in Combustion Measurements, N. Chigier, ed. (Hemisphere, New York, 1991), pp. 339–384.

Mees, L.

G. Gouesbet, K. F. Ren, L. Mees, G. Gréhan, “The cylindrical localized approximation, to speed up computations for Gaussian beams in the GLMT for cylinders, with arbitrary location and orientation of the scatterer,” Appl. Opt. 38, 2647–2665 (1999).
[CrossRef]

G. Gouesbet, L. Mees, G. Gréhan, K. F. Ren, “The structure of generalized Lorenz–Mie theory for elliptical infinite cylinders,” Part. Part. Syst. Charact. (to be published).

G. Gouesbet, L. Mees, G. Gréhan, K. F. Ren, “Localized approximation for Gaussian beams in elliptical cylinder coordinates,” submitted to Appl. Opt.

Onofri, F.

Pogorzelski, R. J.

Polaert, H.

Ren, K. F.

G. Gouesbet, K. F. Ren, L. Mees, G. Gréhan, “The cylindrical localized approximation, to speed up computations for Gaussian beams in the GLMT for cylinders, with arbitrary location and orientation of the scatterer,” Appl. Opt. 38, 2647–2665 (1999).
[CrossRef]

G. Gouesbet, G. Gréhan, K. F. Ren, “Rigorous justification of the cylindrical localized approximation to speed up computations in GLMT for cylinders,” J. Opt. Soc. Am. A 15, 511–523 (1998).
[CrossRef]

K. F. Ren, G. Gouesbet, G. Gréhan, “The integral localized approximation in generalized Lorenz–Mie theory,” Appl. Opt. 37, 4218–4225 (1998).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder in GLMT—framework, formulation and numerical results,” J. Opt. Soc. Am. A 14, 3014–3025 (1997).
[CrossRef]

Z. S. Wu, L. X. Guo, K. F. Ren, G. Gouesbet, G. Gréhan, “Improved algorithms for electromagnetic scattering of plane waves and shaped beams by multilayered spheres,” Appl. Opt. 36, 5188–5198 (1997).
[CrossRef] [PubMed]

G. Gouesbet, C. Letellier, K. F. Ren, G. Gréhan, “Discussion of two quadrature methods of evaluating beam shape coefficients in generalized Lorenz–Mie theory,” Appl. Opt. 35, 1537–1542 (1996).
[CrossRef] [PubMed]

K. F. Ren, G. Gréhan, G. Gouesbet, “Evaluation of laser sheet beam shape coefficients in generalized Lorenz–Mie theory by using a localized approximation,” J. Opt. Soc. Am. A 11, 2072–2079 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Localized approximation of generalized Lorenz–Mie theory. Faster algorithm for computations of the beam shape coefficients,” Part. Part. Syst. Charact. 9, 144–150 (1992).
[CrossRef]

G. Gouesbet, L. Mees, G. Gréhan, K. F. Ren, “The structure of generalized Lorenz–Mie theory for elliptical infinite cylinders,” Part. Part. Syst. Charact. (to be published).

G. Gouesbet, L. Mees, G. Gréhan, K. F. Ren, “Localized approximation for Gaussian beams in elliptical cylinder coordinates,” submitted to Appl. Opt.

Schaub, S. A.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

Tsai, W. C.

Wu, Z. S.

Yeh, C.

Appl. Opt. (12)

L. W. Casperson, C. Yeh, “Rayleigh–Debye scattering with focused laser beams,” Appl. Opt. 17, 1637–1643 (1978).
[CrossRef] [PubMed]

S. Colak, C. Yeh, L. W. Casperson, “Scattering of focused beams by tenuous particles,” Appl. Opt. 18, 294–302 (1979).
[CrossRef] [PubMed]

J. A. Lock, “An improved Gaussian beam scattering algorithm,” Appl. Opt. 34, 559–570 (1995).
[CrossRef] [PubMed]

G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representations of laser beams for use in light scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
[CrossRef] [PubMed]

F. Onofri, G. Gréhan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
[CrossRef] [PubMed]

G. Gouesbet, C. Letellier, K. F. Ren, G. Gréhan, “Discussion of two quadrature methods of evaluating beam shape coefficients in generalized Lorenz–Mie theory,” Appl. Opt. 35, 1537–1542 (1996).
[CrossRef] [PubMed]

G. Gouesbet, “Partial wave expansions and properties of axisymmetric light beams,” Appl. Opt. 35, 1543–1555 (1996).
[CrossRef] [PubMed]

Z. S. Wu, L. X. Guo, K. F. Ren, G. Gouesbet, G. Gréhan, “Improved algorithms for electromagnetic scattering of plane waves and shaped beams by multilayered spheres,” Appl. Opt. 36, 5188–5198 (1997).
[CrossRef] [PubMed]

H. Polaert, G. Gréhan, G. Gouesbet, “Improved standard beams with applications to reverse radiation pressure,” Appl. Opt. 37, 2435–2440 (1998).
[CrossRef]

G. Gouesbet, K. F. Ren, L. Mees, G. Gréhan, “The cylindrical localized approximation, to speed up computations for Gaussian beams in the GLMT for cylinders, with arbitrary location and orientation of the scatterer,” Appl. Opt. 38, 2647–2665 (1999).
[CrossRef]

K. F. Ren, G. Gouesbet, G. Gréhan, “The integral localized approximation in generalized Lorenz–Mie theory,” Appl. Opt. 37, 4218–4225 (1998).
[CrossRef]

G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of laser beams by Mie scatter centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986).
[CrossRef] [PubMed]

J. Appl. Phys. (2)

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

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

J. Opt. (Paris) (4)

G. Gouesbet, “Higher-order descriptions of Gaussian beams,” J. Opt. (Paris) 27, 35–50 (1996).
[CrossRef]

G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz–Mie,” J. Opt. (Paris) 13, 97–103 (1982).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz–Mie theory, using finite series,” J. Opt. (Paris) 19, 35–48 (1988).
[CrossRef]

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. (Paris) 19, 59–67 (1988).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (9)

G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “A localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Evaluation of laser sheet beam shape coefficients in generalized Lorenz–Mie theory by using a localized approximation,” J. Opt. Soc. Am. A 11, 2072–2079 (1994).
[CrossRef]

J. A. Lock, G. Gouesbet, “Rigorous justification of the localized approximation to the beam shape coefficients in generalized Lorenz–Mie theory. I. On-axis beams,” J. Opt. Soc. Am. A 11, 2503–2515 (1994).
[CrossRef]

G. Gouesbet, J. A. Lock, “Rigorous justification of the localized approximation to the beam shape coefficients in generalized Lorenz–Mie theory. II. Off-axis beams,” J. Opt. Soc. Am. A 11, 2516–2525 (1994).
[CrossRef]

G. Gouesbet, G. Gréhan, K. F. Ren, “Rigorous justification of the cylindrical localized approximation to speed up computations in GLMT for cylinders,” J. Opt. Soc. Am. A 15, 511–523 (1998).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder in GLMT—framework, formulation and numerical results,” J. Opt. Soc. Am. A 14, 3014–3025 (1997).
[CrossRef]

J. A. Lock, “Contribution of high-order rainbows to the scattering of a Gaussian laser beam by a spherical particle,” J. Opt. Soc. Am. A 10, 693–706 (1993).
[CrossRef]

G. Gouesbet, “Exact description of arbitrary shaped beams for use in light scattering theories,” J. Opt. Soc. Am. A 13, 2434–2440 (1996).
[CrossRef]

Part. Part. Syst. Charact. (2)

G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” Part. Part. Syst. Charact. 11, 22–23 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Localized approximation of generalized Lorenz–Mie theory. Faster algorithm for computations of the beam shape coefficients,” Part. Part. Syst. Charact. 9, 144–150 (1992).
[CrossRef]

Phys. Rev. A (1)

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

Other (4)

G. Gouesbet, G. Gréhan, “Diffusion des faisceaux laser par des particules,” (Techniques de l’Ingénieur, 249, rue de Crimée, 75019 Paris, 1998).

G. Gouesbet, G. Gréhan, B. Maheu, “Generalized Lorenz–Mie theory and applications to optical sizing,” in Combustion Measurements, N. Chigier, ed. (Hemisphere, New York, 1991), pp. 339–384.

G. Gouesbet, L. Mees, G. Gréhan, K. F. Ren, “The structure of generalized Lorenz–Mie theory for elliptical infinite cylinders,” Part. Part. Syst. Charact. (to be published).

G. Gouesbet, L. Mees, G. Gréhan, K. F. Ren, “Localized approximation for Gaussian beams in elliptical cylinder coordinates,” submitted to Appl. Opt.

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Equations (151)

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UTM=E0n=1 m=-n+ncnpwgn,TMmrjn(kr)Pn|m|(cos θ)exp(imϕ),
UTE=H0n=1 m=-n+ncnpwgn,TEmrjn(kr)Pn|m|(cos θ)exp(imϕ),
cnpw=1k in-1(-1)n 2n+1n(n+1),
gn,TMm=1kE0cnpw 2n+14πn(n+1) (n-|m|)!(n+|m|)! 1Gn(R)×0π02πEr(R, θ, ϕ)Pn|m|(cos θ)×exp(-imϕ)sin θ dθdϕ,
gn,TEm=1kH0cnpw 2n+14πn(n+1) (n-|m|)!(n+|m|)! 1Gn(R)×0π02πHr(R, θ, ϕ)Pn|m|(cos θ)×exp(-imϕ)sin θ dθdϕ,
Gn(R)=jn(R)R,
R=kr.
Er=mErm,
Erm=[E0 exp(-iR cos θ)sin θ exp(imϕ)]Erm(R, θ).
gn,TMm¯=-iL1/2|m|-1Erm(L1/2, π/2),
L=(n-|m|)(n+|m|+1)=(n+12)2-(|m|+12)2.
 (Ex, Ey, Ez)=E0 exp(-iZ)×p=0q=0l=0(Epqlx, Epqly, Epqlz)XpYqZl,
(X, Y, Z)=(kx, ky, kz);
(q+1)Epq+1lz-(l+1)Epql+1y
+i(Epqly+Hpqlx)=0,
(l+1)Epql+1x-(p+1)Ep+1qlz
+i(Hpqly-Epqlx)=0,
(p+1)Ep+1qly-(q+1)Epq+1lx
+iHpqlz=0,
(p+1)Hp+1qlx+(q+1)Hpq+1ly
+(l+1)Hpql+1z=iHpqlz,
(q+1)Hpq+1lz-(l+1)Hpql+1y
+i(Hpqly-Epqlx)=0,
(l+1)Hpql+1x-(p+1)Hp+1qlz
-i(Hpqlx+Epqly)=0,
(p+1)Hp+1qly-(q+1)Hpq+1lx
-iEpqlz=0,
(p+1)Ep+1qlx+(q+1)Epq+1ly
+(l+1)Epql+1z=iEpqlz.
M=p+q+l.
Cpqli=0,M>N,
Er=E0 exp(-iR cos θ)×p=0pq=0+ql=0+l=NRp+q+l sinp+q θ cosl θ cosp ϕ sinq ϕ×(Epqlx sin θ cos ϕ+Epqly sin θ sin ϕ+Epqlz cos θ).
gnm=-14π in-1 (n-|m|)!(n+|m|)! 1Gn Inm,
Inm=p=0pq=0+ql=0+l=NRp+q+l[Xnmpql(EpqlxImpq+EpqlyJmpq)+EpqlzYnmpqlKmpq],
Impq=02π cosp+1 ϕ sinq ϕ exp(-imϕ)dϕ,
Jmpq=02π cosp ϕ sinq+1 ϕ exp(-imϕ)dϕ,
Kmpq=02π cosp ϕ sinq ϕ exp(-imϕ)dϕ
Xnmpql=0π sinp+q+2 θ cosl θ exp(-iR cos θ)Pn|m|(cos θ)dθ,
Ynmpql=0πsinp+q+1θ cosl+1θ exp(-iR cos θ)Pn|m|(cos θ)dθ.
(Xnmpql)p+q=α=(Xnmpql)p+q=α,
Impq=Jmp+1q-1.
02π exp[i(m-m)ϕ]dϕ=2πδmm.
Bnm=0π sinm+1 θ exp(-iR cos θ)Pnm(cos θ)dθ=2(-i)n+m (n+m)!(n-m)! Gn(R)Rm-1,m0,
R2Gn(R)+4RGn(R)+R2Gn(R)
=(n-1)(n+2)Gn(R),
Cpqli=0,p+q+l>0,
E000y+H000x=0,
H000y-E000x=0,
E000z=H000z=0,
Inm=Xnm000(E000xIm00+E000yJm00),
Xn1000=Xn-1000=Bn1,
gn±1=12 (E000x±iE000y),
Cpqli=0,p+q+l>1.
(Epqlz)N=1=E001x=E001y=0,
E000z=-i(E100x+E010y).
In0=π(RXn0100-2iYn0000)(E100x+E010y),
In±1=πXn1000(E000xiE000y),
In±2=π2 RXn2100(E100xiE100yiE010x-E010y).
gn0=i2 n(n+1)(E100x+E010y),
gn±1=(gn±1)0,
gn±2=-i4 (E100xiE100yiE010x-E010y).
gnm¯=gnm.
Cpqli=0,p+q+l>2.
(Epqlz)N=2=E101x=E011x=E002x=E101y=E011y=E002y=E001z=0.
In0=π[RXn0100(E100x+E010y)+2E000zYn0000],
E000z=-iE100x-iE010y,
In0=π(RXn0100-2iYn0000)(E100x+E010y).
In±1=π[14 R2Xn1200(iE110x+E110y+3E200xiE200y+E020x3iE020y)+RYn1100(E100ziE010z+E001xiE001y)+Xn1000(E000xiE000y)].
In±1=π[(14 R2Xn1200-iRYn1100)(iE110x+E110y+3E200xiE200y+E020x3iE020y)+Xn1000(E000xiE000y)].
In±2=π2 RXn2100(E100xiE100yiE010x-E010y),
In±3=π4 R2Xn3200(iE110x-E110y+E200xiE200y-E020x±iE020y).
gn0=(gn0)1,
gn±1=18 (n-1)(n+2)(iE110x+E110y+3E200xiE200y+E020x3iE020y)+(gn±1)1,
gn±2=(gn±2)1,
gn±3=-18 (iE110x-E110y+E200xiE200y-E020x±iE020y).
gnm¯=gnm.
Cpqli=0,p+q+l>3.
(Epqlz)N=3=(Epqlx)N=3,l0=(Epqly)N=3,l0=E002z=E101z=E011z=E002x=E002y=0
In0=π(14 R3Xn0300-2iR2Yn0200-2RYn0001+2iYn0000)×(E120x+E210y+3E300x+3E030y)+(In0)2,
In±1=(In±1)2,
In±2=π2 R2R2 Xn2300-3iYn2200(iE120yiE210x+2E300xiE300yiE030x-2E030y)+(In±2)2,
In±3=(In±3)2,
In±4=π8 R3Xn4300(-E120x±iE120yiE210x-E210y+E300xiE300y±iE030x+E030y).
gn±1=(gn±1)2,
gn±2=-i8 (n-2)(n+3)(iE120yiE210x+2E300xiE300yiE030x-2E030y)+(gn±2)2,
gn±3=(gn±3)2,
gn±4=i16 (-E120x±iE120yiE210x-E210y+E300xiE300y±iE030x+E030y).
gn0=i8 n(n+1)(n-2)(n+3)(E120x+E210y+3E300x+3E030y)+(gn0)2.
gnm¯=gnm,|m|=1, 2, 3, 4,
gn0¯=i8 n2(n+1)2(E120x+E210y+3E300x+3E030y)+(gn0¯)2.
Cpqli=0,p+q+l>4.
(Epqlz)N=4=(Epqlx)N=4,l0=(Epqly)N=4,l0=(Epqlz)N=3,l0=E102x=E102y=E012x=E012y=E003x=E003y=E111x=E111y=E130y=E310y=E002z=0.
Inm=(Inm)3,m=0, 2, 4,
In1=π[18R4Xn1400(E040x-5iE040y-iE130x+E220x-iE220y-iE310x+5E400x-iE400y)+14R3Yn1300(3E201x-iE201y+E021x-3iE021y+E120z-iE210z+3E300z-3iE030z)+14R2Xn1200(-iE110x+E110y+3E200x-iE200y+E020x-3iE020y)+R2Yn1101×(E002x-iE002y+E101z-iE011z)+RYn1100(E001x-iE001y+E100z-iE010z)+Xn1000×(E000x-iE000y)],
In3=-π16 (R4Xn3400-8iR3Yn3300)(3E040x-5iE040y+iE130x+E220x+iE220y+3iE310x-5E400x+3iE400y)+(In3)2,
In5=π16 R4Xn5400(E040x-iE040y+iE130x-E220x+iE220y-iE310x+E400x-iE400y),
gnm=(gnm)3,m=0, 2, 4,
gn3=132(n-3)(n+4)(3E040x-5iE040y+iE130x+E220x+iE220y+3iE310x-5E400x+3iE400y)+(gn3)3,
gn5=132(E040x-iE040y+iE130x-E220x+iE220y-iE310x+E400x-iE400y).
gn0¯=(gn0¯)3,
gn1¯=12(E000x-iE000y)+18(n-1)(n+2)(-iE110x+E110y+3E200x-iE200y+E020x-3iE020y)+116(n-1)2(n+2)2(E040x-5iE040y-iE130x+E220x-iE220y-iE310x+5E400x-iE400y),
gnm¯=gnm,m=2, 3, 4, 5.
gn0¯=(gn0¯)3gn0=(gn0)3,
Ω=R4Xn1400+αR3Yn1300+βR2Xn1200+γR2Yn1101+δRYn1100.
Ω=2(-i)n+1n(n+1)[(A+BR2)Gn+CGn],
γ=4(6-iα),
C=iR[(2+n+n2)α+4iβ+δ+12in(n+1)],
α=-12i2+n(n+1) -4iβ-δ-12i+n(n+1),
α=-12i,
δ=4i(6-β)
Ω=2(-i)n+1n(n+1)(n-1)(n+2)×(n2+n+β-12)Gn,
In1=π8 Ω(E040x-5iE040y-iE130x+E220x-iE220y-iE310x+5E400x-iE400y)+π14 R2Xn1200-iRYn1100
×(-iE110x+E110y+3E200x-iE200y+E020x
-3iE020y)+πXn1000(E000x-iE000y)+Res0,
Res0=π14 R3Yn1300R-β8 R2Xn1200K+R2Yn1101S+RYn1100×iβ2-3K+L,
Λ=14R3Yn1300-iR2Yn1101=(-i)n+2n(n+1)(n-1)(n+2)Gn,
Res0=πΛR+Res1,
Res1=πR2Yn1101(S+iR)-β8 R2Xn1200K+RYn1100×iβ2-3K+L.
Δ=R2Xn1200-4iRYn1100=2(-i)n+1n(n+1)(n-1)(n+2)Gn,
Res1=-β8 πΔK+Res2,
Res2=π[R2Yn1101(S+iR)+RYn1100(L-3iK)].
S+iR=0,
L-3iK=0.
Res0=πΛR.
gn1=12 (E000x-iE000y)+18 (n-1)(n+2)×(-iE110x+E110y+3E200x-iE200y+E020x-3iE020y)+116 (n-1)(n+2)(n-3)(n+4)×(E040x-5iE040y-iE130x+E220x-iE220y-iE310x+5E400x-iE400y)-i4 (n-1)(n+2)R.
E130x+E310x=0.
gn=1-s2(n-1)(n+2)+12s4(n-2)(n-1)(n+2)(n+3),
Ex=E0 exp(-iZ){1+s2[2iZ-(X2+Y2)]+s4[-4Z2-4iZ(1+X2+Y2)+12(X4+Y4)+X2Y2+5X2+3Y2]},
Ey=2E0 XY exp(-iZ)s4,
Ez=2E0 X exp(-iZ)×{is2+s4[-4Z-i(X2+Y2)-2i]},
Bnm=0π sinm+1 θ exp(-iR cos θ)Pnm(cos θ)dθ=2(-i)n+m (n+m)!(n-m)! Gn(R)Rm-1,m0,
Xn1000=Bn1=-2(-i)n-1n(n+1)Gn(R),
Xn2100=Bn2=2(-i)n+2 (n+2)!(n-2)! Gn(R)R,
Xn0100=Bn0+d2Bn0dR2=2(-i)n{RGn(R)+[RGn(R)]},
Yn0000=i dBn0dR=2i(-i)n[RGn(R)],
Xn1200=Bn1+d2Bn1dR2=-2(-i)n-1n(n+1)[Gn(R)+Gn(R)],
Yn1100=i dBn1dR=-2i(-i)n-1n(n+1)Gn(R),
Xn3200=Bn3=2(-i)n+3 (n+3)!(n-3)! Gn(R)R2,
Xn0300=Bn0+2 d2Bn0dR2+d4Bn0dR4=2(-i)n{RGn(R)+2[RGn(R)]+[RGn(R)]},
Yn0200=i dBn0dR+i d3Bn0dR3=2i(-i)n{[RGn(R)]+[RGn(R)]},
Yn0001=-d2Bn0dR2=-2(-i)n2[RGn(R)],
Xn2300=Bn2+d2Bn2dR2=2(-i)n+2 (n+2)!(n-2)! Gn(R)R+Gn(R)R,
Yn2200=i dBn2dR=2i(-i)n+2 (n+2)!(n-2)! Gn(R)R,
Xn4300=Bn4=2(-i)n (n+4)!(n-4)! Gn(R)R3,
Xn1400=Bn1+2 d2Bn1dR2+d4Bn1dR4=2(-i)n+1n(n+1)×[Gn(R)+2Gn(R)+Gn(R)],
Yn1300=i dBn1dR+i d3Bn1dR3
=2i(-i)n+1n(n+1)[Gn(R)+Gn(R)],
Yn1101=-d2Bn1dR2=-2(-i)n+1n(n+1)Gn(R),
Xn3400=Bn3+d2Bn3dR2=2(-i)n+3 (n+3)!(n-3)! Gn(R)R2+Gn(R)R2,
Yn3300=i dBn3dR=2i(-i)n+3 (n+3)!(n-3)! Gn(R)R2,
Xn5400=Bn5=2(-i)n+1 (n+5)!(n-5)! Gn(R)R4.

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