Abstract

A cylindrical localized approximation to speed up numerical computations in generalized Lorenz–Mie theory for cylinders, in a special case of perpendicular illumination, was recently introduced and rigorously justified. We generalize this approximation to the case when the cylinder is arbitrarily located and arbitrarily oriented in a Gaussian beam.

© 1999 Optical Society of America

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  1. G. Gouesbet, “Interaction between an infinite cylinder and an arbitrary-shaped beam,” Appl. Opt. 36, 4292–4304 (1997).
    [CrossRef] [PubMed]
  2. N. Gauchet, T. Girasole, K. F. Ren, G. Gréhan, G. Gouesbet, “Application of generalized Lorenz–Mie theory for cylinders to cylindrical characterization by phase-Doppler anemometry,” Opt. Diagnost. Eng. 2, 1–10 (1997).
  3. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
    [CrossRef]
  4. G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representation of laser beams for use in light scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
    [CrossRef] [PubMed]
  5. E. Lenglart, G. Gouesbet, “The separability theorem in terms of distributions with discussion of electromagnetic scattering theory,” J. Math. Phys. 37, 4705–4710 (1996).
    [CrossRef]
  6. 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]
  7. 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]
  8. J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” J. Phys. 33, 189–195 (1955).
  9. J. A. Lock, “Scattering of a diagonally incident focused Gaussian beam by an infinitely long homogeneous circular cylinder,” J. Opt. Soc. Am. A 14, 640–652 (1997).
    [CrossRef]
  10. J. A. Lock, “Morphology-dependent resonances of an infinitely long circular cylinder illuminated by a diagonally incident plane wave or a focused Gaussian beam,” J. Opt. Soc. Am. A 14, 653–661 (1997).
    [CrossRef]
  11. K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder in the framework of generalized Lorenz–Mie theory: formulation and numerical results,” J. Opt. Soc. Am. A 14, 3014–3025 (1997).
    [CrossRef]
  12. 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]
  13. 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]
  14. J. A. Lock, G. Gouesbet, “A rigorous justification of the localized approximation to the beam shape coefficients in the generalized Lorenz–Mie theory. I. On-axis beams,” J. Opt. Soc. Am. A 11, 2503–2515 (1994).
    [CrossRef]
  15. G. Gouesbet, J. A. Lock, “A rigorous justification of the localized approximation to the beam shape coefficients in the generalized Lorenz–Mie theory. II. Off-axis beams,” J. Opt. Soc. Am. A 11, 2516–2525 (1994).
    [CrossRef]
  16. G. Gouesbet, K. F. Ren, G. Gréhan, “Rigorous justification of the cylindrical approximation to speed up computations in generalized Lorenz–Mie theory for cylinders,” J. Opt. Soc. Am. A 15, 511–523 (1998).
    [CrossRef]
  17. F. Roddier, Distributions et Transformation de Fourier (McGraw-Hill, New York, 1982).
  18. L. Schwartz, Théorie des Distributions (Hermann, Paris, 1951).
  19. E. Butkov, Mathematical Physics (Addison-Wesley, Reading, Mass., 1968).
  20. G. Gouesbet, “Scattering of a first-order Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation,” Part. Part. Syst. Charact. 12, 242–256 (1995).
    [CrossRef]
  21. J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
    [CrossRef]
  22. G. Gouesbet, “Higher-order descriptions of Gaussian beams,” J. Opt. (Paris) 27, 35–50 (1996).
    [CrossRef]
  23. G. Gouesbet, “Scattering of higher-order Gaussian beams by an infinite cylinder,” J of Opt. (Paris) 28, 45–65 (1997).
    [CrossRef]
  24. D. Guo, Methods of Mathematical Physics (People’s Education Press, Beijing, China, 1965), in Chinese.

1998

1997

1996

E. Lenglart, G. Gouesbet, “The separability theorem in terms of distributions with discussion of electromagnetic scattering theory,” J. Math. Phys. 37, 4705–4710 (1996).
[CrossRef]

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

1995

1994

1990

1989

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

1986

1979

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

1955

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” J. Phys. 33, 189–195 (1955).

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]

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]

Butkov, E.

E. Butkov, Mathematical Physics (Addison-Wesley, Reading, Mass., 1968).

Davis, L. W.

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

Gauchet, N.

N. Gauchet, T. Girasole, K. F. Ren, G. Gréhan, G. Gouesbet, “Application of generalized Lorenz–Mie theory for cylinders to cylindrical characterization by phase-Doppler anemometry,” Opt. Diagnost. Eng. 2, 1–10 (1997).

Girasole, T.

N. Gauchet, T. Girasole, K. F. Ren, G. Gréhan, G. Gouesbet, “Application of generalized Lorenz–Mie theory for cylinders to cylindrical characterization by phase-Doppler anemometry,” Opt. Diagnost. Eng. 2, 1–10 (1997).

Gouesbet, G.

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

N. Gauchet, T. Girasole, K. F. Ren, G. Gréhan, G. Gouesbet, “Application of generalized Lorenz–Mie theory for cylinders to cylindrical characterization by phase-Doppler anemometry,” Opt. Diagnost. Eng. 2, 1–10 (1997).

G. Gouesbet, “Scattering of higher-order Gaussian beams by an infinite cylinder,” J of Opt. (Paris) 28, 45–65 (1997).
[CrossRef]

G. Gouesbet, “Interaction between an infinite cylinder and an arbitrary-shaped beam,” Appl. Opt. 36, 4292–4304 (1997).
[CrossRef] [PubMed]

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

E. Lenglart, G. Gouesbet, “The separability theorem in terms of distributions with discussion of electromagnetic scattering theory,” J. Math. Phys. 37, 4705–4710 (1996).
[CrossRef]

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

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 representation of laser beams for use in light scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
[CrossRef] [PubMed]

G. Gouesbet, “Scattering of a first-order Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation,” Part. Part. Syst. Charact. 12, 242–256 (1995).
[CrossRef]

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

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

Gréhan, G.

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

N. Gauchet, T. Girasole, K. F. Ren, G. Gréhan, G. Gouesbet, “Application of generalized Lorenz–Mie theory for cylinders to cylindrical characterization by phase-Doppler anemometry,” Opt. Diagnost. Eng. 2, 1–10 (1997).

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

G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representation 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, 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, 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]

Guo, D.

D. Guo, Methods of Mathematical Physics (People’s Education Press, Beijing, China, 1965), in Chinese.

Lenglart, E.

E. Lenglart, G. Gouesbet, “The separability theorem in terms of distributions with discussion of electromagnetic scattering theory,” J. Math. Phys. 37, 4705–4710 (1996).
[CrossRef]

Lock, J. A.

Maheu, B.

Onofri, F.

Ren, K. F.

Roddier, F.

F. Roddier, Distributions et Transformation de Fourier (McGraw-Hill, New York, 1982).

Schwartz, L.

L. Schwartz, Théorie des Distributions (Hermann, Paris, 1951).

Wait, J. R.

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” J. Phys. 33, 189–195 (1955).

Appl. Opt.

J of Opt. (Paris)

G. Gouesbet, “Scattering of higher-order Gaussian beams by an infinite cylinder,” J of Opt. (Paris) 28, 45–65 (1997).
[CrossRef]

J. Appl. Phys.

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. Math. Phys.

E. Lenglart, G. Gouesbet, “The separability theorem in terms of distributions with discussion of electromagnetic scattering theory,” J. Math. Phys. 37, 4705–4710 (1996).
[CrossRef]

J. Opt. (Paris)

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

J. Opt. Soc. Am. A

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]

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

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

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

J. A. Lock, “Scattering of a diagonally incident focused Gaussian beam by an infinitely long homogeneous circular cylinder,” J. Opt. Soc. Am. A 14, 640–652 (1997).
[CrossRef]

J. A. Lock, “Morphology-dependent resonances of an infinitely long circular cylinder illuminated by a diagonally incident plane wave or a focused Gaussian beam,” J. Opt. Soc. Am. A 14, 653–661 (1997).
[CrossRef]

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

J. Phys.

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” J. Phys. 33, 189–195 (1955).

Opt. Diagnost. Eng.

N. Gauchet, T. Girasole, K. F. Ren, G. Gréhan, G. Gouesbet, “Application of generalized Lorenz–Mie theory for cylinders to cylindrical characterization by phase-Doppler anemometry,” Opt. Diagnost. Eng. 2, 1–10 (1997).

Part. Part. Syst. Charact.

G. Gouesbet, “Scattering of a first-order Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation,” Part. Part. Syst. Charact. 12, 242–256 (1995).
[CrossRef]

Phys. Rev. A

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

Other

F. Roddier, Distributions et Transformation de Fourier (McGraw-Hill, New York, 1982).

L. Schwartz, Théorie des Distributions (Hermann, Paris, 1951).

E. Butkov, Mathematical Physics (Addison-Wesley, Reading, Mass., 1968).

D. Guo, Methods of Mathematical Physics (People’s Education Press, Beijing, China, 1965), in Chinese.

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