Abstract

I expand the radiation potential of an arbitrary monochromatic electromagnetic wave in the cylindrical coordinate eigenfunctions of the scalar Helmholtz equation. Since the resulting beam shape coefficients are found to be an inverse Fourier transform of the z component of the beam fields, the incident Gaussian beam is parameterized by a Fourier angular spectrum of plane waves. The beam's partial-wave coefficients are then obtained, as well as the scattered fields produced by the interaction of the beam with an infinitely long homogeneous circular cylinder. The fields are evaluated analytically in the far zone by the method of stationary phase, and the physical interpretation of the results are discussed extensively.

© 1997 Optical Society of America

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  1. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), pp. 119–126.
  2. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), pp. 39–49.
  3. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 83–101.
  4. P. Debye, “Das elektromagnetische feld um einen zylinder un die theorie des regenbogens,” Phys. Z. 9, 775–778 (1908); reprinted and translated into English in Selected Papers on Geometrical Aspect of Scattering, P. L. Marston, ed., Vol. MS89 of SPIE Milestone Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1994), pp. 198–204.
  5. B. van der Pol, H. Bremmer, “The diffraction of electromagnetic waves from an electrical point source round a finitely conducting sphere, with applications to radiotelegraphy and the theory of the rainbow,” Philos. Mag. 24, 141–176, 825–864 (1937).
  6. G. N. Watson, “The diffraction of electric waves by the earth,” Proc. R. Soc. London, Ser. A 95, 83–99 (1918); reprinted in Ref. 4, pp. 262–270.
    [CrossRef]
  7. H. M. Nussenzveig, “High-frequency scattering by a transparent sphere. I. Direct reflection and transmission,” J. Math. Phys. 10, 82–124 (1969).
    [CrossRef]
  8. Ref. 1, pp. 210–214.
  9. J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
    [CrossRef]
  10. Ref. 2, pp. 255–266.
  11. Ref. 3, pp. 194–204.
  12. N. G. Alexopoulos, P. K. Park, “Scattering of waves with normal amplitude distribution from cylinders,” IEEE Trans. Antennas Propag. AP-20, 216–217 (1972).
    [CrossRef]
  13. T. Kojima, Y. Yanagiuchi, “Scattering of an offset two-dimensional Gaussian beam wave by a cylinder,” J. Appl. Phys. 50, 41–46 (1979).
    [CrossRef]
  14. S. Kozaki, “Scattering of a Gaussian beam by a homogeneous dielectric cylinder,” J. Appl. Phys. 53, 7195–7200 (1982).
    [CrossRef]
  15. S. Kozaki, “A new expression for the scattering of a Gaussian beam by a conducting cylinder,” IEEE Trans. Antennas Propag. AP-30, 881–887 (1982).
    [CrossRef]
  16. T. Kojima, Y. Yanagiuchi, “Scattering of an offset two-dimensional Gaussian beam wave by a cylinder,” J. Appl. Phys. 50, 41–46 (1979).
    [CrossRef]
  17. E. Zimmerman, R. Dandliker, N. Souli, B. Krattiger, “Scattering of an off-axis Gaussian beam by a dielectric cylinder compared with a rigorous electromagnetic approach,” J. Opt. Soc. Am. A 12, 398–403 (1995).
    [CrossRef]
  18. S. Kozaki, “Scattering of a Gaussian beam by an inhomogeneous dielectric cylinder,” J. Opt. Soc. Am. 72, 1470–1474 (1982).
    [CrossRef]
  19. T. C. K. Rao, “Scattering by a radially inhomogeneous cylindrical dielectric shell due to an incident Gaussian beam,” Can. J. Phys. 67, 471–475 (1989).
    [CrossRef]
  20. A. Z. Elsherbeni, M. Hamid, G. Tian, “Iterative scattering of a Gaussian beam by an array of circular conducting and dielectric cylinders,” J. Elect. Waves Appl. 7, 1323–1342 (1993).
  21. G. Gouesbet, G. Gréhan, “Interaction between shaped beams and an infinite cylinder, including a discussion of Gaussian beams,” Part. Part. Syst. Charact. 11, 299–308 (1994).
  22. G. Gouesbet, G. Gréhan, “Interaction between a Gaussian beam and an infinite cylinder with the use of non-Σ-separable potentials,” J. Opt. Soc. Am. A 11, 3261–3273 (1994).
    [CrossRef]
  23. G. Gouesbet, “The separability theorem revisited with applications to light scattering theory,” J. Opt. (Paris) 26, 123–135 (1995).
  24. G. Goeusbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Opt. (Paris) 26, 225–239 (1995).
  25. 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]
  26. G. Gouesbet, “Scattering of higher order Gaussian beams by an infinite cylinder,” submitted to J. Opt. (Paris).
  27. G. Gouesbet, “Interaction between an infinite cylinder and an arbitrary shaped beam,” Appl. Opt. (to be published).
  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 a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
    [CrossRef]
  30. G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism,” J. Opt. (Paris) 16, 83–93 (1985).
    [CrossRef]
  31. 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]
  32. J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical par-ticle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
    [CrossRef]
  33. 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]
  34. 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]
  35. 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]
  36. J. A. Lock, “Improved Gaussian beam-scattering algorithm,” Appl. Opt. 34, 559–570 (1995).
    [CrossRef] [PubMed]
  37. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 48–51.
  38. S. Kozaki, H. Sakurai, “Characteristics of a Gaussian beam at a dielectric interface,” J. Opt. Soc. Am. 68, 508–514 (1978).
    [CrossRef]
  39. E. E. M. Khaled, S. C. Hill, P. W. Barber, “Scattered and internal intensity of a sphere illuminated with a Gaussian beam,” IEEE Trans. Antennas Propag. 41, 295–303 (1993).
    [CrossRef]
  40. Ref. 1, p. 297, Fig. 64.
  41. Ref. 2, p. 256, Fig. 6.1.
  42. M. Kerker, D. Cooke, W. A. Farone, R. A. Jacobsen, “Electromagnetic scattering from an infinite circular cylinder at oblique incidence. I. Radiance functions for m=1.46,” J. Opt. Soc. Am. 56, 487–491 (1966).
    [CrossRef]
  43. 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]
  44. G. Gouesbet, G. Gréhan, B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
    [CrossRef]
  45. 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]
  46. Ref. 1, pp. 208–209.
  47. B. Maheu, G. Gréhan, G. Gouesbet, “Ray localization in Gaussian beams,” Opt. Commun. 70, 259–262 (1989).
    [CrossRef]
  48. H. Chew, D. D. Cooke, M. Kerker, “Raman and fluorescent scattering by molecules embedded in dielectric cylinders,” Appl. Opt. 19, 44–52 (1980).
    [CrossRef] [PubMed]
  49. L. Brillouin, “The scattering cross section of spheres for electromagnetic waves,” J. Appl. Phys. 20, 1110–1115 (1949).
    [CrossRef]
  50. H. M. Nussenzveig, “High-frequency scattering by an impenetrable sphere,” Ann. Phys. (N.Y.) 34, 23–95 (1965); see Fig. 14 on p. 82.
    [CrossRef]
  51. J. A. Lock, E. A. Hovenac, “Diffraction of a Gaussian beam by a spherical obstacle,” Am. J. Phys. 61, 698–707 (1993); see Fig. 4 on p. 704.
    [CrossRef]
  52. J. A. Lock, “Interpretation of extinction in Gaussian-beam scattering,” J. Opt. Soc. Am. A 12, 929–938 (1995).
    [CrossRef]
  53. 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]
  54. J. T. Hodges, G. Gréhan, G. Gouesbet, C. Presser, “Forward scattering of a Gaussian beam by a nonabsorbing sphere,” Appl. Opt. 34, 2120–2132 (1995).
    [CrossRef] [PubMed]
  55. J. A. Lock, J. T. Hodges, “Far field scattering of an axisymmetric laser beam of arbitrary profile by an on-axis spherical particle,” Appl. Opt. 35, 4283–4290 (1996).
    [CrossRef] [PubMed]
  56. J. A. Lock, J. T. Hodges, “Far-field scattering of a non-Gaussian off-axis axisymmetric laser beam by a spherical particle,” Appl. Opt. 35, 6605–6616 (1996).
    [CrossRef] [PubMed]

1997

1996

1995

1994

1993

E. E. M. Khaled, S. C. Hill, P. W. Barber, “Scattered and internal intensity of a sphere illuminated with a Gaussian beam,” IEEE Trans. Antennas Propag. 41, 295–303 (1993).
[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]

A. Z. Elsherbeni, M. Hamid, G. Tian, “Iterative scattering of a Gaussian beam by an array of circular conducting and dielectric cylinders,” J. Elect. Waves Appl. 7, 1323–1342 (1993).

J. A. Lock, E. A. Hovenac, “Diffraction of a Gaussian beam by a spherical obstacle,” Am. J. Phys. 61, 698–707 (1993); see Fig. 4 on p. 704.
[CrossRef]

1990

1989

T. C. K. Rao, “Scattering by a radially inhomogeneous cylindrical dielectric shell due to an incident Gaussian beam,” Can. J. Phys. 67, 471–475 (1989).
[CrossRef]

B. Maheu, G. Gréhan, G. Gouesbet, “Ray localization in Gaussian beams,” Opt. Commun. 70, 259–262 (1989).
[CrossRef]

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

1988

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

1985

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism,” J. Opt. (Paris) 16, 83–93 (1985).
[CrossRef]

1982

S. Kozaki, “Scattering of a Gaussian beam by a homogeneous dielectric cylinder,” J. Appl. Phys. 53, 7195–7200 (1982).
[CrossRef]

S. Kozaki, “A new expression for the scattering of a Gaussian beam by a conducting cylinder,” IEEE Trans. Antennas Propag. AP-30, 881–887 (1982).
[CrossRef]

S. Kozaki, “Scattering of a Gaussian beam by an inhomogeneous dielectric cylinder,” J. Opt. Soc. Am. 72, 1470–1474 (1982).
[CrossRef]

1980

1979

T. Kojima, Y. Yanagiuchi, “Scattering of an offset two-dimensional Gaussian beam wave by a cylinder,” J. Appl. Phys. 50, 41–46 (1979).
[CrossRef]

T. Kojima, Y. Yanagiuchi, “Scattering of an offset two-dimensional Gaussian beam wave by a cylinder,” J. Appl. Phys. 50, 41–46 (1979).
[CrossRef]

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

1978

1972

N. G. Alexopoulos, P. K. Park, “Scattering of waves with normal amplitude distribution from cylinders,” IEEE Trans. Antennas Propag. AP-20, 216–217 (1972).
[CrossRef]

1969

H. M. Nussenzveig, “High-frequency scattering by a transparent sphere. I. Direct reflection and transmission,” J. Math. Phys. 10, 82–124 (1969).
[CrossRef]

1966

1965

H. M. Nussenzveig, “High-frequency scattering by an impenetrable sphere,” Ann. Phys. (N.Y.) 34, 23–95 (1965); see Fig. 14 on p. 82.
[CrossRef]

1955

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

1949

L. Brillouin, “The scattering cross section of spheres for electromagnetic waves,” J. Appl. Phys. 20, 1110–1115 (1949).
[CrossRef]

1937

B. van der Pol, H. Bremmer, “The diffraction of electromagnetic waves from an electrical point source round a finitely conducting sphere, with applications to radiotelegraphy and the theory of the rainbow,” Philos. Mag. 24, 141–176, 825–864 (1937).

1918

G. N. Watson, “The diffraction of electric waves by the earth,” Proc. R. Soc. London, Ser. A 95, 83–99 (1918); reprinted in Ref. 4, pp. 262–270.
[CrossRef]

1908

P. Debye, “Das elektromagnetische feld um einen zylinder un die theorie des regenbogens,” Phys. Z. 9, 775–778 (1908); reprinted and translated into English in Selected Papers on Geometrical Aspect of Scattering, P. L. Marston, ed., Vol. MS89 of SPIE Milestone Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1994), pp. 198–204.

Alexander, D. R.

J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a 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 par-ticle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

Alexopoulos, N. G.

N. G. Alexopoulos, P. K. Park, “Scattering of waves with normal amplitude distribution from cylinders,” IEEE Trans. Antennas Propag. AP-20, 216–217 (1972).
[CrossRef]

Barber, P. W.

E. E. M. Khaled, S. C. Hill, P. W. Barber, “Scattered and internal intensity of a sphere illuminated with a Gaussian beam,” IEEE Trans. Antennas Propag. 41, 295–303 (1993).
[CrossRef]

Barton, J. P.

J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a 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 par-ticle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 83–101.

Bremmer, H.

B. van der Pol, H. Bremmer, “The diffraction of electromagnetic waves from an electrical point source round a finitely conducting sphere, with applications to radiotelegraphy and the theory of the rainbow,” Philos. Mag. 24, 141–176, 825–864 (1937).

Brillouin, L.

L. Brillouin, “The scattering cross section of spheres for electromagnetic waves,” J. Appl. Phys. 20, 1110–1115 (1949).
[CrossRef]

Chew, H.

Cooke, D.

Cooke, D. D.

Dandliker, R.

Davis, L. W.

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

Debye, P.

P. Debye, “Das elektromagnetische feld um einen zylinder un die theorie des regenbogens,” Phys. Z. 9, 775–778 (1908); reprinted and translated into English in Selected Papers on Geometrical Aspect of Scattering, P. L. Marston, ed., Vol. MS89 of SPIE Milestone Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1994), pp. 198–204.

Elsherbeni, A. Z.

A. Z. Elsherbeni, M. Hamid, G. Tian, “Iterative scattering of a Gaussian beam by an array of circular conducting and dielectric cylinders,” J. Elect. Waves Appl. 7, 1323–1342 (1993).

Farone, W. A.

Goeusbet, G.

G. Goeusbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Opt. (Paris) 26, 225–239 (1995).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 48–51.

Gouesbet, G.

G. Gouesbet, “The separability theorem revisited with applications to light scattering theory,” J. Opt. (Paris) 26, 123–135 (1995).

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]

J. T. Hodges, G. Gréhan, G. Gouesbet, C. Presser, “Forward scattering of a Gaussian beam by a nonabsorbing sphere,” Appl. Opt. 34, 2120–2132 (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]

G. Gouesbet, G. Gréhan, “Interaction between shaped beams and an infinite cylinder, including a discussion of Gaussian beams,” Part. Part. Syst. Charact. 11, 299–308 (1994).

G. Gouesbet, G. Gréhan, “Interaction between a Gaussian beam and an infinite cylinder with the use of non-Σ-separable potentials,” J. Opt. Soc. Am. A 11, 3261–3273 (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]

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

B. Maheu, G. Gréhan, G. Gouesbet, “Ray localization in Gaussian beams,” Opt. Commun. 70, 259–262 (1989).
[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]

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism,” J. Opt. (Paris) 16, 83–93 (1985).
[CrossRef]

G. Gouesbet, “Scattering of higher order Gaussian beams by an infinite cylinder,” submitted to J. Opt. (Paris).

G. Gouesbet, “Interaction between an infinite cylinder and an arbitrary shaped beam,” Appl. Opt. (to be published).

Gréhan, G.

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]

J. T. Hodges, G. Gréhan, G. Gouesbet, C. Presser, “Forward scattering of a Gaussian beam by a nonabsorbing sphere,” Appl. Opt. 34, 2120–2132 (1995).
[CrossRef] [PubMed]

G. Gouesbet, G. Gréhan, “Interaction between a Gaussian beam and an infinite cylinder with the use of non-Σ-separable potentials,” J. Opt. Soc. Am. A 11, 3261–3273 (1994).
[CrossRef]

G. Gouesbet, G. Gréhan, “Interaction between shaped beams and an infinite cylinder, including a discussion of Gaussian beams,” Part. Part. Syst. Charact. 11, 299–308 (1994).

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

B. Maheu, G. Gréhan, G. Gouesbet, “Ray localization in Gaussian beams,” Opt. Commun. 70, 259–262 (1989).
[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]

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism,” J. Opt. (Paris) 16, 83–93 (1985).
[CrossRef]

Hamid, M.

A. Z. Elsherbeni, M. Hamid, G. Tian, “Iterative scattering of a Gaussian beam by an array of circular conducting and dielectric cylinders,” J. Elect. Waves Appl. 7, 1323–1342 (1993).

Hill, S. C.

E. E. M. Khaled, S. C. Hill, P. W. Barber, “Scattered and internal intensity of a sphere illuminated with a Gaussian beam,” IEEE Trans. Antennas Propag. 41, 295–303 (1993).
[CrossRef]

Hodges, J. T.

Hovenac, E. A.

J. A. Lock, E. A. Hovenac, “Diffraction of a Gaussian beam by a spherical obstacle,” Am. J. Phys. 61, 698–707 (1993); see Fig. 4 on p. 704.
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 83–101.

Jacobsen, R. A.

Kerker, M.

Khaled, E. E. M.

E. E. M. Khaled, S. C. Hill, P. W. Barber, “Scattered and internal intensity of a sphere illuminated with a Gaussian beam,” IEEE Trans. Antennas Propag. 41, 295–303 (1993).
[CrossRef]

Kojima, T.

T. Kojima, Y. Yanagiuchi, “Scattering of an offset two-dimensional Gaussian beam wave by a cylinder,” J. Appl. Phys. 50, 41–46 (1979).
[CrossRef]

T. Kojima, Y. Yanagiuchi, “Scattering of an offset two-dimensional Gaussian beam wave by a cylinder,” J. Appl. Phys. 50, 41–46 (1979).
[CrossRef]

Kozaki, S.

S. Kozaki, “A new expression for the scattering of a Gaussian beam by a conducting cylinder,” IEEE Trans. Antennas Propag. AP-30, 881–887 (1982).
[CrossRef]

S. Kozaki, “Scattering of a Gaussian beam by a homogeneous dielectric cylinder,” J. Appl. Phys. 53, 7195–7200 (1982).
[CrossRef]

S. Kozaki, “Scattering of a Gaussian beam by an inhomogeneous dielectric cylinder,” J. Opt. Soc. Am. 72, 1470–1474 (1982).
[CrossRef]

S. Kozaki, H. Sakurai, “Characteristics of a Gaussian beam at a dielectric interface,” J. Opt. Soc. Am. 68, 508–514 (1978).
[CrossRef]

Krattiger, B.

Lock, J. A.

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]

J. A. Lock, J. T. Hodges, “Far-field scattering of a non-Gaussian off-axis axisymmetric laser beam by a spherical particle,” Appl. Opt. 35, 6605–6616 (1996).
[CrossRef] [PubMed]

J. A. Lock, J. T. Hodges, “Far field scattering of an axisymmetric laser beam of arbitrary profile by an on-axis spherical particle,” Appl. Opt. 35, 4283–4290 (1996).
[CrossRef] [PubMed]

J. A. Lock, “Interpretation of extinction in Gaussian-beam scattering,” J. Opt. Soc. Am. A 12, 929–938 (1995).
[CrossRef]

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]

J. A. Lock, “Improved Gaussian beam-scattering algorithm,” Appl. Opt. 34, 559–570 (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]

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]

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]

J. A. Lock, E. A. Hovenac, “Diffraction of a Gaussian beam by a spherical obstacle,” Am. J. Phys. 61, 698–707 (1993); see Fig. 4 on p. 704.
[CrossRef]

Maheu, B.

Nussenzveig, H. M.

H. M. Nussenzveig, “High-frequency scattering by a transparent sphere. I. Direct reflection and transmission,” J. Math. Phys. 10, 82–124 (1969).
[CrossRef]

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Appl. Opt.

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[CrossRef]

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[CrossRef]

S. Kozaki, “Scattering of a Gaussian beam by a homogeneous dielectric cylinder,” J. Appl. Phys. 53, 7195–7200 (1982).
[CrossRef]

T. Kojima, Y. Yanagiuchi, “Scattering of an offset two-dimensional Gaussian beam wave by a cylinder,” J. Appl. Phys. 50, 41–46 (1979).
[CrossRef]

J. Elect. Waves Appl.

A. Z. Elsherbeni, M. Hamid, G. Tian, “Iterative scattering of a Gaussian beam by an array of circular conducting and dielectric cylinders,” J. Elect. Waves Appl. 7, 1323–1342 (1993).

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G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism,” J. Opt. (Paris) 16, 83–93 (1985).
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J. Opt. Soc. Am. A

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Ref. 1, pp. 210–214.

Ref. 2, pp. 255–266.

Ref. 3, pp. 194–204.

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Figures (4)

Fig. 1
Fig. 1

Geometry of the incident beam and the scattered wave. The dominant incident propagation vector lies in the xz plane and makes an angle ξ with the x axis. The cylindrical coordinates of the point P in the far zone of the scattered radiation are (r, θ, z).

Fig. 2
Fig. 2

A focused Gaussian beam has the dominant propagation direction AA in the xz plane and making an angle ξ with the x axis. The center of its focal waist is at the coordinate (x0, y0, z0).

Fig. 3
Fig. 3

The horizontal and vertical directions on the viewing screen are θ and η, respectively. The scattered wave produced by each plane-wave component in the Fourier spectrum of the incident beam is a cone with a different opening angle and intersecting the viewing screen at a different vertical coordinate η.

Fig. 4
Fig. 4

The beam ray AA lies in the xy plane. Upon interaction with the cylinder, its trajectory is strongly deflected to the A direction. The beam ray BB lies in the vertical (xz) plane. Upon transmission through the cylinder, its trajectory is only mildly shifted to B by multiple internal reflections.

Equations (134)

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kinc=k[(cos ξ)uˆx-(sin ξ)uˆz].
E(r, θ, z)=-uˆz×ψ(r, θ, z)=1rψθuˆr-ψruˆθ,
B(r, θ, z)=iω×[uˆz×ψ(r, θ, z)]=-iω2ψrzuˆr-iωr2ψθzuˆθ-iωN2k2ψ+2ψz2uˆz,
ψinc(r, θ, z)=-dhl=- il+1k cos ξE0Al(h)×Jl[kr(1-h2)1/2]×exp(ikhz)exp(ilθ),
Al(h)=(-i)lk cos ξ(2π)2(1-h2)Jl[kr(1-h2)1/2]×-dz02πdθ[exp(-ikhz)×exp(-ilθ)]cBz,inc(r, θ, z)/E0,
E(r, θ, z)=icNω×[uˆz×ψμ(r, θ, z)]=-icNω2ψμrzuˆr-icNωr2ψμθzuˆθ-icNωN2k2ψμ+2ψμz2uˆz,
B(r, θ, z, t)=Ncuˆz×ψμ(r, θ, z)=-Ncrψμθuˆr+Ncψμruˆθ,
ψincμ(r, θ, z)=-dhl=- il+1k cos ξE0Bl(h)×Jl(kr(1-h2)1/2)×exp(ikhz)exp(ilθ),
Bl(h)=(-i)lk cos ξ(2π)2(1-h2)Jl(kr(1-h2)1/2)×-dz02πdθ[exp(-ikhz)×exp(-ilθ)]Ez,inc(r, θ, z)/E0,
ψscatt(r, θ, z)=-- dh l=- il+1k cos ξ×E0αl(h)Hl(1)(kr(1-h2)1/2)×exp(ikhz)exp(ilθ),
ψscattμ(r, θ, z)=-- dh l=- il+1k cos ξ×E0βl(h)Hl(1)(kr(1-h2)1/2)×exp(ikhz)exp(ilθ),
ψinterior(r, θ, z)=- dh l=- il+1k cos ξ×E0nγl(h)Jl(nkr(1-h2)1/2)×exp(inkhz)exp(ilθ),
ψinteriorμ(r, θ, z)=- dh l=- il+1k cos ξ×E0nδl(h)Jl(nkr(1-h2)1/2)×exp(inkhz)exp(ilθ),
h=h/n.
αl(h)=al(h)Al(h)+ql(h)Bl(h),
βl(h)=-ql(h)Al(h)+bl(h)Bl(h)
γl(h)=cl(h)Al(h)+pl(h)Bl(h),
δl(h)=-npl(h)Al(h)+dl(h)Bl(h)
xka(1-h2)1/2,ynka(1-h2/n2)1/2,
al(h)=U2W1-nU3W3W1W2-nW32,
bl(h)=U1W2-nU3W3W1W2-nW32,
ql(h)=2nlh(y2-x2)πx2y2Jl2(y)W1W2-nW32,
cl(h)=-2inxπy2W1W1W2-nW32,
dl(h)=-2inxπy2W2W1W2-nW32,
pl(h)=-2nxπy2W3W1W2-nW32,
U1=n2xyJl(x)Jl(y)-Jl(x)Jl(y),
U2=nxyJl(x)Jl(y)-nJl(x)Jl(y),
U3=hl(y2-x2)xy2Jl(x)Jl(y),
W1=n2xyHl(1)(x)Jl(y)-Hl(1)(x)Jl(y),
W2=nxyHl(1)(x)Jl(y)-nHl(1)(x)Jl(y),
W3=hl(y2-x2)xy2Hl(1)(x)Jl(y).
limr Escatt(r, θ, z)=E0cos ξ2πkr1/2[exp(-iπ/4)]×(T5uˆr-T2uˆθ-T3uˆz),
limr Bscatt(r, θ, z)=E0c cos ξ2πkr1/2[exp(-iπ/4)]×(T6uˆr+T1uˆθ-T4uˆz),
T1=- dh l=- (1-h2)1/4βl(h)×exp[ikr(1-h2)1/2]×exp(ikhz)exp(ilθ),
T2=- dh l=- (1-h2)1/4αl(h)×exp[ikr(1-h2)1/2]×exp(ikhz)exp(ilθ),
T3=- dh l=- (1-h2)3/4βl(h)×exp[ikr(1-h2)1/2]×exp(ikhz)exp(ilθ),
T4=- dh l=- (1-h2)3/4αl(h)×exp[ikr(1-h2)1/2]×exp(ikhz)exp(ilθ),
T5=- dh l=- h(1-h2)1/4βl(h)×exp[ikr(1-h2)1/2]×exp(ikhz)exp(ilθ),
T6=- dh l=- h(1-h2)1/4αl(h)×exp[ikr(1-h2)1/2]×exp(ikhz)exp(ilθ).
limr Iscatt(r, θ, z)=ReEscatt*×Bscatt2μ0c=2πkr cos2 ξE022μ0cRe[(T2*T4+T3*T1)uˆr+(T5*T4-T3*T6)uˆθ+(T5*T1+T2*T6)uˆz],
Einc(r, θ, z)=E0[exp(ikinc·r)]uˆy,
Binc(r, θ, z)=E0c[exp(ikinc·r)]×[(sin ξ)uˆx+(cos ξ)uˆz],
r=r(cos θ)uˆx+r(sin θ)uˆy+zuˆz.
Al(h)=δ(h+sin ξ),Bl(h)=0,
Einc(r, θ, z)=E0[exp(ikinc·r)][(sin ξ)uˆx+(cos ξ)uˆz],
Binc(r, θ, z)=-E0c[exp(ikinc·r)]uˆy.
Al(h)=0,Bl(h)=δ(h+sin ξ).
limr Escatt(r, θ, z)=Eμμpw(r, θ, z)+Eμpw(r, θ, z),
limr Bscatt(r, θ, z)=Bμμpw(r, θ, z)+Bμpw(r, θ, z),
Eμμpw(r, θ, z)=ε0pw[Sμpw(θ)][(sin ξ)uˆr+(cos ξ)uˆz],
Bμμpw(r, θ, z)=ε0pwc[Sμpw(θ)](-uˆθ)
Eμpw(r, θ, z)=ε0pw[Sqpw(θ)]uˆθ,
Bμpw(r, θ, z)=ε0pwc[Sqpw(θ)][(sin ξ)uˆr+(cos ξ)uˆz].
ε0pw=-E02πkr cos ξ1/2 exp(-iπ/4)exp(ikscatt·r),
kscatt=k[(cos ξ)uˆr-(sin ξ)uˆz],
Sμpw(θ)=l=- bl(h=-sin ξ)exp(ilθ)=b0+2 l=1 bl cos(lθ),
Sqpw(θ)=l=- ql(h=-sin ξ)exp(ilθ)=2i l=1 ql sin(lθ).
limr Iscatt(r, θ, z)=E022μ0c2πkr cos ξ×[|Sμpw(θ)|2+|Sqpw(θ)|2]kˆscatt.
limr Escatt(r, θ, z)=Epw(r, θ, z)-Eμpw(r, θ, z),
limr Bscatt(r, θ, z)=Bpw(r, θ, z)-Bμpw(r, θ, z),
Epw(r, θ, z)=ε0pw[Spw(θ)]uˆθ,
Bpw(r, θ, z)=ε0pwc[Spw(θ)][(sin ξ)uˆr+(cos ξ)uˆz]
Eμpw(r, θ, z)=ε0pw[Sqpw(θ)][(sin ξ)uˆr+(cos ξ)uˆz],
Bμpw(r, θ, z)=ε0pwc[Sqpw(θ)](-uˆθ),
Spw(θ)=l=-al(h=-sin ξ)exp(ilθ)=a0+2 l=1al cos(lθ).
limr Iscatt(r, θ, z)=E022μ0c2πkr cos ξ[|Spw(θ)|2+|Sqpw(θ)|2]kˆscatt.
Einc(x, y, z)=E0 exp(ikx)Dexp[-(y2+z2)/Dw02]×-2iszw0Duˆx+uˆz,
Binc(x, y, z)=E0 exp(ikx)cDexp[-(y2+z2)/Dw02]×2isyw0Duˆx-uˆy,
s1kw0
D=1+2is2kx.
Bl(h)=(-i)l4sπ3/2(1-h2)Jl(kr(1-h2)1/2)×exp(-h2/4s2) 02π dθD1/2×expikr1-h22cos θ-lθ×exp -s2k2r2 sin2 θD.
Bl(h)=exp(-h2/4s2)2sπ1/2(1-h2)Jl[kr(1-h2/2)]Jl[kr(1-h2)1/2]×1-s2l2(1-h2/2)2+O(s4)+krJl[kr(1-h2/2)]Jl[kr(1-h2)1/2]s2h2/21-h2/2+O(s4).
Bl(h)12sπ1/2(1-h2)[exp(-h2/4s2)]1-s2l21-h212sπ1/2(1-h2)exp(-h2/4s2)×exp[-s2l2/(1-h2)].
Einc(x, y, z)=[Ex,inc(x, y, z)]uˆx+[Ez,inc(x, y, z)]uˆz.
Ez,inc(x0, y, z)=E0 exp[-(y-y0)2/w02]exp(-z2/w02),
Ez,inc(x0, y, z)=E0w024π- k dhy - k dhz×exp(-hy2/4s2)exp(-hz2/4s2)×exp[ikhy(y-y0)]exp(ikhzz).
Ez,inc(x, y, z)=E0w024π- k dhy - k dhz×exp(-hy2/4s2)exp(-hz2/4s2)×exp[ikhx(x-x0)]×exp[ikhy(y-y0)]exp(ikhzz)
hx=(1-hy2-hz2)1/2.
·Einc=0.
Bl(h)=14πs2(1-h2)exp(-h2/4s2) - dhy×exp[-ikx0(1-h2-hy2)1/2]×exp(-ikhyy0)exp(-hy2/4s2)×exp{-il arcsin[hy(1-h2)-1/2]}.
Bl(h)12sπ1/2(1-h2)×exp[-ikx0(1-h2)1/2][1-2is2kx0(1-h2)-1/2]1/2exp(-h2/4s2)×exp-s2[l(1-h2)-1/2+ky0]21-2is2kx0(1-h2)-1/2.
l=-ky0(1-h2)1/2,
l+1/2=ky0.
Ez,inc(x, y, z)=E0w024π- k dhy - k dhz×exp[ikhx(x cos ξ-z sin ξ-x0 cos ξ+z0 sin ξ)]×exp[ikhy(y-y0)]×exp[ikhz(x sin ξ+z cos ξ-x0 sin ξ-z0 cos ξ)]exp(-hy2/4s2)×exp(-hz2/4s2)cos ξ+hzhxsin ξ.
Bl(h)=cos ξ4πs2(1-h2)exp(-ikhz0)exp{-[h2 cos2 ξ+(1-h2)sin2 ξ]/4s2} - dhy×exp[-ikx0(1-h2-hy2)1/2]exp(-ikhyy0)×exp{-[2h(1-h2-hy2)1/2×sin ξ cos ξ+hy2 cos2 ξ]/4s2}×exp{-il arcsin[hy(1-h2)-1/2]}.
Bl(h)cos ξ2sπ1/2(1-h2)F1/2×exp{-ik[hz0+(1-h2)1/2x0]}×exp{-[h cos ξ+(1-h2)1/2 sin ξ]2/4s2}×exp{-s2[l(1-h2)-1/2+ky0]2/F},
F=(cos ξ)[cos ξ-h(1-h2)-1/2 sin ξ]-2is2kx0(1-h2)-1/2.
Al(h)=0,
Bl(h)=cos ξ2sπ1/2(1-h2)F1/2×exp{-ik[hz0+(1-h2)1/2x0]}×exp{-[h cos ξ+(1-h2)1/2 sin ξ]2/4s2}×exp{-s2[l(1-h2)-1/2+ky0]2/F},
Al(h)=cos ξ2sπ1/2(1-h2)F1/2×exp{-ik[hz0+(1-h2)1/2x0]}×exp{-[h cos ξ+(1-h2)1/2 sin ξ]2/4s2}×exp{-s2[l(1-h2)-1/2+ky0]2/F},
Bl(h)=0.
h=-sin ξ,
S(θ, h)=l=- [exp(ilθ)]al(h)×exp{-s2[l(1-h2)-1/2+ky0]2/F},
Sμ(θ, h)=l=- [exp(ilθ)]bl(h)×exp{-s2[l(1-h2)-1/2+ky0]2/F},
Sq(θ, h)=l=- [exp(ilθ)]ql(h)×exp{-s2[l(1-h2)-1/2+ky0]2/F}.
T1(r, θ, z)=cos ξ2sπ1/2- dh Sμ(θ, h)(1-h2)3/4F1/2×exp[ikr(1-h2)1/2]exp(ikhz)×exp{-ik[hz0+(1-h2)1/2x0]}×exp{-[h cos ξ+(1-h2)1/2×sin ξ]2/4s2}.
Φ(h)=k(r-x0)(1-h2)1/2+k(z-z0)h+Phase(Sμ)+Phase(F-1/2).
T1sp(r, θ, z)=GspSμ(θ, hsp),
hsp=z(r2+z2)1/2=sin η,
Gsp=(cos ξ)(cos η)1/2 exp(-iπ/4)s(2kr)1/2[(cos ξ)cos(ξ+η)-2is2kx0]1/2×exp{ik[(r-x0)2+(z-z0)2]1/2}×exp{-[sin2(ξ+η)]/4s2}.
T2sp(r, θ, z)=GspSq(θ, hsp),
T3sp(r, θ, z)=Gsp(cos η)Sμ(θ, hsp),
T4sp(r, θ, z)=Gsp(cos η)Sq(θ, hsp),
T5sp(r, θ, z)=Gsp(sin η)Sμ(θ, hsp),
T6sp(r, θ, z)=Gsp(sin η)Sq(θ, hsp).
limr Escatt(r, θ, z)=Eμμ(r, θ, z)+Eμ(r, θ, z),
limr Bscatt(r, θ, z)=Bμμ(r, θ, z)+Bμ(r, θ, z),
Eμμ(r, θ, z)=ε0[Sμ(θ, hsp)][-(sin η)uˆr+(cos η)uˆz],
Bμμ(r, θ, z)=ε0c[Sμ(θ, hsp)](-uˆθ)
Eμ(r, θ, z)=ε0[Sq(θ, hsp)]uˆθ,
Bμ(r, θ, z)=ε0c[Sq(θ, hsp)][-(sin η)uˆr+(cos η)uˆz],
ε0=iE0w0(cos η)1/2π1/2r[cos ξ cos(ξ+η)-2is2kx0]1/2×exp{ik[(r-x0)2+(z-z0)2]1/2}×exp{-[sin2(ξ+η)]/4s2}.
limr Iscatt(r, θ, z)=E02w02 cos ηπr2[cos2 ξ cos2(ξ+η)+4s2x02/w02]-1/2×({exp-[sin2(ξ+η)]/2s2})×[|Sμ(θ, hsp)|2+|Sq(θ, hsp)|2]×[(cos η)uˆr+(sin η)uˆz].
T1sp(r, θ, z)=-GspSq(θ, hsp),
T2sp(r, θ, z)=GspS(θ, hsp),
T3sp(r, θ, z)=-Gsp(cos η)Sq(θ, hsp),
T4sp(r, θ, z)=Gsp(cos η)S(θ, hsp),
T5sp(r, θ, z)=-Gsp(sin η)Sq(θ, hsp),
T6sp(r, θ, z)=Gsp(sin η)S(θ, hsp).
limr Escatt(r, θ, z)=E(r, θ, z)-Eμ(r, θ, z),
limr Bscatt(r, θ, z)=B(r, θ, z)-Bμ(r, θ, z),
E(r, θ, z)=ε0[S(θ, hsp)]uˆθ,
B(r, θ, z)=ε0c[S(θ, hsp)][-(sin η)uˆr+(cos η)uˆz]
Eμ(r, θ, z)=ε0[Sq(θ, hsp)][-(sin η)uˆr+(cos η)uˆz],
Bμ(r, θ, z)=ε0c[Sq(θ, hsp)](-uˆθ).
limr Iscatt(r, θ, z)=E02w02 cos ηπr2[cos2 ξ cos2(ξ+η)+4s2x02/w02]-1/2×({exp-[sin2(ξ+η)]/2s2})×[|S(θ, hsp)|2+|Sq(θ, hsp)|2]×[(cos η)uˆr+(sin η)uˆz].
limr limθ,η1 Einc(r, θ, z)=-ikE0w022r{exp[ik(r2+z2)1/2]×exp[-(θ2+η2)/4s2]}×(-ηuˆr+uˆz),
limr limθ,η1 Binc(r, θ, z)=-ikE0w022cr{exp[ik(r2+z2)1/2]×exp[-(θ2+η2)/4s2]}×(-uˆθ),
Eμμ(r, θ, z)iE0w0π1/2r{exp[ik(r2+z2)1/2]×[exp(-η2/4s2)]}×[Sμ(θ, η)](-ηuˆr+uˆz),
Bμμ(r, θ, z)iE0w0π1/2cr{exp[ik(r2+z2)1/2]×[exp(-η2/4s2)]}[Sμ(θ, η)](-uˆθ),
Eμ(r, θ, z)iE0w0π1/2r{exp[ik(r2+z2)1/2]×[exp(-η2/4s2)]}[Sq(θ, η)]uˆθ,
Bμ(r, θ, z)iE0w0π1/2cr{exp[ik(r2+z2)1/2]×[exp(-η2/4s2)]}[Sq(θ, η)]×(-ηuˆr+uˆz),
Sμ(θ, η)=l=- [exp(ilθ)][bl(hsp)]exp(-s2l2/cos2 η),
Sq(θ, η)=l=- [exp(ilθ)][ql(hsp)]exp(-s2l2/cos2 η).

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