Abstract

A cylindrical coordinate separation-of-variables solution is developed for the determination of the internal and the near-surface electromagnetic fields for the arrangement of a focused beam incident upon a homogeneous infinite circular cylinder. The angle of incidence and the focal point location of the beam, as well as the beam type (e.g., fundamental Gaussian beam, doughnut mode beam, TEM11 mode beam), can be arbitrarily specified. As a demonstration of the procedure, gray-level and contour plots of calculated electric-field distributions for a fundamental Gaussian beam focused on a cylinder are presented for six different angle-of-incidence and relative index-of-refraction combinations.

© 1999 Optical Society of America

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  1. 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]
  2. J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
    [CrossRef]
  3. J. P. Barton, D. R. Alexander, “Electromagnetic fields for an irregularly-shaped, near-spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 69, 7973–7986 (1991).
    [CrossRef]
  4. J. P. Barton, “Internal and near-surface electromagnetic fields for a spheroidal particle with arbitrary illumination,” Appl. Opt. 34, 5542–5551 (1995).
    [CrossRef] [PubMed]
  5. J. P. Barton, “Internal and near-surface electromagnetic fields for an absorbing spheroidal particle with arbitrary illumination,” Appl. Opt. 34, 8472–8473 (1995).
    [CrossRef] [PubMed]
  6. J. P. Barton, “Electromagnetic field calculations for irregularly-shaped, axisymmetric layered particles with focused illumination,” Appl. Opt. 35, 532–541 (1996).
    [CrossRef] [PubMed]
  7. T. Kojima, Y. Yanagiuchi, “Scattering of an offset two-dimensional Gaussian beam wave by a cylinder,” J. Appl. Phys. 50, 41–46 (1979).
    [CrossRef]
  8. S. Kozaki, “Scattering of a Gaussian beam by a homogeneous dielectric cylinder,” J. Appl. Phys. 53, 7195–7200 (1982).
    [CrossRef]
  9. 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]
  10. E. Zimmermann, 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]
  11. 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]
  12. S. Kozaki, “Scattering of a Gaussian beam by an inhomogeneous dielectric cylinder,” J. Opt. Soc. Am. 72, 1470–1474 (1982).
    [CrossRef]
  13. T. C. K. Rao, “Scattering by a radially inhomogeneous cylindrical dielectric shell due to an incident Gaussian beam,” Can. J. Phys. 67, 471–475 (1988).
    [CrossRef]
  14. J. P. Barton, “Electromagnetic field calculations for irregularly shaped, layered cylindrical particles with focused illumination,” Appl. Opt. 36, 1312–1319 (1997).
    [CrossRef] [PubMed]
  15. 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]
  16. G. Gouesbet, “Scattering of higher-order Gaussian beams by an infinite cylinder,” J. Opt. 28, 45–65 (1997).
    [CrossRef]
  17. G. Gouesbet, “Interaction between an infinite cylinder and an arbitrary-shaped beam,” Appl. Opt. 36, 4292–4304 (1997).
    [CrossRef] [PubMed]
  18. 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]
  19. G. Gouesbet, G. Gréhan, K. F. Ren, “Rigorous justification of the cylindrical localized approximation to speed up computations in the generalized Lorenz–Mie theory for cylinders,” J. Opt. Soc. Am. A 15, 511–523 (1998).
    [CrossRef]
  20. 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]
  21. 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]
  22. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  23. 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]
  24. J. P. Barton, “Electromagnetic field calculations for a sphere illuminated by a higher-order Gaussian beam. I. Internal and near-field effects,” Appl. Opt. 36, 1303–1311 (1997).
    [CrossRef] [PubMed]

1998

1997

1996

1995

1994

1991

J. P. Barton, D. R. Alexander, “Electromagnetic fields for an irregularly-shaped, near-spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 69, 7973–7986 (1991).
[CrossRef]

1989

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (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 particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

T. C. K. Rao, “Scattering by a radially inhomogeneous cylindrical dielectric shell due to an incident Gaussian beam,” Can. J. Phys. 67, 471–475 (1988).
[CrossRef]

1982

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

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]

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]

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]

Alexander, D. R.

J. P. Barton, D. R. Alexander, “Electromagnetic fields for an irregularly-shaped, near-spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 69, 7973–7986 (1991).
[CrossRef]

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (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]

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]

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]

Barton, J. P.

J. P. Barton, “Electromagnetic field calculations for irregularly shaped, layered cylindrical particles with focused illumination,” Appl. Opt. 36, 1312–1319 (1997).
[CrossRef] [PubMed]

J. P. Barton, “Electromagnetic field calculations for a sphere illuminated by a higher-order Gaussian beam. I. Internal and near-field effects,” Appl. Opt. 36, 1303–1311 (1997).
[CrossRef] [PubMed]

J. P. Barton, “Electromagnetic field calculations for irregularly-shaped, axisymmetric layered particles with focused illumination,” Appl. Opt. 35, 532–541 (1996).
[CrossRef] [PubMed]

J. P. Barton, “Internal and near-surface electromagnetic fields for an absorbing spheroidal particle with arbitrary illumination,” Appl. Opt. 34, 8472–8473 (1995).
[CrossRef] [PubMed]

J. P. Barton, “Internal and near-surface electromagnetic fields for a spheroidal particle with arbitrary illumination,” Appl. Opt. 34, 5542–5551 (1995).
[CrossRef] [PubMed]

J. P. Barton, D. R. Alexander, “Electromagnetic fields for an irregularly-shaped, near-spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 69, 7973–7986 (1991).
[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]

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (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]

Dandliker, R.

Gouesbet, G.

Gréhan, G.

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]

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 an inhomogeneous dielectric cylinder,” J. Opt. Soc. Am. 72, 1470–1474 (1982).
[CrossRef]

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

Krattiger, B.

Lock, J. A.

Park, P. K.

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]

Rao, T. C. K.

T. C. K. Rao, “Scattering by a radially inhomogeneous cylindrical dielectric shell due to an incident Gaussian beam,” Can. J. Phys. 67, 471–475 (1988).
[CrossRef]

Ren, K. F.

Schaub, S. A.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (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]

Souli, N.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Yanagiuchi, Y.

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

Zimmermann, E.

Appl. Opt.

Can. J. Phys.

T. C. K. Rao, “Scattering by a radially inhomogeneous cylindrical dielectric shell due to an incident Gaussian beam,” Can. J. Phys. 67, 471–475 (1988).
[CrossRef]

IEEE Trans. Antennas Propag.

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]

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]

J. Appl. Phys.

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, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, “Electromagnetic fields for an irregularly-shaped, near-spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 69, 7973–7986 (1991).
[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]

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

J. Opt.

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

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Other

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

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Figures (7)

Fig. 1
Fig. 1

Geometrical arrangement for the problem of a focused beam incident upon an infinite circular cylinder.

Fig. 2
Fig. 2

Gray-level (upper) and contour (lower) plots of the electric-field magnitude |E| in the xz plane for a linearly polarized fundamental Gaussian beam focused at the center of a circular cylinder that has the same optical properties as the surroundings. Cylinder size parameter, α=20; external dielectric constant, ϵext=1.00; cylinder relative index of refraction, n¯=(1.00, 0.00); beam waist radius, w0=0.5a; beam focal point, (x0=0, y0=0, z0=0); beam angle of incidence, θbd=45°; beam polarization angle ϕbd=90°.

Fig. 3
Fig. 3

Gray-level (upper) and contour (lower) plots of the electric-field magnitude |E| in the xz plane for a linearly polarized fundamental Gaussian beam focused at the center of a circular cylinder with n¯=(1.33, 0.00). Otherwise, the conditions are the same as those of Fig. 2.

Fig. 4
Fig. 4

Gray-level (upper) and contour (lower) plots of the electric-field magnitude |E| in the xz plane for a linearly polarized fundamental Gaussian beam focused at the center of a circular cylinder with n¯=(0.7519, 0.00). The conditions are the same as those of Fig. 3, except that the optical properties of the cylinder and the surrounding medium have been interchanged.

Fig. 5
Fig. 5

Gray-level (upper) and contour (lower) plots of the electric-field magnitude |E| in the xz plane for a linearly polarized fundamental Gaussian beam focused at the center of a circular cylinder with an angle of incidence of θbd=90°. Otherwise, the conditions are the same as those of Fig. 3.

Fig. 6
Fig. 6

Gray-level (upper) and contour (lower) plots of the electric-field magnitude |E| in the xz plane for a linearly polarized fundamental Gaussian beam focused at the center of a circular cylinder with an angle of incidence of θbd=60°. Otherwise, the conditions are the same as those of Fig. 3.

Fig. 7
Fig. 7

Gray-level (upper) and contour (lower) plots of the electric-field magnitude |E| in the xz plane for a linearly polarized fundamental Gaussian beam focused at the center of a circular cylinder with an angle of incidence of θbd=30°. Otherwise, the conditions are the same as those of Fig. 3.

Equations (33)

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(2+k2)E=0,
(2+k2)H=0.
M=×(zˆ),
N=1k×M,
(2+k2)=0,
1rr r+1r22θ2+2z2+k2=0.
m(kz)Zm(krr)exp(ikzz)exp(imθ),
kr2=k2-kz2.
E(s)(r, θ, z)=m=--[am(kz)Nm(s)(kz, r)+bm(kz)Mm(s)(kz, r)]×exp(ikzz)dkzexp(imθ),
Mm(s)(kz, r)=1rimHm(1)[kr(s)r]rˆ+{-kr(s)Hm(1)[kr(s)r]}θˆ+[0]zˆ,
Nm(s)(kz, r)=1k(s){ikr(s)kzHm(1)[kr(s)r]}rˆ+1k(s)-1rmkzHm(1)[kr(s)r]θˆ+1k(s){kr(s)2Hm(1)[kr(s)r]}zˆ.
H(s)(r, θ, z)=-iϵext m=--[am(kz)Mm(s)(kz, r)+bm(kz)Nm(s)(kz, r)]×exp(ikzz)dkzexp(imθ).
E(w)(r, θ, z)=m=--[cm(kz)Nm(w)(kz, r)+dm(kz)Mm(w)(kz, r)]×exp(ikzz)dkzexp(imθ),
H(w)(r, θ, z)=-in¯ϵextm=--[cm(kz)Mm(w)(kz, r)+dm(kz)Nm(w)(kz, r)]×exp(ikzz)dkzexp(imθ),
Mm(w)(kz, r)=1rimJm[kr(w)r]rˆ+{-kr(w)Jm[kr(w)r]}θˆ+[0]zˆ,
Nm(w)(kz, r)=1k(w){ikr(w)kzJm[kr(w)r]}rˆ+1k(w)-1rmkzJm[kr(w)r]θˆ+1k(w){kr(w)2Jm[kr(w)r]}zˆ.
Ez(w)-Ez(s)=Ez(i),
Eθ(w)-Eθ(s)=Eθ(i),
Hz(w)-Hz(s)=Hz(i),
Hθ(w)-Hθ(s)=Hθ(i).
-1k(s)kr(s)2Hm(1)[kr(s)a]am(kz)+1k(w)kr(w)2Jm[kr(w)a]cm(kz)=Am(kz),
+1k(s)mkzHm(1)[kr(s)a]am(kz)+{kr(s)Hm(s)[kr(s)a]}bm(kz)
-1k(w)mkzJm[kr(w)a]cm(kz)
-{kr(w)Jm[kr(w)a]}dm(kz)=Bm(kz),
+1k(s)kr(s)2Hm(1)[kr(s)a]bm(kz)
-n¯k(w)kr(w)2Jm[kr(w)a]dm(kz)=Cm(kz)/(iϵext),
-{kr(s)Hm(1)[kr(s)a]}am(kz)-1k(s)mkzHm(1)[kr(s)a]bm(kz)
+{nk¯r(w)Jm[kr(w)a]}cm(kz)+n¯k(w)mkzJm[kr(w)a]dm(kz)
=Dm(kz)/(iϵext),
Am(kz)=1(2π)202π-Ez(i)(a, θ, z)exp(-ikzz)dz×exp(-imθ)dθ,
Bm(kz)=1(2π)202π-Eθ(i)(a, θ, z)exp(-ikzz)dz×exp(-imθ)dθ,
Cm(kz)=1(2π)202π-Hz(i)(a, θ, z)exp(-ikzz)dz×exp(-imθ)dθ,
Dm(kz)=1(2π)202π-Hθ(i)(a, θ, z)exp(-ikzz)dz×exp(-imθ)dθ.

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