Abstract

The scattering of a two-dimensional Gaussian beam from a homogeneous dielectric cylinder is analyzed using a plane-wave spectrum. Special attention is given to the computation of the evanescent field of the beam and its effect in the scattering. A comparison is made between the evanescent field in Cartesian coordinates and in cylindrical coordinates as a sum of cylindrical waves. The field given by the cylindrical wave equation is found to converge spatially as we include more Bessel modes. The evanescent field incident on the dielectric cylinder is found to cause radiating waves to form and propagate outward.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  15. J. Yang, L. W. Li, K. Yasumoto, and C. H. Liang, “Two-dimensional scattering of a Gaussian beam by a periodic array of circular cylinders,” IEEE Trans. Geosci. Remote Sens. 43, 280-285 (2005).
    [CrossRef]
  16. P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields (Pergamon, 1966).
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    [CrossRef]
  18. E. V. Jull, Aperture Antennas and Diffraction Theory (Peter Peregrinus, 1981).
  19. J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974-980 (1979).
    [CrossRef]
  20. S. Kozaki and H. Sakurai, “Characteristics of a Gaussian beam at a dielectric interface,” J. Opt. Soc. Am. 68, 508-514 (1978).
    [CrossRef]
  21. N. McLachlan, Bessel Functions for Engineers (Oxford Univ. Press, 1955).
  22. J. Mathews and R. L. Walker, Mathematical Methods of Physics (Benjamin/Cummings, 1970).

2009 (1)

G. Gouesbet, “Generalized Lorenz-Mie theories, the third decade: A perspective,” J. Quant. Spectrosc. Radiat. Transf. 110, 1223-1238 (2009).
[CrossRef]

2005 (1)

J. Yang, L. W. Li, K. Yasumoto, and C. H. Liang, “Two-dimensional scattering of a Gaussian beam by a periodic array of circular cylinders,” IEEE Trans. Geosci. Remote Sens. 43, 280-285 (2005).
[CrossRef]

1999 (1)

1998 (2)

P. Varga and P. Török, “The Gaussian wave solution of Maxwell's equations and the validity of scalar wave approximation,” Opt. Commun. 152, 108-118 (1998).
[CrossRef]

Z. Wu and L. Guo, “Electromagnetic scattering from a multilayered cylinder arbitrarily located in a Gaussian beam; a new recursive algorithm,” J. Electromagn. Waves Appl. 12, 725-726 (1998).
[CrossRef]

1997 (2)

1995 (1)

1993 (1)

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

1989 (1)

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

1982 (1)

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

1979 (3)

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

J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974-980 (1979).
[CrossRef]

G. Agrawal and D. Pattanayak, “Gaussian beam propagation beyond the paraxial approximation,” J. Opt. Soc. Am. 69, 575-578 (1979).
[CrossRef]

1978 (1)

1908 (1)

G. Mie, “Considerations on the optics of turbid media, especially colloidal metal sols,” Ann. Phys. 25, 377-442 (1908).
[CrossRef]

1890 (1)

L. Lorenz, “Upon the light reflected and refracted by a transparent sphere,” Vidensk. Selsk. Shrifter 6, 1-62 (1890).

Agrawal, G.

Clemmow, P. C.

P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields (Pergamon, 1966).

Dändliker, R.

Elsherbeni, A.

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

Eom, H. J.

H. J. Eom, Electromagnetic Wave Theory for Boundary-Value Problems: an Advanced Course on Analytical Methods (Springer-Verlag, 2004).

Gouesbet, G.

Gréhan, G.

Guo, L.

Z. Wu and L. Guo, “Electromagnetic scattering from a multilayered cylinder arbitrarily located in a Gaussian beam; a new recursive algorithm,” J. Electromagn. Waves Appl. 12, 725-726 (1998).
[CrossRef]

Hamid, M.

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

Harvey, J. E.

J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974-980 (1979).
[CrossRef]

Jull, E. V.

E. V. Jull, Aperture Antennas and Diffraction Theory (Peter Peregrinus, 1981).

Kojima, T.

T. Kojima and 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, “Scattering of a Gaussian beam by a homogeneous dielectric cylinder,” J. Appl. Phys. 53, 7195-7200 (1982).
[CrossRef]

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

Krattiger, B.

Li, L. W.

J. Yang, L. W. Li, K. Yasumoto, and C. H. Liang, “Two-dimensional scattering of a Gaussian beam by a periodic array of circular cylinders,” IEEE Trans. Geosci. Remote Sens. 43, 280-285 (2005).
[CrossRef]

Liang, C. H.

J. Yang, L. W. Li, K. Yasumoto, and C. H. Liang, “Two-dimensional scattering of a Gaussian beam by a periodic array of circular cylinders,” IEEE Trans. Geosci. Remote Sens. 43, 280-285 (2005).
[CrossRef]

Lorenz, L.

L. Lorenz, “Upon the light reflected and refracted by a transparent sphere,” Vidensk. Selsk. Shrifter 6, 1-62 (1890).

Mathews, J.

J. Mathews and R. L. Walker, Mathematical Methods of Physics (Benjamin/Cummings, 1970).

McLachlan, N.

N. McLachlan, Bessel Functions for Engineers (Oxford Univ. Press, 1955).

Mees, L.

Mie, G.

G. Mie, “Considerations on the optics of turbid media, especially colloidal metal sols,” Ann. Phys. 25, 377-442 (1908).
[CrossRef]

Pattanayak, D.

Rao, T.

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

Ren, K.

Sakurai, H.

Souli, N.

Tian, G.

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

Török, P.

P. Varga and P. Török, “The Gaussian wave solution of Maxwell's equations and the validity of scalar wave approximation,” Opt. Commun. 152, 108-118 (1998).
[CrossRef]

Varga, P.

P. Varga and P. Török, “The Gaussian wave solution of Maxwell's equations and the validity of scalar wave approximation,” Opt. Commun. 152, 108-118 (1998).
[CrossRef]

Walker, R. L.

J. Mathews and R. L. Walker, Mathematical Methods of Physics (Benjamin/Cummings, 1970).

Wu, Z.

Z. Wu and L. Guo, “Electromagnetic scattering from a multilayered cylinder arbitrarily located in a Gaussian beam; a new recursive algorithm,” J. Electromagn. Waves Appl. 12, 725-726 (1998).
[CrossRef]

Yanagiuchi, Y.

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

Yang, J.

J. Yang, L. W. Li, K. Yasumoto, and C. H. Liang, “Two-dimensional scattering of a Gaussian beam by a periodic array of circular cylinders,” IEEE Trans. Geosci. Remote Sens. 43, 280-285 (2005).
[CrossRef]

Yasumoto, K.

J. Yang, L. W. Li, K. Yasumoto, and C. H. Liang, “Two-dimensional scattering of a Gaussian beam by a periodic array of circular cylinders,” IEEE Trans. Geosci. Remote Sens. 43, 280-285 (2005).
[CrossRef]

Zimmermann, E.

Am. J. Phys. (1)

J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974-980 (1979).
[CrossRef]

Ann. Phys. (1)

G. Mie, “Considerations on the optics of turbid media, especially colloidal metal sols,” Ann. Phys. 25, 377-442 (1908).
[CrossRef]

Appl. Opt. (2)

Can. J. Phys. (1)

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

IEEE Trans. Geosci. Remote Sens. (1)

J. Yang, L. W. Li, K. Yasumoto, and C. H. Liang, “Two-dimensional scattering of a Gaussian beam by a periodic array of circular cylinders,” IEEE Trans. Geosci. Remote Sens. 43, 280-285 (2005).
[CrossRef]

J. Appl. Phys. (2)

T. Kojima and 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. Electromagn. Waves Appl. (2)

Z. Wu and L. Guo, “Electromagnetic scattering from a multilayered cylinder arbitrarily located in a Gaussian beam; a new recursive algorithm,” J. Electromagn. Waves Appl. 12, 725-726 (1998).
[CrossRef]

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

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

J. Quant. Spectrosc. Radiat. Transf. (1)

G. Gouesbet, “Generalized Lorenz-Mie theories, the third decade: A perspective,” J. Quant. Spectrosc. Radiat. Transf. 110, 1223-1238 (2009).
[CrossRef]

Opt. Commun. (1)

P. Varga and P. Török, “The Gaussian wave solution of Maxwell's equations and the validity of scalar wave approximation,” Opt. Commun. 152, 108-118 (1998).
[CrossRef]

Vidensk. Selsk. Shrifter (1)

L. Lorenz, “Upon the light reflected and refracted by a transparent sphere,” Vidensk. Selsk. Shrifter 6, 1-62 (1890).

Other (5)

H. J. Eom, Electromagnetic Wave Theory for Boundary-Value Problems: an Advanced Course on Analytical Methods (Springer-Verlag, 2004).

E. V. Jull, Aperture Antennas and Diffraction Theory (Peter Peregrinus, 1981).

P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields (Pergamon, 1966).

N. McLachlan, Bessel Functions for Engineers (Oxford Univ. Press, 1955).

J. Mathews and R. L. Walker, Mathematical Methods of Physics (Benjamin/Cummings, 1970).

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