Abstract

The scattered waves of a shaped beam by an infinite cylinder in the far field are, stricto sensu, neither cylindrical nor spherical, so the asymptotic form of special functions involved in the theories based on the rigorous solution of Maxwell equations cannot be used to evaluate scattered intensities, even in the most simple case of Gaussian beam scattering by an infinite circular cylinder. Thus, although theories exist for the scattering of a shaped beam by infinite cylinders with circular and elliptical sections, the numerical calculations are limited to the near field. The vectorial complex ray model (VCRM) developed by Ren et al. describes waves by rays with a new property: the curvature of the wavefront. It is suitable to deal with the scattering of an arbitrarily shaped beam by a particle with a smooth surface of any form. In this paper, we apply this method to the scattering of an infinite elliptical cylinder illuminated by a Gaussian beam at normal incidence with an arbitrary position and orientation relative to the symmetric axis of the elliptical section of the cylinder. The method for calculating the curvature of an arbitrary surface is given and applied in the determination of the two curvature radii of the Gaussian beam wavefront at any point. Scattered intensities for different parameters of the beam and the particle as well as observation distance are presented to reveal the scattering properties and new phenomena observed in the beam scattering by an infinite elliptical cylinder.

© 2013 Optical Society of America

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References

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  1. J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
    [CrossRef]
  2. C. Yeh, “Backscattering cross section of a dielectric elliptical cylinder,” J. Opt. Soc. Am. 55, 309–312 (1965).
    [CrossRef]
  3. S. Kozaki, “A new expression for the scattering of a Gaussian beam by a conducting cylinder,” IEEE Trans. Antennas Propag. 30, 881–887 (1982).
    [CrossRef]
  4. S. Kozaki, “Scattering of a Gaussian beam by a homogeneous dielectric cylinder,” J. Appl. Phys. 53, 7195–7200 (1982).
    [CrossRef]
  5. 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]
  6. E. Zimmermann, R. Dändliker, N. Souli, and B. Krattiker, “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]
  7. G. Gouesbet, “Interaction between an infinite cylinder and an arbitrary shaped beam,” Appl. Opt. 36, 4292–4304 (1997).
    [CrossRef]
  8. K. F. Ren, G. Gréhan, and 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]
  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. L. Mees, K. F. Ren, G. Gréhan, and G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation, numerical results,” Appl. Opt. 38, 1867–1876 (1999).
    [CrossRef]
  12. G. Gouesbet, L. Mees, and G. Gréhan, “Partial wave description of shaped beams in elliptical cylinder coordinates,” J. Opt. Soc. Am. A 15, 3028–3038 (1998).
    [CrossRef]
  13. G. Gouesbet, L. Mees, and G. Gréhan, “Partial wave expansions of higher-order Gaussian beams in elliptical cylindrical coordinates,” J. Opt. A 1, 121–132 (1999).
    [CrossRef]
  14. G. Gouesbet, L. Mees, G. Gréhan, and K. F. Ren, “Description of arbitrary shaped beams in elliptical cylinder coordinates, by using a plane wave spectrum approach,” Opt. Commun. 161, 63–78 (1999).
    [CrossRef]
  15. G. Gouesbet, L. Mees, G. Gréhan, and K. F. Ren, “Localized approximation for Gaussian beams in elliptical cylinder coordinates,” Appl. Opt. 39, 1008–1025 (2000).
    [CrossRef]
  16. G. Gouesbet, L. Mees, G. Gréhan, and K. F. Ren, “The structure of generalized Lorenz–Mie theory for elliptical infinite cylinders,” Part. Part. Syst. Charact. 16, 3–10 (1999).
    [CrossRef]
  17. G. Gouesbet and L. Mees, “Generalized Lorenz–Mie theory for infinitely long elliptical cylinders,” J. Opt. Soc. Am. A 16, 1333–1341 (1999).
    [CrossRef]
  18. A. R. Steinhardt and L. Fukshansky, “Geometrical optics approach to the intensity distribution in finite cylindrical media,” Appl. Opt. 26, 3778–3789 (1987).
    [CrossRef]
  19. C. L. Adler, J. A. Lock, B. R. Stone, and C. J. Garcia, “High-order interior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder,” J. Opt. Soc. Am. A 14, 1305–1315 (1997).
    [CrossRef]
  20. D. Marcuse, “Light scattering from elliptical fibers,” Appl. Opt. 13, 1903–1905 (1974).
    [CrossRef]
  21. C. L. Adler, J. A. Lock, and B. R. Stone, “Rainbow scattering by a cylinder with a nearly elliptical cross section,” Appl. Opt. 37, 1540–1550 (1998).
    [CrossRef]
  22. E. A. Hovenac, “Calculation of far-field scattering from nonspherical particles using a geometrical optics approach,” Appl. Opt. 30, 4739–4746 (1991).
    [CrossRef]
  23. B. Krattiger, A. Bruno, H. Widmer, M. Geiser, and R. Dändliker, “Laser-based refractive-index detection for capillary electrophoresis: ray-tracing interference theory,” Appl. Opt. 32, 956–965 (1993).
    [CrossRef]
  24. F. Xu, K. F. Ren, and X. Cai, “Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. I. By a spherical particle,” Appl. Opt. 45, 4990–4999 (2006).
    [CrossRef]
  25. F. Xu, K. F. Ren, X. Cai, and J. Shen, “Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. II. By a spheroidal particle with end-on incidence,” Appl. Opt. 45, 5000–5009 (2006).
    [CrossRef]
  26. K. F. Ren, F. Onofri, C. Rozé, and T. Girasole, “Vectorial complex ray model and application to two-dimensional scattering of plane wave by a spheroidal particle,” Opt. Lett. 36, 370–372 (2011).
    [CrossRef]
  27. K. F. Ren, C. Rozé, and T. Girasole, “Scattering and transversal divergence of anellipsoidal particle by using vectorial complex raymodel,” J. Quant. Spectrosc. Radiat. Transfer 113, 2419–2423 (2012).
    [CrossRef]
  28. K. Jiang, X. Han, and K. F. Ren, “Scattering from an elliptical cylinder by using the vectorial complex ray model,” Appl. Opt. 51, 8159–8168 (2012).
    [CrossRef]
  29. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
    [CrossRef]
  30. J. Lock, “Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz–Mie theory. I. Localized model description of an on-axis tightly focused laser beam with spherical aberration,” Appl. Opt. 43, 2532–2544 (2004).
    [CrossRef]
  31. R. Goldman, “Curvature formulas for implicit curves and surfaces,” Comput. Aid. Geom. Des. 22, 632–658 (2005).
    [CrossRef]

2012 (2)

K. F. Ren, C. Rozé, and T. Girasole, “Scattering and transversal divergence of anellipsoidal particle by using vectorial complex raymodel,” J. Quant. Spectrosc. Radiat. Transfer 113, 2419–2423 (2012).
[CrossRef]

K. Jiang, X. Han, and K. F. Ren, “Scattering from an elliptical cylinder by using the vectorial complex ray model,” Appl. Opt. 51, 8159–8168 (2012).
[CrossRef]

2011 (1)

2006 (2)

2005 (1)

R. Goldman, “Curvature formulas for implicit curves and surfaces,” Comput. Aid. Geom. Des. 22, 632–658 (2005).
[CrossRef]

2004 (1)

2000 (1)

1999 (5)

L. Mees, K. F. Ren, G. Gréhan, and G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation, numerical results,” Appl. Opt. 38, 1867–1876 (1999).
[CrossRef]

G. Gouesbet and L. Mees, “Generalized Lorenz–Mie theory for infinitely long elliptical cylinders,” J. Opt. Soc. Am. A 16, 1333–1341 (1999).
[CrossRef]

G. Gouesbet, L. Mees, and G. Gréhan, “Partial wave expansions of higher-order Gaussian beams in elliptical cylindrical coordinates,” J. Opt. A 1, 121–132 (1999).
[CrossRef]

G. Gouesbet, L. Mees, G. Gréhan, and K. F. Ren, “Description of arbitrary shaped beams in elliptical cylinder coordinates, by using a plane wave spectrum approach,” Opt. Commun. 161, 63–78 (1999).
[CrossRef]

G. Gouesbet, L. Mees, G. Gréhan, and K. F. Ren, “The structure of generalized Lorenz–Mie theory for elliptical infinite cylinders,” Part. Part. Syst. Charact. 16, 3–10 (1999).
[CrossRef]

1998 (2)

1997 (5)

1995 (1)

1993 (1)

1991 (1)

1987 (1)

1982 (2)

S. Kozaki, “A new expression for the scattering of a Gaussian beam by a conducting cylinder,” IEEE Trans. Antennas Propag. 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]

1979 (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]

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

1974 (1)

1965 (1)

1955 (1)

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

Adler, C. L.

Bruno, A.

Cai, X.

Dändliker, R.

Davis, L. W.

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

Fukshansky, L.

Garcia, C. J.

Geiser, M.

Girasole, T.

K. F. Ren, C. Rozé, and T. Girasole, “Scattering and transversal divergence of anellipsoidal particle by using vectorial complex raymodel,” J. Quant. Spectrosc. Radiat. Transfer 113, 2419–2423 (2012).
[CrossRef]

K. F. Ren, F. Onofri, C. Rozé, and T. Girasole, “Vectorial complex ray model and application to two-dimensional scattering of plane wave by a spheroidal particle,” Opt. Lett. 36, 370–372 (2011).
[CrossRef]

Goldman, R.

R. Goldman, “Curvature formulas for implicit curves and surfaces,” Comput. Aid. Geom. Des. 22, 632–658 (2005).
[CrossRef]

Gouesbet, G.

G. Gouesbet, L. Mees, G. Gréhan, and K. F. Ren, “Localized approximation for Gaussian beams in elliptical cylinder coordinates,” Appl. Opt. 39, 1008–1025 (2000).
[CrossRef]

L. Mees, K. F. Ren, G. Gréhan, and G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation, numerical results,” Appl. Opt. 38, 1867–1876 (1999).
[CrossRef]

G. Gouesbet and L. Mees, “Generalized Lorenz–Mie theory for infinitely long elliptical cylinders,” J. Opt. Soc. Am. A 16, 1333–1341 (1999).
[CrossRef]

G. Gouesbet, L. Mees, and G. Gréhan, “Partial wave expansions of higher-order Gaussian beams in elliptical cylindrical coordinates,” J. Opt. A 1, 121–132 (1999).
[CrossRef]

G. Gouesbet, L. Mees, G. Gréhan, and K. F. Ren, “Description of arbitrary shaped beams in elliptical cylinder coordinates, by using a plane wave spectrum approach,” Opt. Commun. 161, 63–78 (1999).
[CrossRef]

G. Gouesbet, L. Mees, G. Gréhan, and K. F. Ren, “The structure of generalized Lorenz–Mie theory for elliptical infinite cylinders,” Part. Part. Syst. Charact. 16, 3–10 (1999).
[CrossRef]

G. Gouesbet, L. Mees, and G. Gréhan, “Partial wave description of shaped beams in elliptical cylinder coordinates,” J. Opt. Soc. Am. A 15, 3028–3038 (1998).
[CrossRef]

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

K. F. Ren, G. Gréhan, and 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]

Gréhan, G.

G. Gouesbet, L. Mees, G. Gréhan, and K. F. Ren, “Localized approximation for Gaussian beams in elliptical cylinder coordinates,” Appl. Opt. 39, 1008–1025 (2000).
[CrossRef]

L. Mees, K. F. Ren, G. Gréhan, and G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation, numerical results,” Appl. Opt. 38, 1867–1876 (1999).
[CrossRef]

G. Gouesbet, L. Mees, and G. Gréhan, “Partial wave expansions of higher-order Gaussian beams in elliptical cylindrical coordinates,” J. Opt. A 1, 121–132 (1999).
[CrossRef]

G. Gouesbet, L. Mees, G. Gréhan, and K. F. Ren, “Description of arbitrary shaped beams in elliptical cylinder coordinates, by using a plane wave spectrum approach,” Opt. Commun. 161, 63–78 (1999).
[CrossRef]

G. Gouesbet, L. Mees, G. Gréhan, and K. F. Ren, “The structure of generalized Lorenz–Mie theory for elliptical infinite cylinders,” Part. Part. Syst. Charact. 16, 3–10 (1999).
[CrossRef]

G. Gouesbet, L. Mees, and G. Gréhan, “Partial wave description of shaped beams in elliptical cylinder coordinates,” J. Opt. Soc. Am. A 15, 3028–3038 (1998).
[CrossRef]

K. F. Ren, G. Gréhan, and 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]

Han, X.

Hovenac, E. A.

Jiang, K.

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, “A new expression for the scattering of a Gaussian beam by a conducting cylinder,” IEEE Trans. Antennas Propag. 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]

Krattiger, B.

Krattiker, B.

Lock, J.

Lock, J. A.

Marcuse, D.

Mees, L.

G. Gouesbet, L. Mees, G. Gréhan, and K. F. Ren, “Localized approximation for Gaussian beams in elliptical cylinder coordinates,” Appl. Opt. 39, 1008–1025 (2000).
[CrossRef]

L. Mees, K. F. Ren, G. Gréhan, and G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation, numerical results,” Appl. Opt. 38, 1867–1876 (1999).
[CrossRef]

G. Gouesbet and L. Mees, “Generalized Lorenz–Mie theory for infinitely long elliptical cylinders,” J. Opt. Soc. Am. A 16, 1333–1341 (1999).
[CrossRef]

G. Gouesbet, L. Mees, G. Gréhan, and K. F. Ren, “Description of arbitrary shaped beams in elliptical cylinder coordinates, by using a plane wave spectrum approach,” Opt. Commun. 161, 63–78 (1999).
[CrossRef]

G. Gouesbet, L. Mees, and G. Gréhan, “Partial wave expansions of higher-order Gaussian beams in elliptical cylindrical coordinates,” J. Opt. A 1, 121–132 (1999).
[CrossRef]

G. Gouesbet, L. Mees, G. Gréhan, and K. F. Ren, “The structure of generalized Lorenz–Mie theory for elliptical infinite cylinders,” Part. Part. Syst. Charact. 16, 3–10 (1999).
[CrossRef]

G. Gouesbet, L. Mees, and G. Gréhan, “Partial wave description of shaped beams in elliptical cylinder coordinates,” J. Opt. Soc. Am. A 15, 3028–3038 (1998).
[CrossRef]

Onofri, F.

Ren, K. F.

K. Jiang, X. Han, and K. F. Ren, “Scattering from an elliptical cylinder by using the vectorial complex ray model,” Appl. Opt. 51, 8159–8168 (2012).
[CrossRef]

K. F. Ren, C. Rozé, and T. Girasole, “Scattering and transversal divergence of anellipsoidal particle by using vectorial complex raymodel,” J. Quant. Spectrosc. Radiat. Transfer 113, 2419–2423 (2012).
[CrossRef]

K. F. Ren, F. Onofri, C. Rozé, and T. Girasole, “Vectorial complex ray model and application to two-dimensional scattering of plane wave by a spheroidal particle,” Opt. Lett. 36, 370–372 (2011).
[CrossRef]

F. Xu, K. F. Ren, and X. Cai, “Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. I. By a spherical particle,” Appl. Opt. 45, 4990–4999 (2006).
[CrossRef]

F. Xu, K. F. Ren, X. Cai, and J. Shen, “Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. II. By a spheroidal particle with end-on incidence,” Appl. Opt. 45, 5000–5009 (2006).
[CrossRef]

G. Gouesbet, L. Mees, G. Gréhan, and K. F. Ren, “Localized approximation for Gaussian beams in elliptical cylinder coordinates,” Appl. Opt. 39, 1008–1025 (2000).
[CrossRef]

L. Mees, K. F. Ren, G. Gréhan, and G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation, numerical results,” Appl. Opt. 38, 1867–1876 (1999).
[CrossRef]

G. Gouesbet, L. Mees, G. Gréhan, and K. F. Ren, “The structure of generalized Lorenz–Mie theory for elliptical infinite cylinders,” Part. Part. Syst. Charact. 16, 3–10 (1999).
[CrossRef]

G. Gouesbet, L. Mees, G. Gréhan, and K. F. Ren, “Description of arbitrary shaped beams in elliptical cylinder coordinates, by using a plane wave spectrum approach,” Opt. Commun. 161, 63–78 (1999).
[CrossRef]

K. F. Ren, G. Gréhan, and 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]

Rozé, C.

K. F. Ren, C. Rozé, and T. Girasole, “Scattering and transversal divergence of anellipsoidal particle by using vectorial complex raymodel,” J. Quant. Spectrosc. Radiat. Transfer 113, 2419–2423 (2012).
[CrossRef]

K. F. Ren, F. Onofri, C. Rozé, and T. Girasole, “Vectorial complex ray model and application to two-dimensional scattering of plane wave by a spheroidal particle,” Opt. Lett. 36, 370–372 (2011).
[CrossRef]

Shen, J.

Souli, N.

Steinhardt, A. R.

Stone, B. R.

Wait, J. R.

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

Widmer, H.

Xu, F.

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]

Yeh, C.

Zimmermann, E.

Appl. Opt. (12)

D. Marcuse, “Light scattering from elliptical fibers,” Appl. Opt. 13, 1903–1905 (1974).
[CrossRef]

A. R. Steinhardt and L. Fukshansky, “Geometrical optics approach to the intensity distribution in finite cylindrical media,” Appl. Opt. 26, 3778–3789 (1987).
[CrossRef]

E. A. Hovenac, “Calculation of far-field scattering from nonspherical particles using a geometrical optics approach,” Appl. Opt. 30, 4739–4746 (1991).
[CrossRef]

B. Krattiger, A. Bruno, H. Widmer, M. Geiser, and R. Dändliker, “Laser-based refractive-index detection for capillary electrophoresis: ray-tracing interference theory,” Appl. Opt. 32, 956–965 (1993).
[CrossRef]

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

C. L. Adler, J. A. Lock, and B. R. Stone, “Rainbow scattering by a cylinder with a nearly elliptical cross section,” Appl. Opt. 37, 1540–1550 (1998).
[CrossRef]

L. Mees, K. F. Ren, G. Gréhan, and G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation, numerical results,” Appl. Opt. 38, 1867–1876 (1999).
[CrossRef]

G. Gouesbet, L. Mees, G. Gréhan, and K. F. Ren, “Localized approximation for Gaussian beams in elliptical cylinder coordinates,” Appl. Opt. 39, 1008–1025 (2000).
[CrossRef]

J. Lock, “Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz–Mie theory. I. Localized model description of an on-axis tightly focused laser beam with spherical aberration,” Appl. Opt. 43, 2532–2544 (2004).
[CrossRef]

F. Xu, K. F. Ren, and X. Cai, “Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. I. By a spherical particle,” Appl. Opt. 45, 4990–4999 (2006).
[CrossRef]

F. Xu, K. F. Ren, X. Cai, and J. Shen, “Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. II. By a spheroidal particle with end-on incidence,” Appl. Opt. 45, 5000–5009 (2006).
[CrossRef]

K. Jiang, X. Han, and K. F. Ren, “Scattering from an elliptical cylinder by using the vectorial complex ray model,” Appl. Opt. 51, 8159–8168 (2012).
[CrossRef]

Can. J. Phys. (1)

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

Comput. Aid. Geom. Des. (1)

R. Goldman, “Curvature formulas for implicit curves and surfaces,” Comput. Aid. Geom. Des. 22, 632–658 (2005).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

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

J. Appl. Phys. (2)

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

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. Opt. A (1)

G. Gouesbet, L. Mees, and G. Gréhan, “Partial wave expansions of higher-order Gaussian beams in elliptical cylindrical coordinates,” J. Opt. A 1, 121–132 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (7)

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

K. F. Ren, C. Rozé, and T. Girasole, “Scattering and transversal divergence of anellipsoidal particle by using vectorial complex raymodel,” J. Quant. Spectrosc. Radiat. Transfer 113, 2419–2423 (2012).
[CrossRef]

Opt. Commun. (1)

G. Gouesbet, L. Mees, G. Gréhan, and K. F. Ren, “Description of arbitrary shaped beams in elliptical cylinder coordinates, by using a plane wave spectrum approach,” Opt. Commun. 161, 63–78 (1999).
[CrossRef]

Opt. Lett. (1)

Part. Part. Syst. Charact. (1)

G. Gouesbet, L. Mees, G. Gréhan, and K. F. Ren, “The structure of generalized Lorenz–Mie theory for elliptical infinite cylinders,” Part. Part. Syst. Charact. 16, 3–10 (1999).
[CrossRef]

Phys. Rev. A (1)

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

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Figures (10)

Fig. 1.
Fig. 1.

Definition of the particle coordinate system and the beam coordinate system.

Fig. 2.
Fig. 2.

Scattered intensities of a circular cylinder of radius 30 μm illuminated by a plane wave or a Gaussian beam of the waist radius, w0=80, 20, and 10 μm. The incident beam is polarized in the z direction. The observation distance is 0.1 m.

Fig. 3.
Fig. 3.

Scattered intensities at different observed distances of a circular cylinder of radius 30μm illuminated by a Gaussian beam of the waist radius, w0=20μm. The incident beam is polarized in the xz plane.

Fig. 4.
Fig. 4.

Scattered intensities of an elliptical cylinder illuminated by a Gaussian beam (w0=30μm) with aspect ratio κ=a/b as a parameter. The major axis of the cylinder a is 50 μm; the minor axis b is 50, 45, 40, or 25 μm. The polarization is in the xz plane. The results for κ=1.11, κ=1.25, and κ=2 are offset by 102, 104, and 106 for clarity.

Fig. 5.
Fig. 5.

Scattered intensities of an elliptical cylinder (a=50μm, b=40μm) illuminated by a Gaussian beam (w0=25μm) at different angles. The results for θ0=40°, θ0=60°, and θ0=80° are shifted by 102, 104, and 106 for charity.

Fig. 6.
Fig. 6.

Scattered intensities of an elliptical cylinder (a=50μm, b=40μm) illuminated by the plane wave and a Gaussian beam of three different waist radius (w0=100, 25, and 15 μm). The incident beam is polarized in the z direction and makes an angle, θ0=20°, with the x axis.

Fig. 7.
Fig. 7.

Scattered intensities of an elliptical cylinder (a=30μm, b=12μm) illuminated by a Gaussian beam (w0=5μm) at different incident angles.

Fig. 8.
Fig. 8.

Ray tracing for the case θ0=10° in Fig. 7.

Fig. 9.
Fig. 9.

Scattered intensities of an elliptical cylinder (a=50μm, b=40μm) illuminated by a Gaussian beam (w0=25μm, x0=z0=0) parallel to the x axis with y0 as parameter. The results for y0=25, 40, and 55 μm are offset, respectively, by 102, 104, and 106 for clarity.

Fig. 10.
Fig. 10.

Ray tracing for the case y0=55μm in Fig. 9.

Equations (36)

Equations on this page are rendered with MathJax. Learn more.

kτ=kτ,
kn=k2kτ2.
k=kττ+knn.
kn2kR1=kn2kR1+knknρ1,
kR2=kR2.
D=R11R21R12R22·R12R22R13R23R1pR2p(r+R1p)(r+R2p),
SX,p=π2D|SG|εX,pexp(iφp),
εX,p={rX,0p=0tX,0tX,pn=1p1rX,np1,
SX=p=0SX,p.
SG(u,v,w)=AGexp(iφ),
AG=w0wlexp(u2+v2wl2),
φ(u,v,w)=k{w+u2+v22w[1+(l/w)2]}+tan1(wl),
wl=w0[1+(w/l)2]1/2.
(uvw)=A(xx0yy0zz0).
A=(a11a12a13a21a22a23a31a32a33),
a11=cosαcosγcosβsinαsinγ,a12=sinαcosγ+cosβcosαsinγ,a13=sinβsinγ,a21=cosαsinγcosβsinαcosγ,a22=sinαsinγ+cosβcosαcosγ,a23=sinβcosγ,a31=sinαsinβ,a32=cosαsinβ,a33=cosβ.
A=(sinθ0cosθ00001cosθ0sinθ00).
u=(xx0)sinθ0+(yy0)cosθ0,
v=z,
w=(xx0)cosθ0+(yy0)sinθ0.
F(x,y,z)=φ[u(x,y,z),v(x,y,z),w(x,y,z)]C.
k=kF(x,y,z)F(x,y,z),
F(x,y,z)=(FxFyFz)=(φuφvφw)A,
(uxuyuzvxvyvywxwywz)=A.
φu=kuwl2+w2,φv=kvwl2+w2,φw=kk(u2+v2)(l2w2)2(l2+w2)2+ll2+w2,
κG=F·H*(F)·FT|F|4,
κM=F·H(F)·FT|F|2Trace(H)2|F|3,
H(F)=(FxxFxyFxzFyxFyyFyzFzxFzyFzz),
H(F)=AT(φuuφuvφuwφvuφvvφvwφwuφwvφww)A,
φuu=φvv=kwl2+w2,
φuv=φvu=0,
φuw=φwu=ku(l2w2)(l2+w2)2,
φvw=φwv=kv(l2w2)(l2+w2)2,
φww=kw(u2+v2)(3l2w2)(l2+w2)32lw(l2+w2)2.
κ1,κ2=κM±κM2κG.
Q=(κ100κ2).

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