Abstract

Diffraction of an infinitely long circular cylinder normally illuminated by a plane wave is discussed from the classical Mie theory. A rigorous expression of the diffracted light is obtained, which is simply characterized by a factor (θ/2)/sin(θ/2) and the sinc function sin(αθ)/(αθ). Numerical calculation shows an apparent difference between our results and those from scalar wave diffraction theory, especially in large diffraction angles. The factor (θ/2)/sin(θ/2) is introduced into the diffracted light by a sphere, which leads to an alternative approximation of the diffracted light.

© 2013 Optical Society of America

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References

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  1. M. L. Mishchenko, L. D. Travis, and A. L. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University, 2002).
  2. J. V. Dave, “Scattering of visible light by large water spheres,” Appl. Opt. 8, 155–164 (1969).
    [CrossRef]
  3. L. Wu, H. Yang, X. Li, B. Yang, and G. Li, “Scattering by large bubbles: comparisons between geometrical-optics theory and Debye series,” J. Quant. Spectrosc. Radiat. Transfer 108, 54–64 (2007).
    [CrossRef]
  4. H. Yu, J. Shen, and Y. Wei, “Geometrical optics approximation for light scattering by absorbing spherical particles,” J. Quant. Spectrosc. Radiat. Transfer 110, 1178–1189 (2009).
    [CrossRef]
  5. A. Ungut, G. Grehan, and G. Gouesbet, “Comparison between geometrical optics and Lorenz-Mie theory,” Appl. Opt. 20, 2911–2918 (1981).
    [CrossRef]
  6. H. He, W. Li, X. Zhang, M. Xia, and K. Yang, “Light scattering by a spheroidal bubble with geometrical optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 113, 1467–1475 (2012).
    [CrossRef]
  7. E. A. Hovenac, “Calculation of far-field scattering from nonspherical particles using a geometrical optics approach,” Appl. Opt. 30, 4739–4746 (1991).
    [CrossRef]
  8. P. Yang and K. N. Liou, “An ‘exact’ geomteric-optics approach for computing the optical properties of large absorbing particles,” J. Quant. Spectrosc. Radiat. Transfer 110, 1162–1177 (2009).
    [CrossRef]
  9. P. Yang and K. N. Liou, “Geometric-optics-integral-equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
    [CrossRef]
  10. L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. Baum, “Diffraction and external reflection by dielectric faceted particles,” J. Quant. Spectrosc. Radiat. Transfer 112, 163–173 (2011).
    [CrossRef]
  11. G. L. Stephens, “Scattering of plane waves by soft obstacles: anomalous diffraction theory for circular cylinders,” Appl. Opt. 23, 954–959 (1984).
    [CrossRef]
  12. M. Born and E. Wolf, Principles of Optics (Cambridge University, 2005).
  13. P. Yang and K. N. Liou, “Light scattering by hexagonal ice crystals: comparison of finite-difference time domain and geometric optics models,” J. Opt. Soc. Am. A 12, 162–176 (1995).
    [CrossRef]
  14. Y. Takano, K. N. Liou, and P. Yang, “Diffraction by rectangular parallelepiped, hexagonal cylinder, and three-axis ellipsoid: some analytic solutions and numerical results,” J. Quant. Spectrosc. Radiat. Transfer 113, 1836–1843 (2012).
    [CrossRef]
  15. Y. Takano and M. Tanaka, “Phase matrix and cross sections for single scattering by circular cylinders: a comparison of ray optics and wave theory,” Appl. Opt. 19, 2781–2800 (1980).
    [CrossRef]
  16. P. C. Clemmow and V. H. Weston, “Diffraction of a plane wave by an almost circular cylinder,” Proc. R. Soc. London Ser. A 264, 246–268 (1961).
    [CrossRef]
  17. C. J. Bouwkamp, “Diffraction theory,” Rep. Prog. Phys. 17, 35–100 (1954).
    [CrossRef]
  18. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  19. J. A. Lock and P. Laven, “Mie scattering in the time domain. Part 2. The role of diffraction,” J. Opt. Soc. Am. A 28, 1096–1106 (2011).
    [CrossRef]
  20. W. Guo, “Light-scattering theory of diffraction,” J. Opt. Soc. Am. A 27, 492–494 (2010).
    [CrossRef]
  21. P. Debye, “Das elektromagnetische Feld um einen Zylinder und die Theorie des Regenbogens,” Phys. Z 9, 775–778 (1908).
  22. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 330, 377–445 (1908).
    [CrossRef]
  23. X. Jia, J. Shen, L. Guo, and C. Wan, “Diffraction effects in planar wave-sphere interaction,” Chin. Opt. Lett. 11, 050501 (2013).
    [CrossRef]
  24. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).
  25. W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
    [CrossRef]
  26. L. Bi, P. Yang, and G. W. Kattawar, “Edge-effect contribution to the extinction of light by dielectric disks and cylindrical particles,” Appl. Opt. 49, 4641–4646 (2010).
    [CrossRef]
  27. W. Hergert and T. Wriedt, The Mie Theory: Basics and Applications, Vol. 169 of Springer Series in Optical Sciences (Springer-Verlag, 2012).
  28. J. Shen and H. Wang, “Calculation of Debye series expansion of light scattering,” Appl. Opt. 49, 2422–2428 (2010).
    [CrossRef]
  29. H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge University, 1992).
  30. 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]
  31. A. Sommerfeld, “Mathematische Theorie der Diffraction,” Math. Ann. 47, 317–374 (1896).
    [CrossRef]
  32. P. M. Morse and P. J. Rubenstein, “The diffraction of waves by ribbons and by slits,” Phys. Rev. 54, 895–898 (1938).
    [CrossRef]
  33. N. Gorenflo, “A new explicit solution method for the diffraction through a slit,” Z. Angew. Math. Phys. 53, 877–886 (2002).
    [CrossRef]
  34. N. Gorenflo, “A new explicit solution method for the diffraction through a slit—part 2,” Z. Angew. Math. Phys. 58, 16–36 (2007).
    [CrossRef]
  35. V. M. Serdyuk, “Exact solutions for electromagnetic wave diffraction by a slot and strip,” Int. J. Electron. Commun. (AEÜ) 65, 182–189 (2011).
  36. H. M. Nussenzveig and W. J. Wiscombe, “Complex angular momentum approximation to hard-core scattering,” Phys. Rev. A 43, 2093–2112 (1991).
    [CrossRef]

2013

2012

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]

H. He, W. Li, X. Zhang, M. Xia, and K. Yang, “Light scattering by a spheroidal bubble with geometrical optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 113, 1467–1475 (2012).
[CrossRef]

Y. Takano, K. N. Liou, and P. Yang, “Diffraction by rectangular parallelepiped, hexagonal cylinder, and three-axis ellipsoid: some analytic solutions and numerical results,” J. Quant. Spectrosc. Radiat. Transfer 113, 1836–1843 (2012).
[CrossRef]

2011

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. Baum, “Diffraction and external reflection by dielectric faceted particles,” J. Quant. Spectrosc. Radiat. Transfer 112, 163–173 (2011).
[CrossRef]

V. M. Serdyuk, “Exact solutions for electromagnetic wave diffraction by a slot and strip,” Int. J. Electron. Commun. (AEÜ) 65, 182–189 (2011).

J. A. Lock and P. Laven, “Mie scattering in the time domain. Part 2. The role of diffraction,” J. Opt. Soc. Am. A 28, 1096–1106 (2011).
[CrossRef]

2010

2009

P. Yang and K. N. Liou, “An ‘exact’ geomteric-optics approach for computing the optical properties of large absorbing particles,” J. Quant. Spectrosc. Radiat. Transfer 110, 1162–1177 (2009).
[CrossRef]

H. Yu, J. Shen, and Y. Wei, “Geometrical optics approximation for light scattering by absorbing spherical particles,” J. Quant. Spectrosc. Radiat. Transfer 110, 1178–1189 (2009).
[CrossRef]

2007

L. Wu, H. Yang, X. Li, B. Yang, and G. Li, “Scattering by large bubbles: comparisons between geometrical-optics theory and Debye series,” J. Quant. Spectrosc. Radiat. Transfer 108, 54–64 (2007).
[CrossRef]

N. Gorenflo, “A new explicit solution method for the diffraction through a slit—part 2,” Z. Angew. Math. Phys. 58, 16–36 (2007).
[CrossRef]

2002

N. Gorenflo, “A new explicit solution method for the diffraction through a slit,” Z. Angew. Math. Phys. 53, 877–886 (2002).
[CrossRef]

1996

1995

1991

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

H. M. Nussenzveig and W. J. Wiscombe, “Complex angular momentum approximation to hard-core scattering,” Phys. Rev. A 43, 2093–2112 (1991).
[CrossRef]

1984

1981

1980

1969

1961

P. C. Clemmow and V. H. Weston, “Diffraction of a plane wave by an almost circular cylinder,” Proc. R. Soc. London Ser. A 264, 246–268 (1961).
[CrossRef]

1954

C. J. Bouwkamp, “Diffraction theory,” Rep. Prog. Phys. 17, 35–100 (1954).
[CrossRef]

1938

P. M. Morse and P. J. Rubenstein, “The diffraction of waves by ribbons and by slits,” Phys. Rev. 54, 895–898 (1938).
[CrossRef]

1908

P. Debye, “Das elektromagnetische Feld um einen Zylinder und die Theorie des Regenbogens,” Phys. Z 9, 775–778 (1908).

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 330, 377–445 (1908).
[CrossRef]

1896

A. Sommerfeld, “Mathematische Theorie der Diffraction,” Math. Ann. 47, 317–374 (1896).
[CrossRef]

Baum, B.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. Baum, “Diffraction and external reflection by dielectric faceted particles,” J. Quant. Spectrosc. Radiat. Transfer 112, 163–173 (2011).
[CrossRef]

Bi, L.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. Baum, “Diffraction and external reflection by dielectric faceted particles,” J. Quant. Spectrosc. Radiat. Transfer 112, 163–173 (2011).
[CrossRef]

L. Bi, P. Yang, and G. W. Kattawar, “Edge-effect contribution to the extinction of light by dielectric disks and cylindrical particles,” Appl. Opt. 49, 4641–4646 (2010).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 2005).

Bouwkamp, C. J.

C. J. Bouwkamp, “Diffraction theory,” Rep. Prog. Phys. 17, 35–100 (1954).
[CrossRef]

Clemmow, P. C.

P. C. Clemmow and V. H. Weston, “Diffraction of a plane wave by an almost circular cylinder,” Proc. R. Soc. London Ser. A 264, 246–268 (1961).
[CrossRef]

Dave, J. V.

Debye, P.

P. Debye, “Das elektromagnetische Feld um einen Zylinder und die Theorie des Regenbogens,” Phys. Z 9, 775–778 (1908).

Gorenflo, N.

N. Gorenflo, “A new explicit solution method for the diffraction through a slit—part 2,” Z. Angew. Math. Phys. 58, 16–36 (2007).
[CrossRef]

N. Gorenflo, “A new explicit solution method for the diffraction through a slit,” Z. Angew. Math. Phys. 53, 877–886 (2002).
[CrossRef]

Gouesbet, G.

Grehan, G.

Guo, L.

Guo, W.

Han, X.

He, H.

H. He, W. Li, X. Zhang, M. Xia, and K. Yang, “Light scattering by a spheroidal bubble with geometrical optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 113, 1467–1475 (2012).
[CrossRef]

Hergert, W.

W. Hergert and T. Wriedt, The Mie Theory: Basics and Applications, Vol. 169 of Springer Series in Optical Sciences (Springer-Verlag, 2012).

Hovenac, E. A.

Hu, Y.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. Baum, “Diffraction and external reflection by dielectric faceted particles,” J. Quant. Spectrosc. Radiat. Transfer 112, 163–173 (2011).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Jia, X.

Jiang, K.

Kattawar, G. W.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. Baum, “Diffraction and external reflection by dielectric faceted particles,” J. Quant. Spectrosc. Radiat. Transfer 112, 163–173 (2011).
[CrossRef]

L. Bi, P. Yang, and G. W. Kattawar, “Edge-effect contribution to the extinction of light by dielectric disks and cylindrical particles,” Appl. Opt. 49, 4641–4646 (2010).
[CrossRef]

Lacis, A. L.

M. L. Mishchenko, L. D. Travis, and A. L. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University, 2002).

Laven, P.

Li, G.

L. Wu, H. Yang, X. Li, B. Yang, and G. Li, “Scattering by large bubbles: comparisons between geometrical-optics theory and Debye series,” J. Quant. Spectrosc. Radiat. Transfer 108, 54–64 (2007).
[CrossRef]

Li, W.

H. He, W. Li, X. Zhang, M. Xia, and K. Yang, “Light scattering by a spheroidal bubble with geometrical optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 113, 1467–1475 (2012).
[CrossRef]

Li, X.

L. Wu, H. Yang, X. Li, B. Yang, and G. Li, “Scattering by large bubbles: comparisons between geometrical-optics theory and Debye series,” J. Quant. Spectrosc. Radiat. Transfer 108, 54–64 (2007).
[CrossRef]

Liou, K. N.

Y. Takano, K. N. Liou, and P. Yang, “Diffraction by rectangular parallelepiped, hexagonal cylinder, and three-axis ellipsoid: some analytic solutions and numerical results,” J. Quant. Spectrosc. Radiat. Transfer 113, 1836–1843 (2012).
[CrossRef]

P. Yang and K. N. Liou, “An ‘exact’ geomteric-optics approach for computing the optical properties of large absorbing particles,” J. Quant. Spectrosc. Radiat. Transfer 110, 1162–1177 (2009).
[CrossRef]

P. Yang and K. N. Liou, “Geometric-optics-integral-equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
[CrossRef]

P. Yang and K. N. Liou, “Light scattering by hexagonal ice crystals: comparison of finite-difference time domain and geometric optics models,” J. Opt. Soc. Am. A 12, 162–176 (1995).
[CrossRef]

Lock, J. A.

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 330, 377–445 (1908).
[CrossRef]

Mishchenko, M. L.

M. L. Mishchenko, L. D. Travis, and A. L. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University, 2002).

Morse, P. M.

P. M. Morse and P. J. Rubenstein, “The diffraction of waves by ribbons and by slits,” Phys. Rev. 54, 895–898 (1938).
[CrossRef]

Nussenzveig, H. M.

H. M. Nussenzveig and W. J. Wiscombe, “Complex angular momentum approximation to hard-core scattering,” Phys. Rev. A 43, 2093–2112 (1991).
[CrossRef]

H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge University, 1992).

Ren, K. F.

Rubenstein, P. J.

P. M. Morse and P. J. Rubenstein, “The diffraction of waves by ribbons and by slits,” Phys. Rev. 54, 895–898 (1938).
[CrossRef]

Serdyuk, V. M.

V. M. Serdyuk, “Exact solutions for electromagnetic wave diffraction by a slot and strip,” Int. J. Electron. Commun. (AEÜ) 65, 182–189 (2011).

Shen, J.

Sommerfeld, A.

A. Sommerfeld, “Mathematische Theorie der Diffraction,” Math. Ann. 47, 317–374 (1896).
[CrossRef]

Stephens, G. L.

Takano, Y.

Y. Takano, K. N. Liou, and P. Yang, “Diffraction by rectangular parallelepiped, hexagonal cylinder, and three-axis ellipsoid: some analytic solutions and numerical results,” J. Quant. Spectrosc. Radiat. Transfer 113, 1836–1843 (2012).
[CrossRef]

Y. Takano and M. Tanaka, “Phase matrix and cross sections for single scattering by circular cylinders: a comparison of ray optics and wave theory,” Appl. Opt. 19, 2781–2800 (1980).
[CrossRef]

Tanaka, M.

Travis, L. D.

M. L. Mishchenko, L. D. Travis, and A. L. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University, 2002).

Ungut, A.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

Wan, C.

Wang, H.

Wei, Y.

H. Yu, J. Shen, and Y. Wei, “Geometrical optics approximation for light scattering by absorbing spherical particles,” J. Quant. Spectrosc. Radiat. Transfer 110, 1178–1189 (2009).
[CrossRef]

Weston, V. H.

P. C. Clemmow and V. H. Weston, “Diffraction of a plane wave by an almost circular cylinder,” Proc. R. Soc. London Ser. A 264, 246–268 (1961).
[CrossRef]

Wiscombe, W. J.

H. M. Nussenzveig and W. J. Wiscombe, “Complex angular momentum approximation to hard-core scattering,” Phys. Rev. A 43, 2093–2112 (1991).
[CrossRef]

W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 2005).

Wriedt, T.

W. Hergert and T. Wriedt, The Mie Theory: Basics and Applications, Vol. 169 of Springer Series in Optical Sciences (Springer-Verlag, 2012).

Wu, L.

L. Wu, H. Yang, X. Li, B. Yang, and G. Li, “Scattering by large bubbles: comparisons between geometrical-optics theory and Debye series,” J. Quant. Spectrosc. Radiat. Transfer 108, 54–64 (2007).
[CrossRef]

Xia, M.

H. He, W. Li, X. Zhang, M. Xia, and K. Yang, “Light scattering by a spheroidal bubble with geometrical optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 113, 1467–1475 (2012).
[CrossRef]

Yang, B.

L. Wu, H. Yang, X. Li, B. Yang, and G. Li, “Scattering by large bubbles: comparisons between geometrical-optics theory and Debye series,” J. Quant. Spectrosc. Radiat. Transfer 108, 54–64 (2007).
[CrossRef]

Yang, H.

L. Wu, H. Yang, X. Li, B. Yang, and G. Li, “Scattering by large bubbles: comparisons between geometrical-optics theory and Debye series,” J. Quant. Spectrosc. Radiat. Transfer 108, 54–64 (2007).
[CrossRef]

Yang, K.

H. He, W. Li, X. Zhang, M. Xia, and K. Yang, “Light scattering by a spheroidal bubble with geometrical optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 113, 1467–1475 (2012).
[CrossRef]

Yang, P.

Y. Takano, K. N. Liou, and P. Yang, “Diffraction by rectangular parallelepiped, hexagonal cylinder, and three-axis ellipsoid: some analytic solutions and numerical results,” J. Quant. Spectrosc. Radiat. Transfer 113, 1836–1843 (2012).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. Baum, “Diffraction and external reflection by dielectric faceted particles,” J. Quant. Spectrosc. Radiat. Transfer 112, 163–173 (2011).
[CrossRef]

L. Bi, P. Yang, and G. W. Kattawar, “Edge-effect contribution to the extinction of light by dielectric disks and cylindrical particles,” Appl. Opt. 49, 4641–4646 (2010).
[CrossRef]

P. Yang and K. N. Liou, “An ‘exact’ geomteric-optics approach for computing the optical properties of large absorbing particles,” J. Quant. Spectrosc. Radiat. Transfer 110, 1162–1177 (2009).
[CrossRef]

P. Yang and K. N. Liou, “Geometric-optics-integral-equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
[CrossRef]

P. Yang and K. N. Liou, “Light scattering by hexagonal ice crystals: comparison of finite-difference time domain and geometric optics models,” J. Opt. Soc. Am. A 12, 162–176 (1995).
[CrossRef]

Yu, H.

H. Yu, J. Shen, and Y. Wei, “Geometrical optics approximation for light scattering by absorbing spherical particles,” J. Quant. Spectrosc. Radiat. Transfer 110, 1178–1189 (2009).
[CrossRef]

Zhang, X.

H. He, W. Li, X. Zhang, M. Xia, and K. Yang, “Light scattering by a spheroidal bubble with geometrical optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 113, 1467–1475 (2012).
[CrossRef]

Ann. Phys.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 330, 377–445 (1908).
[CrossRef]

Appl. Opt.

J. V. Dave, “Scattering of visible light by large water spheres,” Appl. Opt. 8, 155–164 (1969).
[CrossRef]

W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
[CrossRef]

Y. Takano and M. Tanaka, “Phase matrix and cross sections for single scattering by circular cylinders: a comparison of ray optics and wave theory,” Appl. Opt. 19, 2781–2800 (1980).
[CrossRef]

G. L. Stephens, “Scattering of plane waves by soft obstacles: anomalous diffraction theory for circular cylinders,” Appl. Opt. 23, 954–959 (1984).
[CrossRef]

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

P. Yang and K. N. Liou, “Geometric-optics-integral-equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
[CrossRef]

A. Ungut, G. Grehan, and G. Gouesbet, “Comparison between geometrical optics and Lorenz-Mie theory,” Appl. Opt. 20, 2911–2918 (1981).
[CrossRef]

J. Shen and H. Wang, “Calculation of Debye series expansion of light scattering,” Appl. Opt. 49, 2422–2428 (2010).
[CrossRef]

L. Bi, P. Yang, and G. W. Kattawar, “Edge-effect contribution to the extinction of light by dielectric disks and cylindrical particles,” Appl. Opt. 49, 4641–4646 (2010).
[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]

Chin. Opt. Lett.

Int. J. Electron. Commun. (AEÜ)

V. M. Serdyuk, “Exact solutions for electromagnetic wave diffraction by a slot and strip,” Int. J. Electron. Commun. (AEÜ) 65, 182–189 (2011).

J. Opt. Soc. Am. A

J. Quant. Spectrosc. Radiat. Transfer

L. Wu, H. Yang, X. Li, B. Yang, and G. Li, “Scattering by large bubbles: comparisons between geometrical-optics theory and Debye series,” J. Quant. Spectrosc. Radiat. Transfer 108, 54–64 (2007).
[CrossRef]

H. Yu, J. Shen, and Y. Wei, “Geometrical optics approximation for light scattering by absorbing spherical particles,” J. Quant. Spectrosc. Radiat. Transfer 110, 1178–1189 (2009).
[CrossRef]

H. He, W. Li, X. Zhang, M. Xia, and K. Yang, “Light scattering by a spheroidal bubble with geometrical optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 113, 1467–1475 (2012).
[CrossRef]

P. Yang and K. N. Liou, “An ‘exact’ geomteric-optics approach for computing the optical properties of large absorbing particles,” J. Quant. Spectrosc. Radiat. Transfer 110, 1162–1177 (2009).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. Baum, “Diffraction and external reflection by dielectric faceted particles,” J. Quant. Spectrosc. Radiat. Transfer 112, 163–173 (2011).
[CrossRef]

Y. Takano, K. N. Liou, and P. Yang, “Diffraction by rectangular parallelepiped, hexagonal cylinder, and three-axis ellipsoid: some analytic solutions and numerical results,” J. Quant. Spectrosc. Radiat. Transfer 113, 1836–1843 (2012).
[CrossRef]

Math. Ann.

A. Sommerfeld, “Mathematische Theorie der Diffraction,” Math. Ann. 47, 317–374 (1896).
[CrossRef]

Phys. Rev.

P. M. Morse and P. J. Rubenstein, “The diffraction of waves by ribbons and by slits,” Phys. Rev. 54, 895–898 (1938).
[CrossRef]

Phys. Rev. A

H. M. Nussenzveig and W. J. Wiscombe, “Complex angular momentum approximation to hard-core scattering,” Phys. Rev. A 43, 2093–2112 (1991).
[CrossRef]

Phys. Z

P. Debye, “Das elektromagnetische Feld um einen Zylinder und die Theorie des Regenbogens,” Phys. Z 9, 775–778 (1908).

Proc. R. Soc. London Ser. A

P. C. Clemmow and V. H. Weston, “Diffraction of a plane wave by an almost circular cylinder,” Proc. R. Soc. London Ser. A 264, 246–268 (1961).
[CrossRef]

Rep. Prog. Phys.

C. J. Bouwkamp, “Diffraction theory,” Rep. Prog. Phys. 17, 35–100 (1954).
[CrossRef]

Z. Angew. Math. Phys.

N. Gorenflo, “A new explicit solution method for the diffraction through a slit,” Z. Angew. Math. Phys. 53, 877–886 (2002).
[CrossRef]

N. Gorenflo, “A new explicit solution method for the diffraction through a slit—part 2,” Z. Angew. Math. Phys. 58, 16–36 (2007).
[CrossRef]

Other

H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge University, 1992).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

W. Hergert and T. Wriedt, The Mie Theory: Basics and Applications, Vol. 169 of Springer Series in Optical Sciences (Springer-Verlag, 2012).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

M. Born and E. Wolf, Principles of Optics (Cambridge University, 2005).

M. L. Mishchenko, L. D. Travis, and A. L. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University, 2002).

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Figures (4)

Fig. 1.
Fig. 1.

Coordinate system describing the interaction between an incident plane wave and an infinitely long circular cylinder.

Fig. 2.
Fig. 2.

Numerical results of the radial-dependent functions Jn(ρ) and Jn(ρ) for n=50.

Fig. 3.
Fig. 3.

Intensity distribution of the diffracted light idiff calculated with Eqs. (13)–(15), α=20.5.

Fig. 4.
Fig. 4.

Intensity distribution of the diffracted light idiff calculated with Eqs. (16), (17), and (20), α=30 and ns=29.

Equations (22)

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Einc=n=Einc,n,
Einc,n=E0exp(inϕ)(i)n{[nJn(ρ)ρer+iJn(ρ)eϕ]cosγ+Jn(ρ)·sinγez},
Ediff=E02n=ns+ns(i)nexp(inϕ){icosγ[inHn(1)(ρ)ρerHn(1)(ρ)eϕ]sinγHn(1)(ρ)ez},
Hn(1)(ρ)2πρ(i)nexp(iπ4)exp(iρ),
Hn(1)(ρ)i2πρ(i)nexp(iπ4)exp(iρ).
Ediff=E02πρexp[i(ρπ4)]·n=ns+ns()nexp(inϕ)·ediff,
ediff=cosγeϕsinγez,
Ediff=E02πρexp[i(ρπ4)]·n=ns+nscos(nθ)·ediff.
Idiff=I02πρ·[n=ns+nscos(nθ)]2=Idiff(0)·idiff(θ),
Idiff(0)=2(ns+1/2)2πρI0,
idiff(θ)={θ/2sin(θ/2)·sin[(ns+1/2)θ](ns+1/2)θ}2,
Idiff(0)=2α2πρI0,
idiff(θ)=[θ/2sin(θ/2)]2·[sin(αθ)αθ]2.
idiff=[sin(αsinθ)αsinθ]2,
idiff=(1+cosθ2)2[sin(αsinθ)αsinθ]2.
idiff=4(ns+1)4[(1+cosθ)πns(θ)12ns+cosθns+1πns(θ)12πns1(θ)]2,
idiff=θsinθ·[2J1(αθ)αθ]2,
idiff=[2J1(αsinθ)αsinθ]2,
idiff=(1+cosθ2)2[2J1(αsinθ)αsinθ]2.
idiff=[θ/2sin(θ/2)]8·[2J1(αθ)αθ]2.
πn(cosθ)=12n(n+1)[J0(u)+J2(u)],τn(cosθ)=12n(n+1)[J0(u)J2(u)],
idiff=[2J1(αθ)αθ]2.

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