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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 9 — Oct. 2, 2013

Diffraction of a plane wave by an infinitely long circular cylinder or a sphere: solution from Mie theory

Jianqi Shen and Xiaowei Jia  »View Author Affiliations


Applied Optics, Vol. 52, Issue 23, pp. 5707-5712 (2013)
http://dx.doi.org/10.1364/AO.52.005707


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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

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(290.4020) Scattering : Mie theory

ToC Category:
Scattering

History
Original Manuscript: March 20, 2013
Revised Manuscript: July 10, 2013
Manuscript Accepted: July 13, 2013
Published: August 7, 2013

Virtual Issues
Vol. 8, Iss. 9 Virtual Journal for Biomedical Optics

Citation
Jianqi Shen and Xiaowei Jia, "Diffraction of a plane wave by an infinitely long circular cylinder or a sphere: solution from Mie theory," Appl. Opt. 52, 5707-5712 (2013)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=ao-52-23-5707


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References

  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]

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