Journal of the Korean Physical Society

, Volume 73, Issue 10, pp 1512–1518 | Cite as

Theory of Scalar Wave Scattering by a Sphere and a Planar Substrate

  • Byong Chon Park
  • Jin Seung Kim


The problem of scalar wave scattering by a sphere on or near a planar substrate is analytically solved. The solution is a set of wave functions coming in the form of infinite series of spherical and plane waves. In air, the incident plane wave is either scattered by the sphere or reflected from the substrate. A part of these scattered or reflected waves propagate to the other object where it is reflected and scattered again. Such processes of scattering and reflection repeat in turn indefinitely to generate multiply scattered waves, which are represented in the corresponding terms in the infinite series. The term in the series can be arranged in a recognizable manner to explicitly reveal the involved process and the multiplicity of scattering.


Scattering Sphere Planar substrate Multiple scattering 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    L. Rayleigh, Philos. Mag. 41, 107 (1871).CrossRefGoogle Scholar
  2. [2]
    G. Mie, Ann. Physik 25, 377 (1908).ADSCrossRefGoogle Scholar
  3. [3]
    H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).Google Scholar
  4. [4]
    M. Kerker, The scattering of light and other electromagnetic radiation (Academic Press, New York, 1969).Google Scholar
  5. [5]
    C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).Google Scholar
  6. [6]
    M. I. Mishchenko, L. D. Travis and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, London, 2002).Google Scholar
  7. [7]
    F. Borghese, P. Denti and R. Saija, Scattering from Model Nonspherical Particles (Springer, Berlin, 2003).CrossRefGoogle Scholar
  8. [8]
    G. Kristensson, Scattering of Electromagnetic Waves by Obstacles (SciTech Publishing, Edison, 2016).CrossRefzbMATHGoogle Scholar
  9. [9]
    A. V. Osipov and S. A. Tretyakov, Modern Electromagnetic Scattering Theory with Applications (Wiley, Chichester, 2017).CrossRefGoogle Scholar
  10. [10]
    H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980).Google Scholar
  11. [11]
    M. I. Mishchenko, L. D. Travis and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge University Press, London, 2006).Google Scholar
  12. [12]
    B. C. Park, M. W. Kim and J. S. Kim, J. Opt. Soc. Korea 18, 188 (2014).CrossRefGoogle Scholar
  13. [13]
    F. Moreno and F. Gonzalez, Eds., Light Scattering from Microstructures (Springer, Berlin, 2000).Google Scholar
  14. [14]
    D. Bedeaux and J. Vlieger, Optical Properties of Surfaces, 2nd ed. (Imperial College Press, London, 2004).CrossRefGoogle Scholar
  15. [15]
    A. Maradudin, Ed., Light Scattering and Nanoscale Surface Roughness (Springer, Berlin, 2007).Google Scholar
  16. [16]
    T. A. Germer, C. Wolters and D. Brayton, Opt. Express 16, 4698 (2008).ADSCrossRefGoogle Scholar
  17. [17]
    P. A. Bobbert and J. Vlieger, Physica 137A, 209 (1986); P. A. Bobbert, J. Vlieger and R. Greed, ibid. 137A, 243 (1986).ADSCrossRefGoogle Scholar
  18. [18]
    K. B. Nahm and W. L. Wolfe, Appl. Opt. 26, 2995 (1987).ADSCrossRefGoogle Scholar
  19. [19]
    I. V. Lindell, A. H. Sihvola, K. O. Muinonen and P. Barber, J. Opt. Soc. Am. A 8, 472 (1991); K. O. Muinonen, A. H. Sihvola, I. V. Lindell and K. A. Lumme, ibid. A 8, 477 (1991).ADSCrossRefGoogle Scholar
  20. [20]
    G. Videen, J. Opt. Soc. Am. A 8, 483 (1991); ibid. 9, 844 (erratum) (1992).ADSCrossRefGoogle Scholar
  21. [21]
    B. R. Johnson, J. Opt. Soc. Am. A 9, 1341 (1992).ADSCrossRefGoogle Scholar
  22. [22]
    G. Videen, Opt. Comm. 115, 1 (1995).ADSCrossRefGoogle Scholar
  23. [23]
    F. Borghese, P. Denti, R. Saija, E. Fucile and O. I. Sindoni, J. Opt. Soc. Am. A 12, 530 (1995).ADSCrossRefGoogle Scholar
  24. [24]
    B. R. Johnson, J. Opt. Soc. Am. A 13, 326 (1996).ADSCrossRefGoogle Scholar
  25. [25]
    J. C. Chao, F. J. Rizzo, I. Elshafiey, Y. J. Liu, L. Upda and P. A. Martin, J. Opt. Soc. Am. A 13, 338 (1996).ADSCrossRefGoogle Scholar
  26. [26]
    E. Fucile, P. Denti, F. Borghese, R. Saija and O. I. Sindoni, J. Opt. Soc. Am. A 14, 1505 (1997).ADSCrossRefGoogle Scholar
  27. [27]
    T. Wriedt and A. Doicu, Opt. Commun. 152, 376 (1998).ADSCrossRefGoogle Scholar
  28. [28]
    T. A. Germer, Opt. Lett. 27, 1159 (2002).ADSCrossRefGoogle Scholar
  29. [29]
    J. H. Kim, S. H. Ehrman, G. W. Mulholland and T. A. Germer, Appl. Opt. 41, 5405 (2002); J. H. Kim, S. H. Ehrman, G. W. Mulholland and T. A. Germer, ibid. 43, 585 (2004).ADSCrossRefGoogle Scholar
  30. [30]
    A. B. Evlyukhin, C. Reinhardt, E. Evlyukhin and B. N. Chichkov, J. Opt. Soc. Am. B 30, 2589 (2013).ADSCrossRefGoogle Scholar
  31. [31]
    A. Egel, D. Theobald, Y. Donie, U. Lemmer and G. Gomard, Opt. Express 24, 25154 (2016).ADSCrossRefGoogle Scholar
  32. [32]
    J. S. Kim, J. Korean Phys. Soc. 70, 574 (2017).ADSCrossRefGoogle Scholar
  33. [33]
    F. W. J. Olver, D. W. Lozier, R. F. Boisvert and C. W. Clark, Eds., NIST Handbook of Mathematical Functions (Cambridge University Press, New York, 2010).zbMATHGoogle Scholar
  34. [34]
    G. Arfken, H. J. Weber and F. E. Harris, Mathematical Methods for Physicists, 7th ed. (Academic Press, Amsterdam, 2013).zbMATHGoogle Scholar
  35. [35]
    A. J. Devaney and E. Wolf, J. Math. Phys. 15, 234 (1974).ADSCrossRefGoogle Scholar
  36. [36]
    C. Cappellin, O. Breinbjerg and A. Frandsen, Radio Science 43, RS1012 (2008).ADSCrossRefGoogle Scholar

Copyright information

© The Korean Physical Society 2018

Authors and Affiliations

  1. 1.Division of Industrial MetrologyKorea Research Institute of Standards and ScienceDaejeonKorea
  2. 2.Institute of Photonics and Information Technology, Department of PhysicsChonbuk National UniversityJeonjuKorea

Personalised recommendations