Abstract
The problem of scalar wave scattering by a planar substrate containing a sphere is analytically solved. The wave functions, as the solution, come in the form of infinite series. The factors in each term of the series explicitly show the involved process and the multiplicity of scattering between the surface of the substrate and the sphere. In air, the incident wave is either reflected by or transmitted into the substrate. The transmitted wave is either scattered by or transmitted into the sphere, and then the backwardly scattered wave going to the surface of the substrate is either transmitted back into air or reflected toward the sphere. The reflected wave is again either scattered by or transmitted into the sphere, and so on. Within the substrate, the scattering by the sphere and the reflection at the planar surface repeat in turn indefinitely to generate multiply scattered waves, which combine to make different wave functions for different regions in the form of infinite series.
Similar content being viewed by others
References
L. Rayleigh, Philos. Magn. 41, 107 (1871).
G. Mie, Ann. Physik 25, 377 (1908).
H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).
M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic Press, New York, 1969).
C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
M. I. Mishchenko, L. D. Travis and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, London, 2002).
F. Borghese, P. Denti and R. Saija, Scattering from Model Nonspherical Particles (Springer, Berlin, 2003).
G. Kristensson, Scattering of Electromagnetic Waves by Obstacles (SciTech Publishing, Edison, 2016).
A. V. Osipov and S. A. Tretyakov, Modern Electromagnetic Scattering Theory with Applications (Wiley, Chichester, 2017).
H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980).
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).
F. Moreno and F. Golzalez, Eds., Light Scattering from Microstructures (Springer, Berlin, 2000).
D. Bedeaux and J. Vlieger, Optical Properties of Surfaces, 2nd ed. (Imperial College Press, London, 2004).
A. A. Maradudin, Ed., Light Scattering and Nanoscale Surface Roughness (Springer, Berlin, 2007).
B. C. Park and J. S. Kim, J. Korean Phys. Soc. 73, 1512 (2018).
H. M. Jol, Ed., Ground Penetrating Radar Theory and Applications (Elsevier Science, Amsterdam, 2009).
B. Saleh, Introduction to Subsurface Imaging (Cambridge University Press, New York, 2011).
B. C. Park and J. S. Kim, J. Korean Phys. Soc. 68, 853 (2016).
G. Videen, J. Opt. Soc. Am. A 10, 110 (1993).
M. J. Jory, E. A. Perkins and J. R. Sambles, J. Opt. Soc. Am. A 20, 1589 (2003).
F. Frezza et al., J. Opt. Soc. Am. A 30, 783 (2013); F. Frezza and F.Mangini, J. Opt. Soc. Am. A 33, 947 (2016).
J. S. Kim, J. Korean Phys. Soc. 70, 771 (2017).
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).
G. Arfken, H. J. Weber and F. E. Harris, Mathematical Methods for Physicists, 7th ed. (Academic Press, Amsterdam, 2013).
A. J. Devaney and E. Wolf, J. Math. Phys. 15, 234 (1974).
C. Cappellin, O. Breinbjerg and A. Frandsen, Radio Science 43, RS1012 (2008).
E. Hecht, Optics, 5th ed. (Pearson, Essex, 2017).
F. Frezza, L. Pajewski, C. Ponti and G. Schettini, J. Opt. Soc. Am. A 27, 687 (2010).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Park, B.C., Kim, J.S. Theory of Scalar Wave Scattering by a Planar Substrate Containing a Sphere. J. Korean Phys. Soc. 74, 951–958 (2019). https://doi.org/10.3938/jkps.74.951
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3938/jkps.74.951