Abstract
The problem of scalar wave scattering by a cylinder buried in a planar substrate is analytically solved. The solution is in the form of a coupled set of linear equations relating the coefficients of reflection and transmission of the planar substrate and those of scattering and transmission of the cylinder. The coupling is due to the process of multiple scattering by the two objects. Iterative substitution gives the solution in the form of a set of infinite series, and each term explicitly shows the effect of multiple scattering of increasing order.
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References
L. Rayleigh, Philos. Mag. 41, 107 (1871).
G. Mie, Ann. Physik 25, 377 (1908).
H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).
H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980).
C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
F. Moreno and F. Gonzalez, Eds., Light Scattering from Microstructures (Springer, Berlin, 2000).
M. I. Mishchenki, 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).
D. Bedeaux and J. Vlieger, Optical Properties of Surfaces, 2nd ed. (Imperial College Press, London, 2004).
A. Maradudin, Ed., Light Scattering and Nanoscale Surface Roughness (Springer, Berlin, 2007).
S. Asano and G. Yamamoto, Appl. Opt. 14, 29 (1975).
J. S. Kim and S. S. Lee, J. Opt. Soc. Am. 73, 303 (1983).
A. Egel, D. Theobald, Y. Donie, U. Lemmer and G. Gomard, Opt. Express 24, 25154 (2016).
C. Liang and Y. T. Lo, Radio Science 2, 1481 (1967).
H. A. Yousif and S. Koehler, J. Opt. Soc. Am. A 5, 1085 (1988) ibid. A 5, 1097 (1988).
B. C. Park, M. W. Kim and J. S. Kim, J. Opt. Soc. Kor. 18, 188 (2014).
B. C. Park and J. S. Kim, J. Korean Phys. Soc. 68, 853 (2016).
J. S. Kim, J. Korean Phys. Soc. 70, 574 (2017).
B. Saleh, Introduction to Subsurface Imaging (Cambridge University Press, London, 2011).
M. Di Vico, F. Frezza, L. Pajewski and G. Schettini, Radio Science 40, RS6S18 (2005).
M. Di Vico, M., F. Frezza, L. Pajewski and G. Schettini, IEEE Trans. Antennas Propag. 53, 719 (2005).
G. Cincotti, F. Gori, M. Santasiero, F. Frezza, F. Furno and G. Schettini, Opt. Comm. 95, 192 (1993)
F. Frezza, G. Schettini and N. Tedeschi, ibid. 284, 3867 (2011).
G. Arfken, H. J. Weber and F. E. Harris, Mathematical Methods for Physicists, 7th ed. (Academic Press, Amsterdam, 2013).
E. Hecht, Optics, 4th ed. (Addison-Wesley, Reading, 2017).
F. Frezza, L. Pajewski, C. Ponti and G. Schettini, J. Opt. Soc. Am. A 27, 687 (2010).
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Kim, J.S. A theory of scalar wave scattering by a cylinder buried in a planar substrate. Journal of the Korean Physical Society 70, 771–776 (2017). https://doi.org/10.3938/jkps.70.771
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DOI: https://doi.org/10.3938/jkps.70.771