The optical theorem is generalized to the case of excitation of a local body by a multipole. To compute the extinction cross-section, it is sufficient to find the derivatives of the scattered field at the single point where the multipole is located. The relationship obtained in this article makes it possible to test software modules developed for studying wave diffraction on transparent bodies.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
H. Henl, A. Maue, and C. Westphal, Diffraction Theory [Russian translation], Mir, Moscow (1964).
M. I. Mishchenko, “The electromagnetic optical theorem revisited,” J. Quantitat. Spectr. Radiat. Trans., 101, 404–410 (2006).
V. G. Farafonov, V. B. Il’in, and A. A. Vinokurov, “Light scattering by nonspherical particles in the near and the far zone: applicability of methods with a spherical basis,” Optika i Spektroskopiya, 109, 476–487 (2010).
R. G. Newton, Scattering Theory of Waves and Particles, Springer, New York (1982).
S. Ström, “The scattered field,” in: V.V. Varadan, A. Lakhtakia, V.K. Varadan (editors), Field Representation and Introduction to Scattering, Elsevier Science Publisher (1991), pp. 143-149.
M. J. Berg, C. M. Sorensen, and A. Chakrabarti, “Extinction and the optical theorem. Part I: Single particles,” J. Opt. Soc. Am. A, 25, No. 7, 1504–1513 (2008).
L. D. Landau and E. M. Lifshits, Quantum Mechanics (Nonrelativisitc Theory), 4th Ed., Nauka, Moscow (1989).
V. G. Farafonov and V. B. Il’in, Light Scattering by Nonhomogeneous Nonspherical Particles [in Russian], VVM, Sankt Peterburg State University (2009).
D. W. Mackowski, “Calculation of total cross sections of multiple-sphere clusters,” J. Opt. Soc. Am. A, 11, 2851–2861 (1994).
P. S. Carney, J. C. Schotland, and E. Wolf, “Generalized optical theorem for reflection, transmission, and extinction of power in scalar fields,” Phys. Rev. E, 70, No. 3, 036611 (2004).
Yu. A. Eremin, “Generalization of the optical theorem using integro-functional relationships,” Diff. Uravn., 43, No. 9, 1168–1172 (2007).
A. Small, J. Fung, and V. N. Manoharan, “Generalization of the optical theorem for light scattering from a particle at a planar interface,” J. Opt. Soc. Am. A, 30, No. 12, 2519–2525 (2013).
C. Athanasiadis, P. A. Martin, A. Spyropoulos, and I. G. Stratis, “Scattering relations for point sources. Acoustic and electromagnetic waves,” J. Math. Phys., 43, No. 11, 5683–5697 (2002).
M. Venkatapathi, “Emitter near an arbitrary body: Purcell effect, optical theorem and the Wheeler–Feynman absorber,” J. Quantitat. Spectr. Radiat. Transfer, 113, 1705–1711 (2012).
Yu. A. Eremin and A. G. Sveshnikov, “Optical theorem for multipole sources in wave diffraction theory,” Akust. Zh., 62, No. 3, 271–276 (2016).
A. J. Devaney and E. Wolf, “Multipole expansions and plane wave representations of the electromagnetic field,” J. Math. Phys., 15, 234–244 (1974).
D. Colton and R. Kress, Integral Equation Methods in Scattering Theory [Russian translation], Mir, Moscow (1987).
V. S. Vladimirov, Generalized Functions in Mathematical Physics [in Russian], Nauka, Moscow (1979).
V. A. Trenogin, Functional Analysis [in Russian], Nauka, Moscow (1980).
G. Korn and T. Korn, Maathematical Handbook for Scientists and Engineers [Russian translation], Nauka, Moscow (1973).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Matematika i Informatika, No. 52, 2016, pp. 26–33.
Rights and permissions
About this article
Cite this article
Eremin, Y.A. Generalization of the Optical Theorem to the Case of Excitation of a Local Obstacle by a Multipole. Comput Math Model 28, 158–163 (2017). https://doi.org/10.1007/s10598-017-9354-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10598-017-9354-5