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Variational methods for wave scattering from random systems

  • Classical Scattering Theory
  • Conference paper
  • First Online:
Book cover Mathematical Methods and Applications of Scattering Theory

Part of the book series: Lecture Notes in Physics ((LNP,volume 130))

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Abstract

The scattering of waves by random surfaces and media has long been of considerable interest from both theoretical and experimental viewpoints. This paper briefly reviews the work of our group toward developing variational principles which are applicable to the scattering of scalar and vector waves from stochastic systems. These principles have the general form 4π<T> = <N 1><N 2>/<D> for arbitrary scattering statistics. In this expression, T is the far-field scattering amplitude, N 1 is the usual noninvariant integral representation of T, and the ratio of integrals N 2/D is the variational correction factor. Application to a simple model of a random rough surface has shown this stochastic variational approach to account in large measure for multiple scattering. The potential tractability of stochastic variational principles should allow broader application of variational techniques to random scattering problems.

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Footnotes and References

  1. A. Ishimaru: Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vols. 1, 2

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  3. R. W. Hart, R. A. Farrell: “A variational principle for scattering from rough surfaces,” IEEE Trans. AP-2, 708–710 (1977)

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  4. H. Levine, J. Schwinger: “On the theory of electromagnetic wave diffraction by an aperture in an infinite plane conducting screen,” Comm. Pure Appl. Math 3, 355–391 (1950)

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  5. J. A. Krill, R. H. Andreo: “Vector stochastic variational principles for electromagnetic wave scattering,” to be submitted to IEEE Trans. Ant. Prop. (1979)

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  6. E. P. Gray, R. W. Hart, R. A. Farrell: “An application of a variational principle for scattering by random rough surfaces,” Radio Science 13, 333–348 (1978)

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  7. V. Twersky: “On scattering and reflection of electromagnetic waves by rough surfaces,” IRE Trans. AP-5, 81–90 (1957)

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  8. J. A. Krill, R. A. Farrell: “Comparisons between variational, perturbationat, and exact solutions for scattering from a random rough surface model,” J. Opt. Soc. Am. 68, 768–774 (1978)

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Authors and Affiliations

  1. Applied Physics Laboratory, The Johns Hopkins University, Laurel, 20810, Maryland

    R. H. Andreo

Authors
  1. R. H. Andreo
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John A. DeSanto Albert W. Sáenz Woodford W. Zachary

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© 1980 Springer-Verlag

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Andreo, R.H. (1980). Variational methods for wave scattering from random systems. In: DeSanto, J.A., Sáenz, A.W., Zachary, W.W. (eds) Mathematical Methods and Applications of Scattering Theory. Lecture Notes in Physics, vol 130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10023-7_99

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  • DOI: https://doi.org/10.1007/3-540-10023-7_99

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10023-2

  • Online ISBN: 978-3-540-38184-6

  • eBook Packages: Springer Book Archive

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