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Wave Intensity Fluctuations in a One Dimensional Discrete Random Medium

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Directions in Electromagnetic Wave Modeling

Abstract

The propagation of electromagnetic waves in a one dimensional discrete random medium is considered. It is assumed that the medium is bounded within a slab of thickness L and the random inhomogeneities are distributed according to a Poisson impulse process of density A. In the absence of absorption, an exact equation is obtained for the m-moments of the wave intensity using the Kolmogorov-Feller approach. In the limit of low concentration of inhomogeneities, we use a two-variable perturbation technique, valid for A small and L large, to obtain approximate solutions for the moments of the intensity. It is shown that the wave intensity increases with the slab thickness and the peak of the higher moments occur inside the medium.

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References

  1. W. Kohler and G.C. Papanicolaou, “Power statistics for wave propagation in one dimension and comparison with radiative transfer theory”, J. Math. Phys.14, 1733–1745 (1973).

    Article  ADS  MathSciNet  Google Scholar 

  2. W. Kohler and G.C. Papanicolaou, Tower statistics for wave propagation in one dimension and comparison with radiative transfer theory.II”, J. Math. Phys.15, 2186–2197 (1974).

    Article  ADS  MathSciNet  Google Scholar 

  3. R.H. Lang, “Probability density function and moments of the field in a slab of one-dimensional random medium”, J. Math. Phys., 14, 1921–1926 (1973).

    Article  ADS  MATH  Google Scholar 

  4. Yu.L. Gazaryan, “The one dimensional problem of propagation of waves in a medium with random inhomogeneities”, Sov. Phys. JETP29, 996–1003 (1969).

    ADS  Google Scholar 

  5. J. Bazer, “Multiple scattering in one dimension”, J.Soc. Indust. Appl. Math.12, 539–579 (1964).

    Article  MATH  MathSciNet  Google Scholar 

  6. V.I. Klyatslrin, “Wave stochastic parametric resonance” (wave intensity fluctuations in a one-dimensional randomly inhomogeneous medium), Izv. Vuzov Radiofisika 22(2), 180–191, 1979.

    Google Scholar 

  7. S.S. Saatchi and R.H. Lang, “Average reflected power from a one dimensional slab of discrete scatterers”, Radio Science 25(4), 407–417 (1990).

    Article  ADS  Google Scholar 

  8. S.S. Saatchi and R. Lang, “Mean wave propagation in a slab of one-dimensional discrete random medium”, submitted to Wave Motion, 1990.

    Google Scholar 

  9. R. Bellman and R. Kalaba, “Functional equations, wave propagation, and invariant imbedding”, J. Math. Mech.8, 683–704 (1959).

    MathSciNet  Google Scholar 

  10. A. Erde’lyi, W. Magnus, F. Oberhettinger and F.G. Tricomi, Higher Transcendai Functions, McGraw-Hill Book Co., New York (1953).

    Google Scholar 

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© 1991 Springer Science+Business Media New York

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Saatchi, S.S., Lang, R.H. (1991). Wave Intensity Fluctuations in a One Dimensional Discrete Random Medium. In: Bertoni, H.L., Felsen, L.B. (eds) Directions in Electromagnetic Wave Modeling. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-3677-6_43

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  • DOI: https://doi.org/10.1007/978-1-4899-3677-6_43

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-3679-0

  • Online ISBN: 978-1-4899-3677-6

  • eBook Packages: Springer Book Archive

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