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
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).
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).
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).
Yu.L. Gazaryan, “The one dimensional problem of propagation of waves in a medium with random inhomogeneities”, Sov. Phys. JETP29, 996–1003 (1969).
J. Bazer, “Multiple scattering in one dimension”, J.Soc. Indust. Appl. Math.12, 539–579 (1964).
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.
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).
S.S. Saatchi and R. Lang, “Mean wave propagation in a slab of one-dimensional discrete random medium”, submitted to Wave Motion, 1990.
R. Bellman and R. Kalaba, “Functional equations, wave propagation, and invariant imbedding”, J. Math. Mech.8, 683–704 (1959).
A. Erde’lyi, W. Magnus, F. Oberhettinger and F.G. Tricomi, Higher Transcendai Functions, McGraw-Hill Book Co., New York (1953).
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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
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