Abstract
For some purposes, both analytical and numerical, it is useful to transform the linear second order differential equation for the wave amplitude into a non-linear first order Riccati type differential equation for a quantity related to the reflection amplitude. The advantage lies in dealing directly with the quantity one wants to calculate. A disadvantage is the non-linearity of the resulting equations.
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References
L. R. Walker and N. Wax (1946) “Non-uniform transmission lines and reflection coefficients”, J. Applied Phys. 17, 1043–1045.
W. Kofink (1947) “Reflexion elektromagnetischer Wellen an einer inhomogenen Schicht”, Annalen der Physik 1, 119–132.
L. M. Brekhovskikh (1949) “Reflection of plane waves from layered inhomogeneous media”, Zhurnal Technicheskoi Fiziki 19, 1126–1135.
L. M. Brekhovskikh (1980) “Waves in layered media”, Academic Press, second edition.
S. A. Schelkunoff (1951) “Remarks concerning wave propagation in stratified media”, Commun. Pure and App. Math. 4, 117–128.
P. M. Morse and W. P. Allis (1933) “The effect of exchange on the scattering of electrons”, Phys. Rev. 44, 269–276.
F. Calogero (1967) “Variable phase approach to potential scattering”, Academic Press.
R. Courant and D. Hilbert (1953) “Methods of mathematical physics”, Interscience Publishers, Volume 1, p. 322.
J. Heading (1962) “An introduction to phase integral methods”, Methuen.
F. W. J. Olver (1964) “Bessel functions of fractional order” (Chapter 10 of “Handbook of mathematical functions”, edited by M. Abramowitz and I. A. Stegun, N.B.S. Applied Math. Series 55 ).
J. C. P. Miller (1971) “The Airy integral”, British Association Mathematical Tables, Part-volume B, Cambridge.
J. W. S. Rayleigh (1912) “On the propagation of waves through a stratified medium, with special reference to the question of reflection”, Proc. Roy. Soc. 86, 207–266.
H. Bremmer (1951) “The W.K.B. approximation as the first term of a geometric-optical series”, Commun. Pure and App. Math. 4, 105–115.
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© 1987 Springer Science+Business Media Dordrecht
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Lekner, J. (1987). Equations for the reflection amplitudes. In: Theory of Reflection of Electromagnetic and Particle Waves. Developments in Electromagnetic Theory and Applications, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7748-9_5
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DOI: https://doi.org/10.1007/978-94-015-7748-9_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8299-2
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