Geodesic
On the Kramers--Kronig dispersion relations for the complex reflection coefficient of a~layered dispersive medium
Matematičeskoe modelirovanie, Tome 2 (1990) no. 6, pp. 90-96.

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A possibility to obtain the frequency dependence of phase $\varphi(\omega)$ of the complex reflection coefficient form the spectral dependence of its modulus $\rho(\omega)$ is considered for the case of a plasma–like flat–layered dispersive medium. Basing on the study of analytical properties of the reflection coefficient $r(\omega)=\rho(\omega)\exp[i\varphi(\omega)]$ the sufficient conditions for the absence of zeros of the function $r(\omega)$ in the upper half plane of the complex frequency $\omega$ are formulated. In these conditions a standard amplitude-phase dispersion relation of Kramers–Kronig used for analysis of a homogeneous media holds true. 
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     author = {N. A. Denisova and A. V. Rezvov},
     title = {On the {Kramers--Kronig} dispersion relations for the complex reflection coefficient of a~layered dispersive medium},
     journal = {Matemati\v{c}eskoe modelirovanie},
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     publisher = {mathdoc},
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N. A. Denisova; A. V. Rezvov. On the Kramers--Kronig dispersion relations for the complex reflection coefficient of a~layered dispersive medium. Matematičeskoe modelirovanie, Tome 2 (1990) no. 6, pp. 90-96. http://geodesic.mathdoc.fr/item/MM_1990_2_6_a8/