On the Kramers–Kronig dispersion relations for the complex reflection coefficient of a layered dispersive medium

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.