Kramers-Kronig relations for an interferometer

The treatment in the literature of the transfer functions for interferometers does not allow for a proper use of the Kramers-Kronig (KK) relations between amplitude and phase. We will present a systematic description of transfer functions. We show that if the full frequency dependence of all the optical parameters, including the complex index of refraction,is properly taken into account KK relations do exist. The modification of KK relations for amplitude and phase due to zeros of transfer functions is described. As an example, numerical results for the phase calculated from the amplitude of light reflected from a Gires-Tournois interferometer are presented.