Transparency threshold in the insulating phase of layered copper oxides

The dielectric function of the insulating antiferromagnetic phase of high-Tc layered cuprates is calculated, as function of frequency, at different dopings and temperatures. It is shown that at frequencies below the energy gap the dielectric constant is real but can change its sign. This means that there exists a transparency threshold. The corresponding frequency is calculated, as function of temperature at different dopings. It vanishes in both limits: T→0, and T→TN, if the transition at TN is a second order transition. In case of a first order transition the threshold frequency remains finite at TN