Dispersion models exhibiting natural optical activity: theory of the dielectric response of isotropic systems

In this study, dispersion models of the dielectric response of optically active isotropic media based on coupled harmonic oscillators are derived and discussed. These models are suitable for describing disordered condensed matter. In the isotropic case, the optical activity is an effect of the dielectric response of systems with chiral symmetry, which occurs in the medium due to spatial dispersion. Therefore, in addition to the frequency, the proposed dispersion models also depend on the direction and size of the wave vector. Moreover, the models satisfy all fundamental conditions imposed on the dielectric response, i.e., the time-reversal symmetry, Kramers–Kronig consistency, and conformity with the sum rules. It then follows that dispersion models have physically correct static and asymptotic behavior. The proposed models of optical activity go beyond the phenomenological models (approximations) commonly used in practice. It is shown that these phenomenological models correspond to certain approximations of the presented models. The main advantage of these models is that it is possible to introduce parameters controlling the radius on the non-local response, which is important from a theoretical point of view, and it could also be useful for the study of condensed matter in practice.