The local-field correction factor beyond the Onsager–Böttcher approach: Mixing of states from the interaction with atoms in the surrounding medium

The radiative transition of an emitter dipole is a fundamental process in many natural phenomena and can be modified by a dielectric environment. The Onsager–Böttcher (OB) approach predicts the experimental results in the frame of the local-field correction; however, there remains controversy when the macroscopic approximation is used. In this work, the main mechanism to explain the local-field correction arises dynamic coupling (DC). Although the OB and DC models consider the effect of the polarisation of the neighbouring atoms (NN) from the emitter and from the electric field of the light, respectively, we show that these effects arise naturally when the mixing of states from the interaction with the atoms in the surrounding medium is considered. Using perturbation theory, we show that the local field depends on the polarisability of the NN, and in contrast to the OB model, the concept of the polarisability of an emitter in transition is not necessary. Our expression is reduced to the OB model when the NN have spherical symmetry and do not absorb light.