Microscopic approach to polaritons

The interaction between excitons and light has been investigated in detail. The perturbational approach turns out to be invalid. However, an exact solution can be obtained directly from the Schrödinger equation for a fixed light field. This solution corresponds to a nonlinear optical response contrary to experimental experience. In order to remove this absurdity the semiclassical approach must be abandoned and the electromagnetic field quantized. A simple microscopic polariton model is then derived. From this the wave function for the interacting exciton-photon complex is obtained. It is discussed whether the magnitude of the exciton-photon interaction energy has any influence on the exciton binding. The concept of polariton fields is introduced (i.e., the electric and polarization field per polariton), and it is seen that close to resonance the electric field per polariton is essentially zero while the polarization field per polariton is essentially the excitonic dipole moment per unit volume. From the wave function of the polariton it is seen that in a very broad spectral range around the resonance the polariton is essentially an exciton that travels through the crystal with the speed of light of the crystal. The introduction of damping smears out the excitonic spectra. The wave function of the polariton, however, turns out to be very independent of damping up to large damping values. Finally, this simplified microscopic polariton model is compared with the exact solutions obtained for the macroscopic polariton model by Hopfield. It is seen that standing photon and exciton waves must be included in an exact microscopic polariton model. However, it is concluded that for practical purposes, only the propagating waves are of importance and the simple microscopic polariton wave function derived in the present work is then sufficient.