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Additional resources for Electronic Excitations in Organic Based Nanostructures, Volume 31
In these materials, the Umklapp processes may not be neglected and the multiple scattering involving the radiation field in various Brillouin zones gives rise to the opening of a stopgap . An other interesting aspect of polaritons in infinite crystals is that they do not decay through spontaneous emission of photons, because they already fully account for the interaction between the excitons and the electromagnetic field. In large but finite crystals, polaritons decay spontaneously through emission at the crystal boundaries, in other words, the size of the crystal becomes an important factor in the spontaneous emission rate [67,68].
This leads to sum-over-states expressions, where for the single molecule this sum runs over all molecular excited states. A well-known approach to calculate from these molecular susceptibilities the susceptibilities of the crystal, is the local-field method. In this approach one solves in a self-consistent way the polarization field in the system by allowing the individual molecular dipoles to respond to both the exciting external field and the local fields created by the surrounding dipoles .
48) i,j It is known  that all mentioned poles corresponding to transverse and other normal waves coincide with the frequencies of so-called Coulomb excitons. These excitons are the solutions of the coupled equations for matter (polarization) and electromagnetic fields in the limit c → ∞. In the language of microscopic theory we can say that in this approximation the retarded interaction is neglected and only the non-retarded Coulomb interaction is taken into account. It is important to note that this approximation is the basis of the microscopic theory of excitons (see, for example,  and ).