Polariton mechanism of exciton luminescence

Above we have assumed that the exciton wavevector is a good quantum number. However, it is clear that even in ideal crystals, in some cases, this assumption may not be valid. Consider, for example, exciton states in a very narrow exciton band. Since there always exist processes leading to scattering 

40Here we assume for simplicity that the exciton has a positive effective mass and for this reason the mentioned process of energy relaxation goes in the direction of small polariton energies. 

4 The dielectric tensor and the phenomenology of long-wavelength excitons 

The analysis of excitons in the presence of retardation given in the previous sections of this chapter was based on making use of the Hamiltonian (4.2), (4.4). This Hamiltonian (see (1)) corresponds to the microscopic Maxwell equations. Since we are interested in long-wavelengths electromagnetic waves in crystals, 

In the case of nonmagnetic media, and without distinguishing the magnetic induction B and the magnetic field intensity H, the macroscopic Maxwell equations take the form 

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