In crystal optics with spatial dispersion there are two alternative approaches to the polariton problems starting from either mechanical excitons ~ME’s ! or Coulomb excitons ~CE’s !, respectively. The difference between them arises from the different treatment of that part of the polarized crystal unit interaction which is associated with the long-range curl-free proper crystal field, generated by fictitious charges of macroscopic dielectric polarization. In the case of the CE scheme the unperturbed ~by electromagnetic field! energy operator contains that part, while in the case of the ME scheme it does not. This is the peculiarity that makes their dispersion laws and all other characteristics, including the boundary conditions, essentially different. Both primary conceptions are equally used in theoretical research and have their own advantages and shortcomings. The agreement between those for infinite space has been proven by a lot of investigations, but solving the same problem for finite media has not been done. Moreover, the majority of papers in the field use the same boundary conditions for excitonic polarizations in both schemes. This makes them all true only for some particular cases but, certainly, the contradictions appearing should be eliminated. The aim of this paper is the critical analysis of the existing inconsistencies and the fitting of the solutions to the boundary-value problems for polaritons formed from those two different types of exciton states. Partially we fill the arised recess by making both approaches in line with the case of the N-exponential Frenkel exciton model, when describing the polarization of some bounded spatially dispersive dielectrics in the excitonic spectrum region. The light reflection coefficient is taken as the main quantity to be fitted in both of the above calculation schemes. This is possible only by including several exciton transport mechanisms at once ~that is, for N>2) and by using the concept of Pekar’s ‘‘missing’’ electromagnetic wave. With success in this particular case, we hope to induce further investigations in the area for other exitonic models and in a general enough case, such as the case for infinite media.
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