Does the phenomenological approach contradict the quantum theory of exciton-polariton spatial dispersion?

Abstract

This paper clarifies the controversial issue over 40 years between the quantum approach by Pekar and the phenomenological approach by Ginzburg about the exciton-polariton spatial dispersion theory. For an isotropic nongyrotropic medium, the analytical explicit function of the impermeability tensor eta(ij)(omega, (k) over right arrow) (the inverse of the permittivity tensor) is obtained from the anisotropic undamped-wave harmonic oscillator model. After expanding eta(ij)(omega, (k) over right arrow) with respect to small parameters within it rather than to wavevector (k) over right arrow, the approximate refractive indices can be determined from the eigenvalue equation. By this treatment, the phenomenological approach is proved to be the approximation of the quantum approach near the resonance frequency. The condition for the approximation is discussed.