Exciton-polariton propagation in Bragg quantum wells embedded in an uniaxial bilayer

The present study investigates the exciton-polariton propagation in an anisotropic quantum well Bragg reflector, where linear and squared wave vector dependences, due to the spatial dispersion effects [1], appear in the dielectric tensor of the multilayer. It is well known that in isotropic quantum well Bragg reflectors the strong enhancement of light-matter interaction (polaritons), and the large density of states at the electronic band edge (excitons), allow to observe polaritonic splitting energies also in the presence of an homogeneous background dielectric function [2,3]. Notice, that, at variance of the two levels model, in the Wannier exciton dynamics a key role is taken by the center-of-mass motion components (in-plane, and along the multilayer periodicity) [3]. In fact, it is at basis of linear and non-linear optical response, namely: the exciton-photon strong-coupling (polaritons) [4], and the exciton-exciton scattering [5] respectively, and therefore, it has a crucial role in the exciton-polariton wave-packed propagation [6] . Recently, in a spatially periodic system, obtained by alternating two anisotropic layers, was demonstrated that it is possible to perform the tailoring of the photonic dispersion curves by altering the relative orientation of the optical axis of the two adjacent uniaxial layers [7]. In particular, for the optical axis on the surface of the slabs and performing an angle (in the range ) in a two-layers periodic crystal a large redistribution of the photon density of states is observed in the dispersion curves, due to the interference between ordinary and extraordinary waves. Moreover, band gaps, that are usually localized at the borders of the Brillouin zone, can be localized inside this zone and, moreover, the band curvature indicates the possibility of observing negative refraction [7]. The main aim of the present work is twofold: i) to perform the tailoring of the absolute gap in a particular zone of the dispersion curves where high density of states are presents and left propagation of the exciton-polariton can be observed, ii) and to study exciton-polariton propagation in 1D resonant photonic crystal in the presence of two different dependences from the wave vector, quadratic for exciton-polariton in cubic crystal and linear for photon propagation in uniaxial crystal .