Exciton-polaritonic quasicrystalline and aperiodic structures

Abstract

We have theoretically studied propagation of exciton-polaritons in deterministic aperiodic multiple-quantum-well structures, particularly, in the Fibonacci and Thue-Morse chains. The attention is concentrated on the structures tuned to the resonant Bragg condition with two-dimensional quantum-well exciton. Depending on the number of wells, the super-radiant either photonic-quasicrystal regimes are realized in these aperiodic structures. For moderate values of the exciton nonradiative damping rate $\ensuremath{\Gamma}$, the developed theory based on the two-wave approximation allows one to perceive and describe analytically the exact transfer-matrix computations for transmittance and reflectance spectra in the whole frequency range except for a narrow region near the exciton resonance ${\ensuremath{\omega}}_{0}$. In this region the optical spectra and the exciton-polariton dispersion demonstrate scaling invariance and self-similarity which can be interpreted in terms of the ``band-edge'' cycle of the trace map, in the case of Fibonacci structures, and in terms of zero reflection frequencies, in the case of Thue-Morse structures. With decreasing $\ensuremath{\Gamma}$, in the whole allowed polariton band the two-wave approximation stops to be valid, and a transition occurs from Bloch-like to localized states, with modes closer to ${\ensuremath{\omega}}_{0}$ becoming localized first.