Exciton-polaritonic quasicrystalline and aperiodic structures

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 ?, 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 ?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 ?, 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 ?0 becoming localized first.