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Resonant Photonic 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. The superradiant or photonic-quasicrystal regimes are realized in these structures depending on the number of the wells. The developed theory based on the two-wave approximation allows one to 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. 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.