Resonant Photonic Quasicrystalline and Aperiodic Structures

TL;DR

This paper theoretically investigates exciton-polariton propagation in resonant aperiodic quantum-well structures, revealing self-similarity and scaling invariance in optical spectra near exciton resonance, with implications for photonic quasicrystals.

Contribution

It develops an analytical two-wave approximation theory for exciton-polariton spectra in Fibonacci and Thue-Morse structures, explaining their unique optical properties.

Findings

Optical spectra exhibit scaling invariance near exciton resonance.

Self-similarity observed in exciton-polariton dispersion.

Analytical model agrees with transfer-matrix computations.

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. 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.