| Summary: | In this thesis, we develop a generalised unfolding formalism to investigate the electronic and photonic properties of aperiodically-structured materials. We initially focus on GaAsBi alloys for electronic systems and Penrose-structured materials for photonic systems, aperiodic materials that cannot be easily studied using conventional band structure methods. We then extend our study to the supercell approach which facilitates an accurate modelling of the aperiodic structures at the price of obscuring essential physical information, due to a band folding effect. Then introducing a generalised unfolding algorithm, we return the supercell band structure to a traditional form that can again be used to analyse the electronic and photonic properties of the system. GaAsBi, which is a material with the potential to suppress the dominant loss mechanisms in telecommunications devices, was studied using the unfolded supercell band structure approach. We investigated the effect of bismuth on the properties of a host GaAs structure, including band movement, band broadening and effective mass. We validated our approach through a detailed comparison of both band movement and effective masses to the currently available experimental data. Then, we introduced a formalism for calculating the CHSH Auger recombination rates from our unfolded band structure, which will assist in determining the efficiency of the material. Quasicrystalline photonic materials built on the skeleton of Penrose lattices have proven to display photonic properties comparable to the ones found in photonic crystals, but with the added promise of increased isotropy. The photonic band structure of these materials is a prime target for the unfolding formalism because it allows a full exploration of the influence of the increased geometrical symmetry on their photonic characteristics. Furthermore, the network structure investigated demonstrated the existence of a sub-fundamental photonic band gap, a characteristic unique to quasicrystalline structures. The unfolded band structure enabled the investigation of the mechanisms responsible for the formation of this peculiar band gap. Finally, we depart from the frequency domain approach and employ time domain simulations to investigate the photonic and plasmonic properties of a hybrid structure consisting of a polymer based opal with a quasi-2D gold nanoparticle grid on the surface. The optical response of the structure displays an intricate interplay between the plasmonic resonances and the photonic stop band effects. Adopting a renormalised Maxwell-Garnett effective index for describing the gold nanogrid, we successfully elucidate the main physical mechanisms governing the optical response of these structures in good agreement with the results of experimental investigations.
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