Metamaterials based on photonic quasicrystals: from superlensing to new photonic devices

In this Ph.D thesis we verified that metamaterials based on photonic quasicrystals can have superlensing properties and that the same type of material, in a different configuration, is able to localize photons and thus suggests the possibility to build new photonic devices, namely optomechanical switches. We saw that a slab cut from a two dimensional 12-fold quasicrystalline tiling constitutes a metamaterial because of its effective refactive index that becomes negative in some frequency ranges. These regions of the spectrum where negative refraction and superlensing occurr can be found with the help of computational methods that calculate dispersion curves, equifrequency surfaces and electromagnetic field distribution of the system under study. In the particular case of quasicrystals, where the lack of translational symmetry forces to use big supercells, the amount of data and information contained in the dispersion curves and equifrequency surfaces is very dense and sometimes difficult to disentangle, suggesting particular care when predicting the behaviour of the physical system without the experimental counterpart. Examiming the electromagnetic field patterns of the quasicrystalline slab we found that several modes could be useful for cloaking, since they do not propagate in the whole structure but they are inhibited to go through certain regions, that remain hidden at particular frequencies. We think that other configurations of this kind of metamaterial give rise to interesting physical properties, more easily predictable, that can lead to the realization of new photonic devices. If we place two 12-fold quasicrystalline slabs together, separated by a vacuum layer of a precise thickness, we obtain the right conditions to localize photons between the two slabs. The localization takes place between two indentations of the slabs’ surfaces, that are a kind of intrinsic defects formed when the surface are created from the bigger quasicrystalline lattice. This type of defects is unique to quasicrystalline systems and originates from their lack of translational periodicity. The capability of localizing photons opens up the possibility of building devices exploiting this feature: for instance, we could realize a photonic switch with two states, one where the photon is localized and the other where the photon propagates, and as we discussed, the choice between these two states can be made only varying the distance between the two slabs. This double slab system seems to be exploitable for cloaking too, since we saw that point defects in the lattice, characterized by a different dielectric constant, do not affect the localization properties of the device.