Shear based gap control in 2D photonic quasicrystals of dielectric cylinders

2D dielectric photonic quasicrystals can be designed to show isotropic band gaps. The system here studied is a quasiperiodic lattice made of silicon dielectric cylinders arranged as periodic unit cell based on a decagonal approximant of a quasiperiodic Penrose lattice. We analyze the bulk properties of the resulting lattice as well as the bright states excited in the gap which correspond to localized resonances of the electromagnetic field in specific cylinder clusters of the lattice. Then we introduce a controlled shear deformation which breaks the decagonal symmetry and evaluate the width reduction of the gap together with the evolution of the resonances, for all shear values compatible with physical constraints (cylinder collision). The gap is reduced up to a 18.5 % while different states change their frequency in different ways. Realistic analysis about the actual transmission of the electromagnetic radiation, often missing in the literature, have been performed for a finite slice of the proposed quasicrystals structure. Two calculation procedures based on MIT Photonic Bands (MPB) and Finite Integration Technique (FIT) are used for the bulk and the finite structures finding an extremely good agreement among them.