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

2D dielectric photonic quasicrystals can be designed to show isotropic band gaps. In this work we study a quasiperiodic lattice made of silicon dielectric cylinders (ɛ = 12) 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 γ 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 contact). The gap width reduction reaches 18.5% while different states change their frequency in several ways. Realistic analysis of the actual transmission of the electromagnetic radiation, often missing in the literature, has 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 showing an excellent agreement between them.