  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.
