  Light confinement induced by resonant states in aperiodic photonic structures
are interesting for many applications. A particular case of these resonances
can be found in 2D quasi-crystalline arrangements of dielectric cylinders.
These systems present a rather isotropic band gap as well as isolated in-gap
photonic states (as a result of spatially localized resonances). These states
are built by high symmetry polygonal clusters that can be regarded as photonic
molecules. In this paper we study the transmission properties of a slab of
glass cylinders arranged in approximants of decagonal quasi-crystalline
structure. In particular, we investigate the influence of the slab width in the
transmission contrast between the states and the gap. The study is both
experimental and numerical in the microwave regime. We find that the best
transmission contrast is found for a width of around 3 times the radiation
wavelength. The transmission at the band gap region is mediated by the
resonances of the photonic molecules. If the samples are thin enough they
become transparent except around a resonance of the photonic molecule which
reflects the incoming light. In this case the behavior is reminiscent of an
absorbing molecule.
