We present the key results from a comprehensive study of the refraction and focusing properties of a two-dimensional dodecagonal photonic "quasicrystal" (PQC), carried out via both full-wave numerical simulations and microwave measurements on a slab made of alumina rods inserted in a parallel-plate waveguide. We observe anomalous refraction and focusing in several frequency regions, confirming some recently published results. However, our interpretation, based on numerical and experimental evidence, differs substantially from the one in terms of "effective negative refractiveindex" that was originally proposed. Instead, our study highlights the critical role played by shortrange interactions associated with local order and symmetry.PACS numbers: 42.70. Qs, 41.20.Jb, 61.44.Br, Since the pioneering work by Yablonovitch 1 and John 2 , "photonic crystals" (PCs) have elicited great attention from the scientific community, in view of the variety of peculiar electromagnetic (EM) bandgap, waveguiding/confinement, refraction, and emission effects attainable through their use. Among the most intriguing applications, it is worth mentioning those to negative refraction and subwavelength imaging ("superlensing") 3,4,5,6 . The most typical PC configurations are based on dielectric inclusions (or voids) arranged according to periodic lattices in a host medium, and can thus be studied using well-established tools and concepts such as Bloch theorem, unit cell, Brillouin zone, equifrequency surfaces, etc.With specific reference to lensing applications, two different approaches have been presented to obtain subwavelength resolution using a dielectric PC slab. In the first one, a PC with high dielectric contrast is tuned so as to behave (usually near a frequency band edge) like a homogeneous material with a negative refractive index n = −1 3 , and the focus position of the flat lens follows a simple ray-optical construction 7 . In the second approach, "all angle negative refraction" (AANR) is achieved without an effective negative index, provided that the equifrequency surfaces (EFSs) of the PC are all convex and larger than the one pertaining to the host medium 8 . In this case, the focus position does not follow the ray-optical construction and is restricted 9 .During the last decade, the discovery in solidstate physics of certain metallic alloys (the so-called "quasicrystals" 10,11 ) whose X-ray diffraction spectra exhibit "noncrystallographic" rotational symmetries (e.g., 5-fold or (K > 6)-fold, known to be incompatible with spatial periodicity) has generated a growing interest toward aperiodically-ordered geometries, leading to the study of the so-called "photonic quasicrystals" (PQCs). In this framework, useful tools for geometrical parameterization can be borrowed from the theory of "aperiodic tilings" 12 . Several recent numerical and experimental studies have explored the EM properties of PQCs, in the form of two-dimensional (2-D) aperiodic arrays of cylindrical rods or holes, as well as 3-D structures fabricated via stere...

At the exit surface of a photonic crystal, the intensity of the diffracted wave can be periodically modulated, showing a maximum in the "positive" (forward diffracted) or in the "negative" (diffracted) direction, depending on the slab thickness. This thickness dependence is a direct result of the so-called Pendell osung phenomenon, consisting of the periodic exchange inside the crystal of the energy between direct and diffracted beams. We report the experimental observation of this effect in the microwave region at about 14GHz by irradiating 2D photonic crystal slabs of different thickness and detecting the intensity distribution of the electromagnetic field at the exit surface and inside the crystal itself.

We present a study of the lensing properties of two-dimensional (2-D) photonic quasicrystal (PQC) slabs made of dielectric cylinders arranged according to a 12fold-symmetric square-triangle aperiodic tiling. Our full-wave numerical analysis confirms the results recently emerged in the technical literature and, in particular, the possibility of achieving focusing effects within several frequency regions. However, contrary to the original interpretation, such focusing effects turn out to be critically associated to local symmetry points in the PQC slab, and strongly dependent on its thickness and termination. Nevertheless, our study reveals the presence of some peculiar properties, like the ability to focus the light even for slabs with a reduced lateral width, or beaming effects, which render PQC slabs potentially interesting and worth of deeper investigation.