  Multiple-beam holography has been widely used for the realization of photonic
quasicrystals with high rotational symmetries not achievable by the
conventional periodic crystals. Accurate control of the properties of the
interfering beams is necessary to provide photonic band-gap structures. Here we
show, by FDTD simulations of the transmission spectra of 8-fold quasiperiodic
structures, how the geometric tiling of the structure affects the presence and
properties of the photonic band-gap for low refractive index contrasts. Hence,
we show an interesting approach to the fabrication of photonic quasicrystals
based on the use of a programmable Spatial Light Modulator encoding
Computer-Generated Holograms, that permits an accurate control of the writing
pattern with almost no limitations in the pattern design. Using this
single-beam technique we fabricated quasiperiodic structures with high
rotational symmetries and different geometries of the tiling, demonstrating the
great versatility of our technique.
