  Quasicrystals, realized in metal alloys, are a class of lattices exhibiting
symmetries that fall outside the usual classification for periodic crystals.
They do not have translational symmetry and yet the lattice points are well
ordered. Furthermore, they exhibit higher rotational symmetry than periodic
crystals. Because of the higher symmetry (more spherical), they are more
optimal than periodic crystals in achieving complete photonic bandgaps in a new
class of materials called photonic crystals in which the propagation of light
in certain frequency ranges is forbidden. The potential of quasicrystals has
been demonstrated in two dimensions for the infrared range and, recently, in
three-dimensional icosahedral quasicrystals fabricated using a stereo
lithography method for the microwave range. Here, we report the fabrication and
optical characterization of icosahedral quasicrystals using a holographic
lithography method for the visible range. The icosahedral pattern, generated
using a novel 7-beam optical interference holography, is recorded on
photoresists and holographic plates. Electron micrographs of the photoresist
samples show clearly the symmetry of the icosahedral quasicrytals in the
submicron range, while the holographic plate samples exhibit bandgaps in the
angular-dependent transmission spectra in the visible range. Calculations of
the bandgaps due to reflection planes inside the icosahedral quasicrystal show
good agreement with the experimental results.
