Quasicrystalline structures may have optical bandgap properties-frequency ranges in which the propagation of light is forbidden-that make them well-suited to the scientific and technological applications for which photonic crystals are normally considered. Such quasicrystals can be constructed from two or more types of dielectric material arranged in a quasiperiodic pattern whose rotational symmetry is forbidden for periodic crystals (such as five-fold symmetry in the plane and icosahedral symmetry in three dimensions). Because quasicrystals have higher point group symmetry than ordinary crystals, their gap centre frequencies are closer and the gaps widths are more uniform-optimal conditions for forming a complete bandgap that is more closely spherically symmetric. Although previous studies have focused on one-dimensional and two-dimensional quasicrystals, where exact (one-dimensional) or approximate (two-dimensional) band structures can be calculated numerically, analogous calculations for the three-dimensional case are computationally challenging and have not yet been performed. Here we circumvent the computational problem by doing an experiment. Using stereolithography, we construct a photonic quasicrystal with centimetre-scale cells and perform microwave transmission measurements. We show that three-dimensional icosahedral quasicrystals exhibit sizeable stop gaps and, despite their quasiperiodicity, yield uncomplicated spectra that allow us to experimentally determine the faces of their effective Brillouin zones. Our studies confirm that they are excellent candidates for photonic bandgap materials.
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