Experimental measurement of the photonic properties of icosahedral quasicrystals

TLDR: 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, confirming that they are excellent candidates for photonic bandgap materials.

Abstract: Quasicrystalline structures may have optical bandgap properties — frequency ranges in which the propagation of light is forbidden — that will make them well suited for applications in which photonic crystals are normally used. Previous work has focused on one- and two-dimensional quasicrystals for which exact theoretical calculations can be made. But when it comes to three dimensions, computation of the optical properties remains a tough challenge. Man et al. tackled the three-dimensional case experimentally using a large photonic quasicrystal made of plastic. They find that the periodic structure yields surprisingly simple spectra, and the resulting structural insights confirm that quasicrystals are excellent candidates for photonic bandgap materials. 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 crystals1,2,3 are normally considered4. 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 quasicrystals4,5,6,7, 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.