  Quasicrystals have a higher degree of rotational and point-reflection
symmetry than conventional crystals. As a result, quasicrystalline
heterostructures fabricated from dielectric materials with micrometer-scale
features exhibit interesting and useful optical properties including large
photonic bandgaps in two-dimensional systems. We demonstrate the holographic
assembly of two-dimensional and three-dimensional dielectric quasicrystalline
heterostructures, including structures with specifically engineered defects.
The highly uniform quasiperiodic arrays of optical traps used in this process
also provide model aperiodic potential energy landscapes for fundamental
studies of transport and phase transitions in soft condensed matter systems.
