Intrinsic photonic wave localization in a three-dimensional icosahedral quasicrystal

Wave transport is one of the most interesting topics related to quasicrystals. This is due to the fact that the translational symmetry strongly governs the transport properties of every form of wave. Although quasiperiodic structures with(1-4) or without(1,5-7) disorder have been studied, a clear mechanism forwave transport in three-dimensional quasicrystals including localization is missing(8,9). To study the intrinsic quasiperiodic effects on wave transport, the time invariance of the lattice structure and the loss-free condition must be controlled(10,11). Here, using finite-difference methods, we study the diff usive-like transport and localization of photonic waves in a three-dimensional icosahedral quasicrystal without additional disorder. This result appears at odds with the well-known theory(12) of wave localization (Anderson localization), but we found that in quasicrystals the short mean free path of the photonic waves makes localization possible.