Quasiperiodic light

Abstract

Quasiperiodicity is a form of spatial order that has been observed in quasicrystalline matter but not light. We construct a quasicrystalline surface out of a light emitting diode. Using a nanoscale waveguide as a microscope (NSOM), we directly image the light field at the surface of the diode. Here we show, using reciprocal space representations of the images, that the light field is quasiperiodic. We explain the structure of the light field with wave superposition. Periodic ordering is limited to at most six-fold symmetry. The light field exhibits 12-fold quasisymmetry, showing order while disproving periodicity. This demonstrates that a new class, consisting of projections from hyperspace, exists in the taxonomy of light ordering.