Design and fabrication of two-dimensional holographic photonic quasi crystals with high-order symmetries

From group theory, we have deduced the minimum number of laser beams to create corresponding two-dimensional photonic quasilattices with high-order symmetries. One case is that a quasi-periodicity with eightfold, tenfold, or twelvefold symmetry can be formed by only five linearly polarized beams, which can reduce fabrication complexity and considerably improve feasibility. Accordingly, we have fabricated large-area eightfold and twelvefold photonic quasi crystals by use of a minimum beam single-exposure holographic lithography technique. The high-order symmetries of the fabricated microstructures are confirmed by scanning electron microscopy images and diffraction patterns.