Two-Dimensional Quasi-Periodic Diffraction Properties of the Scalar and Vector Optical Fields

Abstract

As is known, quasi-periodicity attracts great attention in many scientific regions. For instance, the discovery of the quasicrystal was rewarded the Nobel Prize in 2011, leading to a series of its applications. However, in the area of manipulating optical fields, the two-dimensional quasi-periodicity is rarely considered. Here, we study the two-dimensional quasi-periodic diffraction properties of the scalar and vector optical fields based on the Penrose tiling, which is one of the most representative kinds of two-dimensional quasi-periodic patterns. We propose type-A and type-B Penrose tiling masks (PTMs) with phase modulation, and further show the diffraction properties of the optical fields passing through these masks. The intensity of the diffraction field holds a tenfold symmetry. It is proved that the iteration number n of the PTM shows the “weeding” function in the diffraction field, and this property is useful in filtering, shaping, and manipulating diffraction fields. Meanwhile, we also find that the diffraction patterns have the label of the Golden ratio, which can be applied in areas such as optical encryption and information transmission.

Keywords

• diffraction
• vector beam
• quasi-periodicity
• structured light