Projection of phase singularities in moiré fringe onto a light field

A moiré pattern, which is a kind of spatial interference between two periodic patterns, is regarded as a spatial modulation of a “field.” By defining the displacement field, we reveal that moiré patterns can have a topological phase singularity, similar to a disclination in liquid crystal and, more generally, a vector field treated in the singular optics. We propose that topological singularities in the moiré displacement field can be projected by passing an electromagnetic field through a metasurface. We designed a metasurface constructed from two layers of a metal disk array operating in the terahertz band; then we numerically estimated the spatial distribution of its transmission properties. The phase singularities in the electromagnetic fields coincided with the singularities appearing in the moiré pattern. We found two kinds of singularities, and the phase of the electromagnetic field changed by 2π or 4π around them. These phase changes were independent of the light frequency, implying that the topological properties of the moiré fields were projected onto the electromagnetic field. This feature of moiré metasurfaces can potentially be exploited in spiral phase plate arrays with no frequency dispersion of the phase change.