Phase Singularities in Moiré Type Metasurfaces

When two similar periodic patterns are overlaid, spatial interference pattern is generated, which is referred to as moiré. We report a novel method to generate optical vortex array utilizing geometrical phase in moiré patterns. By connecting nearest neighbor unit cells of two two-dimensional periodic patterns, one can define a displacement vector field for a moiré pattern. In the vector field, arrays of geometrical singularity in which the vector direction can not be defined are found. We point out that this vector field resembles to the metasurface design for dispersionless phase discontinuities consisting of dipole antennas with gradually varying directions [1]. Hence, a moiré pattern consisting of metallic structures shorter than wavelength, called moiré type metasurface (MTMS), is expected to provide an optical vortex array with a dispersionless feature. We fabricated two types of MTMS. One is 'a rotation moiré' and the other is 'a scaling moiré.' In the former case, the displacement for a moiré is introduced by rotation and in the latter case, the lattice constants of two periodic structures are slightly different. The structural parameters were determined through FDTD simulation so that the meta-surfaces work at the sub-terahertz (THz) region, which has advantages in ease of a sample fabrication and availability of phase measurement of time domain spectroscopy. The periodic structures of Au were printed on both surfaces of a polyimide film by means of ion beam sputtering and lift-off process. By changing the rotation angle and choosing appropriate period of masks, different moiré patterns are prepared, which can be visually confirmed. We performed THz spectroscopic imaging for both MTMSs with a THz-time domain spectrometer. In order to realize a circular crossed-Nicol configuration, which is necessary to measure the phase delay at the meta-surface, we numerically reconstructed the spectra from the THz transmission spectra measured in four independent configurations for linearly polarized measurements. Note that it is unavoidable as a circular polarizer and analyzer for THz-region are not available. In the imaging results, we found arrays of phase singularities corresponding to the topological features shown in the moiré patterns. Thus we experimentally showed that the topological feature in moiré patterns was projected on an electromagnetic field.