Modal interface for structured light via liquid-crystal planar optics

Recent advances in planar optics with geometric phase superstructures have brought an alternative paradigm in the control of structured light and, in particular, have substantially enhanced the capabilities of generating and detecting orbital angular momentum (OAM) states of light and associated spatial modes. However, the structured modal interface that can reciprocally link OAM states via adiabatic control and access an associated higher-order geometric phase remains absent in planar optics. In this work, we propose and experimentally demonstrate a planar optical astigmatic retarder fabricated with a liquid-crystal (LC) geometric phase. The LC superstructure is designed based on the principle of fractional Fourier transformation and is capable of reciprocal conversion between all possible OAM states on the same modal sphere. Such a planar device paves the way towards an easily deployed modal interface of paraxial OAM states, unlocks the resource of a higher-order geometric phase, and has promising applications in high-dimensional classical and quantum information.