Metasurface-Based Spatial Hilbert Transformer on an SOI Platform

The Hilbert transform operation in the optical domain plays an important role in optical signal processing and computing. Optical Hilbert transformers based on conventional lenses in free space face limitations such as bulky sizes, complicated structures, and alignment errors. Metasurfaces composed of nanoscale meta-atoms are able to precisely control the optical wavefront on a subwavelength scale, providing an alternative solution of functional optical components with compact sizes. Here, we propose and experimentally demonstrate an in-plane metasurface-based spatial Hilbert transformer that can overcome the aforementioned limitations in conventional optical Hilbert transformers. The device consists of three cascaded in-plane metasurfaces based on an optical 4f system, wherein two identical metalenses serve as Fourier transformers, and the other one serves as the convolution kernel inserted between the metalenses. The fabricated device performs an accurate Hilbert transform on the input signal and achieves a coefficient of determination (R²) of 0.94 between the theoretical and experimental results. This work provides a potential approach for realizing high-performance optical analog computation with in-plane metasurfaces on a silicon-on-insulator platform.