A nonlocal metasurface for optical edge detection in the far-field

Recent studies on nonlocal metasurfaces have shown possibilities of optical image processing, such as edge detection, without the need for Fourier optics and have significantly reduced the form factor. However, the analog edge detection using nonlocal metasurfaces still requires the use of multiple lenses to image the edge-enhanced results, and the edge-detected image generally suffers from image distortion originating from the free space propagation before reaching the detector otherwise. In this work, we propose a nonlocal metasurface that not only enhances the edge features but also delivers them to the far-field with considerably less distortion by combining the conventional edge detection metasurface with a uniaxial slab that has a transfer function of the free space with a negative propagation length. This space expander cancels out the diffraction of the edge-enhanced image that occurs during the free space propagation, the thickness of which reaches several orders of magnitude larger than the slab thickness. This nonlocal metasurface for the far-field edge detection will open a path towards compact optical systems for high-quality analog image processing.