Imaging with an ultra-thin reciprocal lens postprint

Abstract: Imaging is of great importance in everyday life and various fields of science and technology. Conventional imaging is achieved by bending light rays originating from an object with a lens. Such ray bending requires space-variant structures, inevitably introducing a geometric center to the lens. To overcome the limitations arising from the conventional imaging mechanism, we consider imaging elements that employ a different mechanism, which we call reciprocal lenses. This type of imaging element relies on ray shifting, enabled by momentum-space-variant phase modulations in periodic structures. As such, it has the distinct advantage of not requiring alignment with a geometric center. Moreover, upright real images can be produced directly with a single reciprocal lens as the directions of rays are not changed. We realized an ultra-thin reciprocal lens based on a photonic crystal slab. We characterized the ray shifting behavior of the reciprocal lens and demonstrated imaging. Our work gives an alternative mechanism for imaging, and provides a new way to modulate electromagnetic waves.