Large-scale 2D mode couplers via liquid-crystal metasurfaces

Optical degrees of freedom, such as those associated with spatial, spectro-temporal, or polarization features of the optical field, s erve a s a c onvenient r esource f or e ncoding i nformation. T he a bundance o f t ools f or their accurate manipulation established photonics as a versatile platform for both classical and quantum information processing tasks. Optical processors based on linear circuits, performing a variety of tasks, are often referred to as photonic circuits, in analogy with canonical circuits processing electrical signals. Here we demonstrate a compact photonic circuit in free space that implements all-optical mode-coupling operations in two spatial dimensions, operating in large-scale regimes. This provides a valuable alternative to the traditional integrated waveguides approach to optical information processing. We tested it by implementing unitary transformations associated with 2D quantum walks on transverse modes of structured light.