Coherent control of Snell's law at metasurfaces

It was recently demonstrated that the well-known Snell's law must be corrected for phase gradient metasurfaces to account for their spatially varying phase, leading to normal and anomalous transmission and reflection of light on such metasurfaces. Here we show that the efficiency of normal and anomalous transmission and reflection of light can be controlled by the intensity or phase of a second coherent wave. The phenomenon is illustrated using gradient metasurfaces based on V-shaped and rectangular apertures in a metal film. This coherent control effect can be exploited for wave front shaping and signal routing.