Optical negative refraction by four-wave mixing in thin metallic nanostructures

The law of refraction first derived by Snellius and later introduced as the Huygens-Fermat principle(1), states that the incidence and refracted angles of a light wave at the interface of two different materials are related to the ratio of the refractive indices in each medium. Whereas all natural materials have a positive refractive index and therefore exhibit refraction in the positive direction, artificially engineered negative index metamaterials have been shown capable of bending light waves negatively(2-8). Such a negative refractive index is the key to achieving a perfect lens that is capable of imaging well below the diffraction limit(9-11). However, negative index metamaterials are typically lossy, narrow band, and require complicated fabrication processes. Recently, an alternative approach to obtain negative refraction from a very thin nonlinear film has been proposed(12,13) and experimentally demonstrated in the microwave region(14-16). However, such approaches use phase conjugation, which makes optical implementations difficult. Here, we report a simple but different scheme to demonstrate experimentally nonlinear negative refraction at optical frequencies using four-wave mixing in nanostructured metal films. The refractive index can be designed at will by simply tuning the wavelengths of the interacting waves, which could have potential impact on many important applications, such as superlens imaging.