  A simple optical lens plays an important role for exploring the microscopic
world in science and technology by refracting light with tailored spatially
varying refractive index. Recent advancements in nanotechnology enable novel
lenses, such as, superlens, hyperlens, Luneburg lens, with sub-wavelength
resolution capabilities by specially designing materials' refractive indices
with meta-materials and transformation optics. However, these artificially
nano/micro engineered lenses usually suffer high losses from metals and are
highly demanding in fabrication. Here we experimentally demonstrate for the
first time a nonlinear dielectric magnifying lens using negative refraction by
degenerate four-wave mixing in a plano-concave glass slide, obtaining magnified
images. Moreover, we transform a nonlinear flat lens into a magnifying lens by
introducing transformation optics into nonlinear regime, achieving an
all-optical controllable lensing effect through nonlinear wave mixing, which
may have many potential applications in microscopy and imaging science.
