  Nonlinear metasurfaces incorporate many of the functionalities of their
linear counterparts such as wavefront shaping but simultaneously they perform
nonlinear optical transformations. This dual functionality leads to a rather
unintuitive physical behavior which is still widely unexplored for many
photonic applications. The nonlinear processes render some basic principles
governing the functionality of linear metasurfaces not directly applicable,
such as the superposition principle and the geometric optics approximation. On
the other hand, nonlinear metasurfaces facilitate new phenomena that are not
possible in the linear regime. Here, we study the imaging of objects through a
dielectric nonlinear metalens. We illuminate objects by infrared light and
record their generated images at the visible third-harmonic wavelengths. We
revisit the classical lens theory and suggest a generalized Gaussian lens
equation for nonlinear imaging, verified both experimentally and analytically.
We also demonstrate experimentally higher-order spatial correlations
facilitated by the nonlinear metalens, resulting in additional image features.
