  Optical lenses are pervasive in various areas of sciences and technologies.
It is well-known that the resolving power of a lens and thus optical systems is
limited by the diffraction of light. Recently, various plasmonics and
metamaterials based superlenses have been emerging to achieve super resolution.
Here, we show that the phase compensated negative refraction lenses perform as
"Janus Lenses", i.e. either converging lenses or diverging lenses depending on
the illumination directions. Extraordinary imaging equations and properties
that are different from those of all the existing optical lenses are also
presented. These new imaging properties, along with the super resolving power,
significantly expand the horizon of imaging optics and optical system design.
