  All-optical information communication, processing and computation have
received substantial interest of both fundamental and applied research due to
its unrivaled speed and broad bandwidth. Compared to its electronic
counterpart, photons seldom interact with each other which makes them obtain a
long coherence time on one hand and relieved from heavy energy dissipation on
the other. However, one of the hindrances to achieve all-optical circuits is
the large volume of all-optical devices to achieve specific functionalities. In
this work, we propose and demonstrate experimentally three meta-lenses for
differential imaging employing the framework of weak measurement: (1) partial
differential lens, (2) total differential lens and (3) second order
differential lens compatible with the requirement of miniaturization to achieve
all-optical technology. Based on Fresnel-lens-like structures, our meta-lenses
incorporated the previous weak-measurement compartment into wavelength scale,
which induces a miniature differential operation system as a result. In
addition to its potential importance in heavily integrated all-optical neural
networks, the differential lens can be easily incorporated in the existing
imaging systems like a conventional lens without increasing the complexity of
the system of interest.
