  A cornerstone equation of optics, Snell's law, relates the angles of
incidence and refraction for light passing through an interface between two
media. It is built on two fundamental constrains: the conservation of
tangential momentum and the conservation of energy. By relaxing the classical
Snell law photon momentum conservation constrain when using space-gradient
phase discontinuity, optical metasurfaces enabled an entirely new class of
ultrathin optical devices. Here, we show that by eradicating the photon energy
conservation constrain when introducing time-gradient phase discontinuity, we
can further empower the area of flat photonics and obtain a new genus of
optical devices. With this approach, classical Snell relations are developed
into a more universal form not limited by Lorentz reciprocity, hence, meeting
all the requirements for building magnetic-free optical isolators. Furthermore,
photons experience inelastic interaction with time-gradient metasurfaces, which
modifies photonic energy eigenstates and results in a Doppler-like wavelength
shift. Consequently, metasurfaces with both space- and time-gradients can have
a strong impact on a plethora of photonic applications and provide versatile
control over the physical properties of light.
