Mirrors without spatial boundaries

Mirrors are one of the most elementary and ubiquitous components of optical systems. They use a sharp refractive index contrast to provide the basic capability of reflecting light. Motivated by recent developments of photonic time-varying media, here we investigate the fundamental question on whether it is possible to have a mirror without any spatial boundary. In this vein, we first discuss how purely temporal mirrors are in general forbidden by the conservation of Minkowski momentum. However, we show that an exotic class of metamaterials, namely, temporal non-Foster left-handed media, exhibit anti-parallel Minkowski momentum and energy flow, thereby enabling mirrors without spatial boundaries. Upon this ground, we put forward some related photonic functionalities, including temporal cavities, pulse freezing, and frequency comb generators, which can be understood as the precursor of temporal lasers.