  Platforms for all-optical computing possess photonic circuits made of
silicon-based channels, metal wires or optical fibers, etc. However, such solid
waveguides suffer from the lack of reversibility and reconfigurability if
facing the next generation of light-guiding-light (LGL) computing scheme, which
envisions circuitry-free and rapidly reconfigurable systems powered by dynamic
interactions between light beams. Here, we proposed the ubiquitous air as a
restorable LGL signal manipulation medium with transient air-plasma waveguide
circuits. Briefly, by focusing femtosecond laser beams in the free space, the
created atmospherical plasma filament array via photoionization was able to
guide terahertz (THz) pulses along its epsilon-near-zero (ENZ) zone with a
1/f-profile spectral response. Consequently, this achieved a time-domain
integration of the THz pulse in broad bandwidth. When the pumping laser was
sequentially turned off and on, this multi-filament air-plasma structure was
erased and rebuilt within nano- and femto-seconds, respectively, allowing rapid
and repeated rearrangements of the all-optical stage. Furthermore, this
air-based LGL information processing approach is promising to pave the way
towards all-optical calculations during free-space directional transmission of
THz waves, by which means the delivered THz signal can be remotely controlled.
