  Air turns into a nonlinear medium for electromagnetic waves under
exceptionally strong fields. However up to present, its minuscule nonlinear
response has limited the exploration to the optical frequency regime owing to
the availability of intense near-infrared lasers. Here, we report on the
observation of large-amplitude nonlinearity in air induced by an extremely
intense light bullet at Terahertz frequencies (0.1-10 THz) provoking strong air
birefringence. The observed nonlinearity manifests itself as third order
susceptibility. The presented nonlinear observations break the barrier for the
entire exciting THz-induced nonlinear phenomena in air ranging from THz-induced
self-focusing and self-phase modulation to THz solitons and filamentation.
