  High-order terahertz (THz) sideband generation (HSG) in semiconductors is a
phenomenon with physics similar to high-order harmonic generation but in a much
lower frequency regime. It was found that the electron-hole pairs excited by a
weak optical laser can accumulate Berry phases along a cyclic path under the
driving of a strong THz field. The Berry phases appear as the Faraday rotation
angles of the emission signal under short-pulse excitation in monolayer
MoS$_2$. In this paper, the theory of Berry phase in THz extreme nonlinear
optics is applied to biased bilayer graphene with Bernal stacking, which has
similar Bloch band features and optical properties to the monolayer MoS$_2$,
such as time-reversal related valleys and valley contrasting optical selection
rules. The bilayer graphene has much larger Berry curvature than monolayer
MoS$_2$, which leads to a giant Faraday rotation of the optical emission
($\sim$ 1 rad for a THz field with frequency 1 THz and strength 8 kV/cm). This
provides opportunities to use bilayer graphene and low-power THz lasers for
ultrafast electro-optical devices.
