  Microscopic nonlinear quantum theory of interaction of coherent
electromagnetic radiation with gapped bilayer graphene is developed. The
Liouville-von Neumann equation for the density matrix is solved numerically at
the multiphoton excitation regime. The developed theory of interaction of
charged carriers with strong driving wave field is valid near the Dirac points
of the Brillouin zone. We consider the harmonic generation process in the
nonadiabatic regime of interaction when the Keldysh parameter is of the order
of unity. On the basis of numerical solutions, we examine the rates of odd and
even high-harmonics at the particle-hole annihilation in the field of a strong
pump wave of arbitrary polarization. Obtained results show that the gapped
bilayer graphene can serve as an effective medium for generation of even and
odd high harmonics in the THz and far infrared domains of frequencies.
