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.
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