  The higher order harmonic generation process in the nonperturbative regime at
the interaction of coherent electromagnetic radiation with the AB-stacked
bilayer graphene at high Fermi energies is considered. The applied coherent
low-frequency radiation field in the high Fermi energy zone of electrons
excludes the interband transitions enhancing high harmonic rates. The developed
microscopic nonlinear quantum theory for charged carriers interaction with a
strong pump wave is valid near the Dirac points of the Brillouin zone. The
Liouville-von Neumann equation for the density matrix in the multiphoton
excitation regime is solved both analytically and numerically. Based on the
numerical solutions, we examine the rates of higher-order harmonics of the pump
wave of arbitrary polarization. Obtained results show that bilayer graphene can
serve as an effective material for the generation of higher-order harmonics
from THz to the mid-IR domain of frequencies at the pump wave moderate
intensities.
