  The quantum theory of multiphoton stimulated bremsstrahlung of charged
carriers on an arbitrary electrostatic potential of impurity ion in doped
bilayer graphene at the presence of coherent electromagnetic radiation is
developed. A terahertz wave field is considered exactly, while the
electrostatic potential of doped ions as a perturbation. The essentially
nonlinear response of bilayer graphene to a pump wave and significant
differences from the case of a single layer graphene are shown, which can be
associated to nonlinear parabolic dispersion. The latter opens new way to
manipulate with the electronic transport properties of conductive electrons of
bilayer graphene by coherent radiation field of terahertz or near-infrared
frequencies.
