  The microscopic quantum theory of nonlinear stimulated scattering of chiral
particles in doped $AB$ stacked bilayer graphene on Coulomb field of charged
impurities in the presence of strong coherent electromagnetic radiation is
presented. The Liouville-von Neumann equation for the density matrix is solved
analytically. Here the interaction of electrons with the scattering potential
is taken into account as a perturbation. The absorption rate of nonlinear
inverse-bremsstrahlung for a grand canonical ensemble of fermionic chiral
particles is calculated using the obtained solution. The analysis of the
obtained rate shows that in the terahertz and near-infrared range of
frequencies there is significant absorption of incident radiation via
multiphoton stimulated bremsstrahlung mechanism.
