The laws of conservation of momentum and angular momentum of the electromagnetic field in nonlinear optics of inhomogeneous media with nonlocal optical response

We have obtained formulas for the components of densities and flux densities of momentum and angular momentum of light, as well as for the densities of force and torque acting on the electromagnetic field, associated with nonlinear wave interaction in a nonabsorbing weakly inhomogeneous medium with nonlocal optical response exhibiting nonlinearity of nth order. It is shown that the expressions for the components of densities and flux densities of momentum and angular momentum coincide with the corresponding formulas for homogeneous media, but the components of the tensors of local and nonlocal nonlinear optical susceptibility contained in them must be considered dependent on the spatial coordinates. The direction of the force density associated with the medium's inhomogeneity is determined by the gradients of its local and nonlocal optical susceptibilities.