Orbital and Spin Parts of Angular Momentum Flux Density of Monochromatic Radiation in Nonabsorbing Media with Nonlocal Nonlinear Optical Response

Using the conservation law for the angular momentum of electromagnetic field in the form of a balance equation, which links the angular momentum density, the angular momentum flux density, and the torque density caused by the anisotropy of the medium in a nonabsorbing medium, formulas for the densities of the orbital and spin parts of the angular momentum and the flux densities of these quantities are derived in the case of the interaction of monochromatic waves in a nonabsorbing medium with spatial dispersion that demonstrates an \(n\)th order nonlinear optical response to an external light field. In media without spatial and frequency dispersion, the obtained expressions coincide with the canonical expressions for the densities of the orbital and spin parts of the angular momentum, as well as their flux densities. Related to the nonlinearity of the medium, additional terms to the greatest components of the spin parts of the angular momentum and its flux densities can reach ten percent of the corresponding linear parts during the self-focusing of an elliptically polarized Gaussian laser beam in an isotropic gyrotropic medium near the area of its collapse.