The possibility of channeling a light beam in a nonlinear medium with spatially inhomogeneous amplification and absorption

An analysis is presented of the propagation of a monochromatic light beam in an unbounded active medium, taking into account the effect of diffraction spreading, nonlinear refraction, nonlinear amplification, and linear absorption on the transverse structure of the beam. In the case of a specified dependence of the absorption coefficient (or the inverse population) on the transverse coordinate, the beam propagates in a nonlinear active medium without change of its structure and power. The shapes of required absorption and amplification profiles and the field structure in a compensated beam are determined. Particular consideration is given to an active medium with an inhomogeneously broadened luminescence line.