Modes and threshold condition of a gradient waveguide with inhomogeneous amplification and absorption

An analysis of the modes of a linear gradient optical waveguide with a quadratic radial dependence of absorption and amplification has been conducted. In this case, the profiles of the refractive index and absorption/amplification differ. The parameters at which the generation threshold is achieved have been calculated, meaning that the absorption of radiation is compensated by the amplification, which ensures the propagation of a radiation beam with a constant amplitude.