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A new three-dimensional (3-D) full-vectorial finite-difference (FD)-based beam-propagation method (BPM) is introduced for the analysis of magnetooptic and nonlinear materials. The refractive-index growth in the nonlinear material is allowed to saturate at high optical power densities (cubic-quintic media). The new formalism is capable of handling any combination of linear, nonlinear, and magnetooptic media, and combines, for the first time, the alternating-direction implicit technique (to improve computational performance) with the leapfrog longitudinal scheme (to simplify the solution of the coupled equations for transverse field components). The result is a numerical method that is both computationally efficient and numerically robust. The proposed BPM formalism is applied to investigate a (nonreciprocal) magnetooptic rib waveguide, as well as the new striking phenomena of light condensates propagation in cubic-quintic (saturable) media, the dynamics of which resemble those of liquid droplets.