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A finite element beam propagation method to analyze nonlinear active optical waveguides is presented. The model takes into account the mutual coupling among the equations describing the electromagnetic field propagation and the ones governing the signal amplification due to a doped medium. The approach is able to distinguish the different behavior of Ex (quasi-TE) and Ey (quasi-TM) polarizations. The performances of nonlinear and doped couplers are analyzed in detail by varying the input power, the field polarization and the pumping scheme.