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A new full-vectorial beam propagation algorithm based on the computationally-efficient finite element method is presented which can accurately model nonlinear directional couplers. The robust perfectly matched layer boundary condition is incorporated into the formulation so as to effectively absorb the unwanted radiation out of the computational domain. The accuracy of the proposed vectorial propagation approach is demonstrated through comparison with other semivectorial approaches and the weaknesses of the commonly-used scalar approaches are highlighted. The proposed full-vectorial approach considers only two transverse components of the magnetic field without destroying the sparsity of the matrix equation, so it is numerically very efficient.