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Shifted-elementary-mode representation for partially coherent vectorial fields

A representation of partially spatially coherent and partially polarized stationary electromagnetic fields is given in terms of mutually uncorrelated, transversely shifted, fully coherent and polarized elementary electric-field modes. This representation allows one to propagate non-paraxial partially coherent vector fields using techniques for spatially fully coherent fields, which are numerically far more efficient than methods for propagating correlation functions. A procedure is given to determine the elementary modes from the radiant intensity and the far-zone polarization properties of the entire field. The method is applied to quasihomogeneous fields with rotationally symmetric cosine-modulated radiant intensity distributions. This is an adequate model for fields emitted by, e.g., many light-emitting diodes.