A scalar-mode representation of stochastic, planar, electromagnetic sources

A very useful theoretical tool for investigating coherence properties of stochastic scalar sources and stochastic scalar fields is the so-called coherent-mode representation. We introduce a somewhat similar new representation for planar, secondary stochastic electromag netic sources which generate beams. It consists of three expansions for the three independent elements of the 2 × 2 electric cross-spectral density matrix of the beam. The expansion of the diagonal elements of the matrix are coherent-mode representations in the sense of the scalar theory. The third one, for each off-diagonal element, is a bi-modal expansion, expressed in terms of the coherent modes of the diagonal elements.