Effects of coherence and polarization on the coupling of stochastic electromagnetic beams into optical fibers

We study the problem of coupling an electromagnetic beam of any state of coherence and polarization into a multimode optical fiber. Using the well-known concept of the cross-spectral density matrix, we derive a general expression for the coupling efficiency of a stochastic electromagnetic beam into a multimode fiber in terms of the cross-spectral density matrix of the incident beam and another matrix representing field distributions of fiber modes. We apply this result to a specific case in which the incident beam belongs to a broad class of so-called electromagnetic Gaussian Schell-model beams and obtain a simple analytical expression for the coupling efficiency in the case of single-mode fibers. We use this expression to study how coupling efficiency depends on the coherence and polarization properties of the incident beam.