Realizability conditions for electromagnetic Gaussian Schell-model sources

The electromagnetic Gaussian Schell-model (EGSM) beam is the simplest analytical model of a random electromagnetic beam. The model can be successfully used in studies of spectral, polarization and coherence properties of random electromagnetic beams on propagation in free space or in any linear medium, deterministic or random. The most general type of source which produces electromagnetic Gaussian Schell-model beam is characterized by 10 parameters. Using properties of the cross-spectral density matrix of such a beam, we derive necessary and sufficient conditions which the parameters of the source must satisfy in order to generate a physically realizable beam of this type. The conditions provide certain constraints for synthesis, simulations and any application of such beams.