Abstract:Within the framework of the correlation theory of electromagnetic laser beams, the far field cross-spectral density matrix of the light radiated from an electromagnetic Hermite-Gaussian model source is derived. By utilizing the convergence property of Hermite polynomials, the conditions of the matrices for the source to generate an electromagnetic Hermite-Gaussian beam are obtained. Furthermore, in order to generate a scalar Hermite-Gaussian model beam, it is required that the source should be locally rather coherent in the spatial domain.