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.
