Physical significance of complete coherence and complete polarization of random electromagnetic beams in the space–frequency domain

The notion of statistical similarity is extended to vector field in the framework of the space–frequency representation. Then based on the two definitions of the degree of coherence for electromagnetic beams, two conclusions are established for the sufficient and necessary conditions of complete spatial coherence of random electric fields. The sufficient and necessary condition of complete polarization of random electric fields is also derived in the space–frequency domain. Moreover, the physical meanings of complete spatial coherence and complete polarization of the electromagnetic beams are elucidated.

► The notion of statistical similarity is extended to vector field.
► The condition for complete coherence of the random electric fields is derived.
► The condition for complete polarization of the random electric fields is derived.
► The physical meaning of complete coherence of the electromagnetic beams is elucidated.
► The physical meaning of complete polarization of the electromagnetic beams is elucidated.