  This paper is concerned with an inverse random source problem for the
three-dimensional time-harmonic Maxwell equations. The source is assumed to be
a centered complex-valued Gaussian vector field with correlated components, and
its covariance operator is a pseudo-differential operator. The well-posedness
of the direct source scattering problem is established and the regularity of
the electromagnetic field is given. For the inverse source scattering problem,
the micro-correlation strength matrix of the covariance operator is shown to be
uniquely determined by the high frequency limit of the expectation of the
electric field measured in an open bounded domain disjoint with the support of
the source. In particular, we show that the diagonal entries of the strength
matrix can be uniquely determined by only using the amplitude of the electric
field. Moreover, this result is extended to the almost surely sense by deducing
an ergodic relation for the electric field over the frequencies.
