Until now, there have been many reports concerning the generation and propagation of partially coherent beams due to their less influencing ability in turbulent atmosphere and random media. Of particular interest, a Gaussian-Schell model beam has been widely chosen as a special example of partially coherent beam, since its spatial coherence degree is dependent on position only through the difference between the two position vectors. In the scalar domain, many coherent models have been well studied such as Gaussian and multi-Gaussian Schell-model sources, Bessel-Gaussian and Laguerre-Gaussian Schell-model sources and so on. Based on the theory for devising genuine cross-spectral density matrices for a stochastic electromagnetic beam, several scalar models have been also extended to the electromagnetic domain. In recent years, the propagation of partially coherent beams with spatially varying and non-uniform correlations has become a hot topic, because of their interesting characteristics such as locally sharpened and laterally shifted intensity maxima. In one of our previous studies, we have experimentally investigated the generation of non-uniformly correlated partially coherent beams. However, to the best of our knowledge, so far, there has been no investigation on the generation of non-uniformly correlated stochastic electromagnetic beams. In this paper, we theoretically and experimentally investigate the generation of non-uniformly correlated stochastic electromagnetic beams. Based on the relation between phase correlation and optical coherence, we investigate the 22 cross-spectral density matrix and the coherence distribution of the non-uniformly correlated stochastic electromagnetic beam we generated. It is shown that the coherence degree between two points in the generated beam depends not only on the distance between them, but also on the distances between the points and the center of the beam. In experiment, we use the Matlab rand function to generate a random phase pattern with uniform distribution. The modulation magnitudes of different positions are different and follow an inverse Gaussian distribution in position. Dynamic phase patterns are created from a series of random grey-scale images. Two phase-only liquid crystal spatial light modulators are employed to display computer-generated dynamic phase patterns and modulate the two orthogonally polarized components of the incident coherent light, respectively, and generate a stochastic electromagnetic beam. We measure the correlation distribution of the generated beam in Young's two-pinhole experiment. It is shown that the experimental observations are in agreement with our theoretical analyses. Other kinds of non-uniformly correlated stochastic electromagnetic beams can also be obtained by this approach. Non-uniformly correlated stochastic electromagnetic beams may have some applications in optical manipulation and free-space optical communication.
