Propagation characteristics of a non-uniformly Hermite-Gaussian correlated beam

We introduce a new kind of partially coherent beam, non-uniformly Hermite-Gaussian correlated beam, by employing a non-uniformly Hermite function to modulate the spectral degree of coherence. The evolution of such scalar beam on propagation in free space and turbulent atmosphere are investigated. It is demonstrated that the spectral intensity distributions exhibit extraordinary propagation characteristics, such as self-focusing and laterally shifted intensity maxima. The position of the maximum intensity and the intensity profile can be controlled by the order of the Hermite function. The results can be useful in free-space optical communications and beam shaping.