“…A well-known example of partially coherent beams is the Gaussian Schell-model (GSM) beam, which has been studied extensively [1]. Besides GSM beams, there are a variety of partially coherent beams which can be produced by various sources, e.g., see [2][3][4][5] and have different propagation properties. On the other hand, in practical applications, such as the laser materials processing, micromachining in the electronics industry, laser fusion, atom trapping and guiding, different intensity profiles including flat-topped one, beams with central dip whose central intensity minimum I min 6 ¼0, and bottle beams, i.e., beams with a dark focus I min ¼ 0 surrounded by regions of higher intensity, etc.…”