Partially coherent dual and quad airy beams

We investigate the partially coherent dual and quad Airy beams, which are the partially coherent version of multiple Airy beams, in the framework of cross-spectral density functions. They are constructed by the superposition of two and four partially coherent Airy beams without reduced acceleration properties (rate and range). In the case where the interference effect is not considered, the property of lacking side lobes in the partially coherent quad Airy beams leads to the performance of the optical frame during propagation. In the case with constructive interference, we find that the interference pattern produced by the partially coherent dual and quad Airy beams can remain stable and display a spot right in the center of the optical frame. The shape and peak intensity of this interference spot can be controlled by the transverse width of the beams. These results may provide new understanding for the partially coherent field of accelerating beams.