Theoretical and experimental studies of the spectral changes of a focused polychromatic partially coherent flat-topped beam

An analytical propagation formula for a focused polychromatic partially coherent flat-topped beam with circular symmetry is derived in a tensor form that is based on the alternative flat-top beams model proposed by Li (Opt Lett 27:1007, 2002). The dependence of the relative spectral shift on the flat-top order N is investigated numerically in detail. It is shown that the on-axis maximum relative spectral shift occurs at the back focal plane, while the no spectral shift observes at the image plane. Furthermore, we report the experimental generation of a polychromatic partially coherent FT beam. The on-axis and off-axis spectral measurement verifies the theoretical study.