General spectral density formula of polychromatic GSM beam passing through the Young’s double slits

In order to study the spectral shift and spectral switch phenomena in the near field and far field of polychromatic Gaussian-Schell model(GSM)beam uniformly,based on the general diffraction integral formula of partially coherent light,the analytical spectral density formula of polyehromatic GSM beam passing though the Young's double slits and ABCD optical system was derived.From the general spectral density formula it can be shown that the Fresnel number varies with the frequency,which is the physical reason of the axial spectral shift of the polychromatie GSM beam.Taking the free space as a typical example of the ABCD optical system,the on-axis spectral shift and spectral switch in the near field and the off-axis spectral shift and spectral switch in the far field were studied numerically by means of the general formula.The result shows that the analytical spectral density formula has some theoretical value in researching spectral shift and spectral switch phenomenon of GSM beam diffracted by Young's double slits.