Modulation of defect on Kerr medium for the intensity properties of Gaussian-Schell-model beam

Using Huygens-Fresnel diffraction integral formula, the expression for the cross-spectral density of the Gaussian-Schell model (GSM) beam which is modulated by the defect of the nonlinear Kerr medium surface is derived. The intensity distribution of GSM beam through the thin Kerr medium is studied. Numerical simulation shows that defect leads to the emergence of extreme intensity point near the rear of the nonlinear medium, which is more far away from the medium when the size of defect is increased. The partially coherent beam can also converge or diverge after passing through the medium with positive or negative nonlinear refractive index. A longer spatial coherence length, and a greater additional phase shift in the medium or a bigger size of defect, will lead to a more serious modulation for the light intensity.