Formation of hot image in an intense laser beam through a saturable nonlinear medium slab

In high-power laser system such as Petawatt lasers, the laser beam can be intense enough to result in saturation of nonlinear refraction index of medium. We present an analytical and simulative investigation of hot image formation in an intense laser beam through a saturable nonlinear medium slab based on Fresnel-Kirchhoff diffraction integral and the standard split-step Fourier method. The analytical results are found in agreement with the simulative ones. It is shown that, hot images can still form in an intense laser beam through a saturable nonlinear medium slab, additionally, the saturable nonlinearity does not change the location of hot images, while may decrease the intensity of hot images, i.e., the intensity of hot images decreases with the saturation light intensity lowering, and can stop to increase with the intensity of the incident laser beam heightening due to saturation of nonlinearity. Moreover, variations of intensity of hot images with the obscuration type and the slab thickness are discussed.