Theoretical analysis on the hot-image evolution in the case of thick nonlinear medium with gain and loss

In this paper, we extend corresponding theory which can only deal with thin medium based on thin sheet approximation to a new area which can deal with thick medium with gain and loss. An analytical expression for the location and the peak intensity of the hot-image in the case of thick nonlinear medium with gain and loss are deduced by using propagation matrix method. In order to confirm our analysis as a reliable tool to forecast the hot-image damage risk, we provide some numerical results to verify its validity. The predictions of the theory are found to be in good agreement with the numerical simulations. The theoretical analysis can be used for forecasting the intensity and location of the hot-image. It can provide rules for estimating the damage risk of the hot-image and warn us of the critical areas that may be vulnerable to the hot-image.