Obscuration size dependence of hot image in laser beam through a Kerr medium slab with gain and loss

We present a study of the formation of a hot image in an intense laser beam through a slab of Kerr medium with gain and loss, beyond the thin-medium approximation, to especially disclose the dependence of the hot image on the size of obscuration. Based on the angular spectrum description of light propagation and the mean-field approximation we obtain the expression for intensity of the hot image, which clearly shows the dependence of intensity of the hot image on the size of obscuration. It is shown that, as the size of obscuration increases, the intensity of the corresponding hot image first increases gradually, after reaching a maximum value, it decreases rapidly to a minimum value, meaning that there exists an optimum size of obscuration, which leads to the most intense hot image. Further analysis demonstrates that the optimum size of obscuration is approximately determined by the effective fastest growing spatial frequency for a given case. For the output light beam of a given intensity, with the gain coefficient of the Kerr medium slab increasing, or the loss coefficient decreasing, the optimum size of obscuration becomes bigger, while the hot image from the obscuration of a given size becomes weaker, suggesting that high gain and low loss can efficiently suppress the hot image from obscurations. The theoretical predictions are confirmed by numerical simulations.