Nonlinear hot-image formation of an intense laser beam in media with gain and loss

An analytical treatment and results of numerical calculations are presented for the hot-image formation in media with gain and loss. A new approximately functional expression of the hot-image intensity is derived, showing that it is several times larger than the background light intensity, indicating a great damage threat to high-power laser systems. The image appears in a plane located downstream from the nonlinear medium at a distance equal to that from the scatterer to the medium. Finally, it is validated that the hot-image formation is akin to real-time, in-line and volume-phase Fraunhofer holographic imaging. The predictions of the theory are found to be in good agreement with simulations carried out for ns-pulse propagation.