On the possibility of increasing the intensity of high-order harmonics due to stimulated emission

We propose a new method for the amplification of high-order harmonics of laser radiation based on stimulated emission accompanying the propagation of a probe pulse of a high-order harmonic through a gas medium irradiated by a high-power pump wave. It is demonstrated that such an amplification becomes noticeable in the case when a probe wave of a high-order harmonic enters the interaction area with some delay time with respect to the pump wave. Our estimates for the gain of high-order harmonics show that this gain is proportional to the delay time, reaching unity even for rather short delay times (corresponding to several optical cycles of the pump wave).