Generalized Linford formula and its application to Traveling Wave Excitation

Abstract
The Linford formula for the intensity output from a medium undergoing Amplified Spontaneous Emission (ASE) is generalized to the case when the gain coefficient is position dependent. The most evident application of this theory relates to the frequently encountered situation that the pump intensity and therefore the gain coefficient vary along the line-focus. A second application arises in Traveling Wave Excitation (TWE) ASE lasers if the excitation velocity and the group velocity of the amplified pulse are not the same. Using the new formula an explanation of the early roll-off in the emitted intensity of Transient Collisional Excitation (TCE) x-ray lasers is given and the design of a more effective TWE set-up is put forward