Theory of Pulse Propagation in a Laser Amplifier

The growth of a radiation pulse traversing a medium with an inverted population is described by nonlinear, time-dependent photon transport equations, which account for the effect of the radiation on the medium as well as vice versa. The equations are solved in closed form for an arbitrary input pulse and an arbitrary initial distribution of inverted population. The solutions are discussed in detail for the particular cases of a square pulse and a Lorentzian pulse, both with a uniform initial population inversion.