Theory of optical maser amplifiers

The interaction between an electromagnetic (em) pulse and a maser medium is described by a general set of five equations, under the assumption of a homogeneously broadened electric-dipole transition with two Bloch relaxation times T
2
and T
1
and of a linear broadband loss mechanism. When the equations are specialized at resonance, their solutions include the results of the previous treatments on the amplifier problem obtained under particular assumptions. The steady-state pulse (S. S. P.) introduced by Wittke and Warter for
T_{2}/T_{1} = 0
is here generalized for
T_{2}/T_{1} \neq 0
and it is shown to propagate at the same velocity of the light in the medium. In the case
T_{2}/T_{1} = 0
the steady state is described by exact analytical relations. For times short in comparison to the relaxation times, a solution is given which generalizes the usual interaction formula between an em field and a two-level system by introducing propagation effects. In the general case out of resonance, it is shown that an S. S. P. exists, and that its frequency coincides with the frequency of the atomic transition, independent of the frequency of the input field.