Self-modulation of radiation transmitted by an amplifying medium with a finite rate of relaxation of the gain

It is shown theoretically that noncoherent interaction of a light pulse with an amplifying medium characterized by a finite rate of relaxation of the gain results in damped self-modulation of the transmitted light. Formulas are obtained for the period of the resultant pulsations of the profile of the transmitted signal representing the degree of distortion of the amplified light pulse.