Gain, dispersion, and emission characteristics of three-level molecular laser amplifier and oscillator systems

Interaction of two coherent fields of arbitrary intensity with a general homogeneously broadened three-level molecular system for both an amplifier as well as a laser oscillator under general conditions of pumping is discussed. The amplifier solution is obtained through the time-averaged density-matrix formalism with two coherent fields treated classically. A detailed consideration of both real and imaginary parts of the electric susceptibility at pump and emission frequencies, corresponding to gain and dispersion in the active medium has been taken into account. The results obtained are used to study a number of situations for weak and strong pumping in the laser amplifier. Subsequently these are applied to a mode analysis of a unidirectional single-mode laser oscillator to determine the output characteristics of the laser and to establish conditions under which emission becomes dynamically unstable resulting in sustained oscillatory emission. The results obtained are found to be in good agreement with those of a full numerical analysis of the atomic and field coupled equations describing the system.