Gain Saturation and Mode Competition

When the pump power of a laser is increased beyond its threshold value, laser oscillation will start at first at a frequency v where the difference between total gain minus total losses has a maximum. During the buildup time of laser oscillation the gain is larger than the losses and the stimulated wave inside the resonator is amplified at each round trip until the radiation energy is sufficiently large to deplete the population inversion AN down to the threshold value Under stationary conditions 

In the case of a homogeneous laser transition all molecules in the upper level can contribute to stimulated emission at the laser frequency v. with 

Saturation of a homogeneous gain profile. The dashed curve is the line profile during the buildup time the dotted-dashed curve gives the stationary saturated profile 

In the case of inhomogeneous laser transitions, the whole line profile can be divided into homogeneously broadened subsections with a spectral width where is, for example, the natural linewidth or the pres- 

This implies that with increasing saturation more molecules from a larger spectral interval Av can contribute to the amplification. The gain factor decreases by a factor 1/(1 + S) due to the decrease of aN caused by satur-ation. It increases by a factor (1 + S) due to the increased homogeneous width. The combination of both effects gives 

---