Gain saturation homogeneously

From equation (13.6) it would appear that the intensity of radiation bouncing to and fro inside the laser cavity would increase indefinitely. This is an unphysical situation and occurs because we have so far neglected the effect of stimulated emission on the populations of the laser levels. As soon as oscillation commences, stimulated transitions start to reduce the inversion density below the value that it had in the absence of oscillation. In a time of the order of the inverse of the cavity linewidth, Au, a steady state is established in which the gain at the oscillation frequency is reduced to a value equal to that required to replace the cavity losses. This process is known as gain saturation. 

The changes which occur in the population inversion density, 

We now proceed to consider gain saturation in detail for the case of a homogeneously-broadened transition. Although experimentally this is not the most common situation the analysis required is somewhat less involved than that necessary in the case of the inhomogeneously-broadened lines. 

The unsaturated inversion density, (N /gj -N /g ), which exists under small signal conditions is obtained from equation (13.12) by allowing I(id)- -0, giving 

Thus the connection between the saturated and unsaturated inversion densities is given by the simple expression 

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Gain bandwidth Type, gain saturation Homogeneous saturation flux Decay lifetime (lower level) Inversion density Small signal gain coefficient Pump power density Output power density Laser size (diameter length) Excitation current/voltage Excitation current density Excitation power Output power Efficiency... 

The different gain saturation of homogeneous and inhomogeneous transitions strongly affects the frequency spectrum of multimode lasers, as can be understood from the following arguments ... 

Fiq 5.16. Mode competition due to gain saturation of a homogeneous gain profile... 

We have discussed gain saturation in detail for a homogeneously-broadened line since simple explicit expressions can be obtained for the gain coefficient and the intensity of laser radiation. Unfortunately this is not possible in the case of inhomogeneous broadening which we examine in the following section. 

From Fig.13.7 we see that even at the lowest input signal of 7 8 yW there is clear evidence of gain saturation. For a homogeneously-broadened line we have from equation (13,19)... 

The frequency dependence of the gain coefficient a(v) is related to the line profile g(y — vq) of the amplifying transition. Without saturation effects (i.e., jfor small intensities), a(v) directly reflects this line shape, for homogeneous as well as for inhomogeneous profiles. According to (2.83) we obtain with the Einstein coefficienct Bik... 

In the case of a homogeneous profile g(v —vo)> all molecules in the upper level can contribute to stimulated emission at the laser frequency Ua with the probability Bikpgiva I d), see (5.8). Although the laser may oscillate only with a single frequency v, the whole homogeneous gain profile a(v) = ANa v) saturates until the inverted population difference AN has decreased to the threshold value AAthr (Fig- 5.23a). The saturated amplification coefficient asat(v) at the intracavity laser intensity / is, according to Sect. 3.6,... 

This implies that with increasing saturation more molecules from a larger spectral interval Ayv, can contribute to the amplification. The gain factor decreases by the factor 1/(1-f 5) because of a decrease of A A caused by saturation. It increases by the factor (1+5) / because of the increased homogeneous width. The combination of both phenomena gives (Sect. 7.2)... 

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