Population Inversion and Molecular Amplification

Here N is the total number density of molecules, Qj and Qv are the rotational and vibrational state sums, and gj=2 / +1 is the statistical weight of the level. Qj and Qv are approximated as 

The most important requirement for a laser is that a positive population difference ANvj exists between two vibrational-rotational states. 

Now we consider a P-branch transition (AJ = +1 in emission) where v = v— 1, J =J +1. By substituting Eq. (6) into (9), one obtains the population inversion ANvj for a sample of molecules where both TVn and TRot correspond to an equilibrium energy distribution but may still be defined independently  

Obviously, to make this difference positive the expression in brackets has to be positive. Thus with some rearrangement a limiting condition for the existence of a population inversion is obtained, as first proposed by J. C. Polanyi 5  

an inversion is always found if the vibrational and rotational temperatures differ such that Tyib exceeds Ta0t sufficiently to satisfy this inequality. This is illustrated in Fig. 2 for the case NV=NV-1- The situation here corresponds to an infinite vibrational temperature Tvtb= In the extreme case of such an inversion TRot- -0 and Tvib 0, all the molecules in the various vibrational states are found in the rotational ground state J =0. It can be seen that inversion then exists for the P(l) transitions (J =0- -J — 1). As this discussion shows, inversion can exist of some J values can only as long as the vibrational temperature is positive (Tvib °°)-This is called a partial population inversion. If Tvib attains a negative value, all J transitions may show inversion. This situation, called a total inversion, can arise only if Nv Nv-i. 

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Contents Population Inversion and Molecular Amplification. Energy-partitioning in Elementary Chemical Reactions Vibrational Relaxation. Requirements for Laser Oscillation. Design Parameters of Pulsed Chemical Lasers. Specific Chemical Laser Systems. Future Chemical Lasers. Present Perspectives of High-Power Chemical Lasers. Kinetic Information through Chemical Laser Studies. 

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