Everyone, I hope you are as proud of us as I am. We have made it to the big stuff, the rate equations for gain media! This is first understood by keeping in mind that the effect of a signal on a collection of atoms is to induce a polarization P($\omega$) in the material. The strength of this response, or the amount of output power, is then proportional to the population difference between two energy levels of a particular transition. The rate of change of these populations as the signal is continuously applied and the population difference begins to change is decribed by the rate equations, hence the subject of this chapter! This section goes through some of the heuristic and exact derivations of the rate of change of laser level populations, and the equations will actually be solved in Section 6.
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