In Chapter 1, we introduced the standard rate equations (SRE) for a laser containing two-level atoms between which stimulated emission is possible. But real lasers exhibit much more complicated energy level schemes. Throughout this chapter, we consider several models in which the light–matter interaction is described by population equations for all the levels involved in the laser operation. Although they are mathematically more complicated, we shall investigate these equations in the same way as in Chapter 1, i.e. by formulating dimensionless equations and by analyzing the stability properties of the steady states.

The basic ingredients of the SRE model used up to here, namely pumping and relaxation processes, play key roles in the efficiency of lasers. But already during the pioneering days of the laser, it appeared important to investigate three- and four-level models in order to obtain more reliable information on quantities such as the power conversion efficiency or the response time. The common extensions of the two-level SRE typically consider an open two-level system, or three- or four-level systems, depending on the nature of the active medium. Restriction to as few as four levels is again a crude simplification of the complex population dynamics occurring in most lasers. But it is rather surprising to see how good these simple kinetic models are. As we demonstrate by studying specific examples, the solution of the three- or four-level rate equations differs only slightly from the solution of the SRE.