In Chapters 1 to 5, we have dealt with single-mode ring cavities, either for lasers or for optical bistability. In this chapter, we come back to laser theory to consider the properties of multimode cavities. This subject is immense and our goal can only be modest.

The single-mode unidirectional ring laser is the model of choice for theoreticians who want to study fundamental aspects of laser theory. The simplicity of its evolution equations, equations (1.58)–(1.60), makes the model attractive. Its equivalence with the Lorenz equations [1], which have become the generic model to study chaos in ordinary differential equations, increases the relevance of the ring laser model. Of importance is the fact that the laser model lends itself quite naturally to a complexification of the variables. It suffices that the detuning be nonzero to have a coupling between the phase and the amplitude of the electric field and of the atomic polarization. This opens the door to an even richer phenomenology of complex behaviors.

The ring configuration for a laser is not simply an idealization intended for theoreticians. A number of lasers operate in this configuration. Dye lasers and some coherently pumped lasers are built with ring cavities. Laser gyroscopes are essentially ring lasers. If the ring cavity is perfectly symmetric with respect to the two directions of propagation, there is no preferential direction of oscillation and both directions must be taken into account. This is the simplest example of a multimode laser and we analyze some of its properties in Section 9.3.