22 - Dynamical aspects in the laser

Summary

While the stationary behavior of the laser was described in Part I, now we focus on its dynamical aspects. Some of them have been illustrated already in Chapter 19, but only in the single-mode regime and for class-A and class-B lasers, in which the only instability which arises concerns the trivial stationary solution and leads to the transition from the non lasing to the lasing state. Chapter 20, on the other hand, provided a general picture of single-mode and multimode instabilities in active as well as in passive systems, and of the structural relations which link single-mode and multimode instabilities. In this chapter we focus on the instabilities which arise in the laser and lead to spontaneous temporal oscillations and chaos.

We start in Section 22.1 with the linear-stability analysis of the trivial stationary solution in the general multimode case for the standard laser. The results of this analysis have been anticipated in previous chapters, but here you will find their derivation. The same problem is considered in Section 22.2 for the laser without inversion, but limited to the single-mode case under fully resonant conditions as in Section 17.5.

Of fundamental importance is the analogy between the single-mode laser model and the Lorenz model, which is prototypical for the general field of chaos. This matter is discussed in Section 22.3, and is immediately followed by the treatment of the resonant single-mode laser instability in Section 22.4.

On the other hand, multimodal instabilities in the ring laser are discussed in Sections 22.5 and 22.6. The first is devoted to the amplitude instability, completing the picture given in Section 20.2, and the second to the phase instability. The multimode amplitude instability is related to a classic dynamical phenomenon in lasers, mode-locking, which topic is illustrated in Chapter 23.

Finally, Section 22.7 is devoted to the matter of amplitude instabilities again, but in the case of a Fabry–Perot laser containing an ultrathin medium discussed in Section 14.5.