In the previous chapter, we investigated the case of weakly modulated lasers. We found that a bistable response is possible if the modulation frequency is close to the relaxation oscillation (RO) frequency or to twice the RO frequency of the laser. In this section, we consider stronger modulation amplitudes, which is the case in most experimental studies. A strongly modulated laser may lead to chaos through successive period-doubling bifurcations as we shall see in this chapter.

In the late 1970s and early 1980s, there was a lot of excitement about “deterministic chaos” in all fields of physics, chemistry, and even biology. Deterministic refers to the idea that the future state of a system can be predicted using a mathematical model that does not include random or stochastic influences. Chaos refers to the idea that a system displays extreme sensitivity to initial conditions so that arbitrary small errors in measuring the initial state of the system grow exponentially large and hence practical, long term predictability of the future state of the system is lost. As far as optics was concerned, Kensuke Ikeda suggested in 1979 that an optical ring resonator containing a two-level medium and subject to a delayed feedback could exhibit chaos. His work triggered a lot of experimental research on optical chaos but, as explained in Section 4.2, it took several years before quantitative comparisons were possible. Following a quite different approach, Arecchi et al. modulated the losses of a CO2 laser at a frequency close to the RO frequency and obtained in 1982 a clear period-doubling cascade to chaos (see Figure 6.1).