Effect of the external cavity length in the dynamics of a semiconductor laser with optical feedback

The dynamics of a semiconductor laser with optical feedback is studied numerically for increasing time delay. Although the dimension of the attractors generally increases with the delay time, i.e., for short external cavities the attractor is a fixed point or a limit cycle, while for longer external cavities the attractor is a complicated torus or a chaotic attractor, special behavior is found when the external cavity length is chosen such that the product of the delay time tau with the relaxation oscillation frequency of the laser f(rsol) yields a number close to integer. For these values of the time delay, the attractors become topologically simpler, i.e., in the regions where the attractor is a limit cycle, for tau f(rsol) approximate to n it becomes a fixed point, in the regions where is a two-torus, it becomes a limit cycle. Also, Lyapunov analysis indicates that in the resonance regions, the stability of the attractors changes strongly. The effects of the resonances are strong for short external cavities but become difficult to detect as the delay rime increases.