Color maps of the Kaplan-Yorke dimension in optically driven lasers: Maximizing the dimension and almost-Hamiltonian chaos

In this paper we investigate the geometrical complexity of chaotic attractors in optically injected lasers by calculating the Kaplan-Yorke dimension (D-KY) together with the largest Lyapunov exponent (LLE). For the first time to the best of our knowledge, a color map is constructed indicating regions in the parameter space with high and low dimensionality. It is shown that as the injection power K of the master to the slave laser is increased to high values, the dimension of the attractor decreases for all ranges of the frequency detuning omega. The relation between the trace of the Jacobian matrix and the Kaplan-Yorke dimension shows that the optically injected laser is a system capable to span the dimension anywhere between 2 and 3. A qualitative analysis is finally made in order to identify the material parameters of the slave device for this coupled laser system for a result in the maximized possible dimension, leading to the need for a high electron lifetime and a high linewidth enhancement factor that occur at low temperature operation for a solitary slave semiconductor laser.