Estimation of delay times from a delayed optical feedback laser experiment

We estimate delay times from high-dimensional chaotic time series experimentally obtained from a fast optical time-delayed feedback system. The experiment consists of a semiconductor laser, where the instabilities are induced by an external T-shaped cavity introducing two delay times into the laser. The delay times are determined by a filling factor analysis and found to give a better estimate than those obtained by autocorrelation functions. Finally, the possibility of this method for the reconstruction of the system's differential equations is discussed.