High resolution mapping of the dynamics of a nonlinear semiconductor laser system

Abstract

Summary form only given. Optical feedback is known to cause a range of complex dynamical states in the output power of semiconductor lasers. These types of systems have been much studied [1]. The dynamic state of the laser output can be controlled by varying the level of optical feedback and also the injection current to the laser [2]. Traditionally, analysis of nonlinear dynamics produced by semiconductor lasers has been based on optical and/or RF spectra, due to the high frequencies involved. More recently, the availability of high bandwidth real-time oscilloscopes has facilitated direct measurement of the output power time series and allowed the temporal information, missing from earlier investigations, to be captured. Computer controlled experimental setups have also improved the resolution at which system parameters can be varied and the amount of data that can be captured. We present high resolution dynamic maps categorising the dynamical output of a semiconductor laser as a function of the optical feedback level and injection current. An automated experimental process, in which the feedback level is finely tuned using an acousto-optic modulator, produces very high density data sets on which a variety of complexity analysis tools have been implemented. The maps in Fig.1 were generated from analysis of 87,500 individual time series consisting of 20,000 data points, sampled at 50 ps intervals. This resolution allows inspection of dynamics throughout the entire parameter space, rather than generating a bifurcation map from experimental system data. This ensures that no small windows of differentiated dynamics are missed.One of the measures used to quantify and map the complexity of the dynamics is the permutation entropy (PE) [3]. This technique takes advantage of the recorded temporal information by calculating the frequency of ordinal permutations. PE has a value between 0 and 1, where zero represents a completely regular and predictable time series and a 1 represents a stochastic unpredictable one. The complexity of the nonlinear dynamics are mapped in Fig. 1(b) and compared with the RMS amplitude of the power fluctuations in Fig. 1(a). These results indicate that no unexpected `islands' are observed in the main coherence collapse region (the large area of increased amplitude in Fig. 1(a)), affirming the quality of prior bifurcation diagrams generated for such systems. However, there is a small region of previously unidentified nonlinear dynamics at low feedback levels and high injection current, just below the coherence collapse boundary which will be discussed in more detail. Another new result to come out of this experimental work, which has not been addressed previously, is the reproducibility of the system dynamics. The automated setup allows for repeatable experimental runs from which direct comparison of the resulting maps have been made. System stability results, over a range of time periods, will be presented.