Detection Dependencies of Statistical Properties for Semiconductor Laser Chaos

The statistical properties of chaotic signals generated from semiconductor lasers are important in different applications such as secure communications and random bit generation. While the laser dynamics determines the intrinsic statistics of the emission, the process of detection can significantly affect the statistics of the output signals. Using the rate-equation model, the role of detection on the statistical properties of the output signal is systematically investigated for a chaotic laser subject to optical injection. The chaotic emission is converted into electrical outputs using different detection schemes. The statistics of the output signals are evaluated through the probability density functions (PDFs). By low-passed direct detection, the PDF becomes nearly Gaussian when the cutoff frequency of the filter is lower than the relaxation resonance frequency of the laser. Alternatively, the PDF becomes nearly Gaussian when strong frequency components are avoided in band-passed direct detection, optical heterodyne detection, or electrical heterodyne detection. Additionally, through reconstructing the detected state space, the divergence of neighboring states is quantified by the time-dependent exponent (TDE). Gaussian PDFs are yielded using the abovementioned detection schemes without much affecting the TDE slopes. The results indicate the importance of detection on the statistics associated with chaotic lasers in random signal generation.