Entropy Extraction from Chaotic Semiconductor Lasers for Random Bit Generation

Abstract

Chaotic dynamical behaviors of semiconductor lasers have been widely investigated over the past decades. The broadband and noise-like chaotic waveforms have found a range of novel applications including secure communication, optical ranging, and most recently high-speed random bit generation (RBG). Amongst different chaos-based RBG techniques using semiconductor lasers, the most commonly employed scheme adopts a mirror for providing feedback into a semiconductor laser, unavoidably leading to time-delay signatures (TDSs) which degrade the randomness of the bits. We proposed a scheme of chaos-based RBG using an optically injected laser. The scheme avoids the TDS from feedback. The injected laser allows RBG with the flexibility of parallelization through optical and electrical heterodyning, thereby yielding RBG at a high bit rate of 200 Gbps. In order to better harness the fast nonlinear dynamics, it is necessary to explore on the randomness properties associated with the chaotic lasers. In this thesis, chaotic semiconductor lasers subject to optical injection are investigated through studying the fundamental processes of randomness extraction, statistical optimization, and synchronization for high-speed physical RBG. First of all, state-space reconstruction of the chaotic attractors is considered for deducing the randomness fundamentally. The attractors are reconstructed by the intensity time series from both simulations and experiments. The time-dependent exponent (TDE) is adopted for estimating the divergence between nearby trajectories, thus estimating the Lyapunov exponents to be approximately as fast as 15 ns−1. The chaotic dynamics is observed to quickly amplify the inherent laser noise, generating the Shannon entropy of the output bits. This fundamentally confirms the provision of non-deterministic randomness by the chaotic lasers. Moreover, the statistical properties of the chaotic waveforms are investigated in detail. Changes in the bandwidths of the practical detection electronics are found to significantly modify the intensity probability distribution, an effect that is often ignored. A nearly Gaussian distribution is obtained when the bandwidth is sufficiently smaller than the relaxation resonance frequency, which potentially simplifies the postprocessing in RBG. Furthermore, utilizing the unique property of chaos, correlated RBG is numerically investigated through synchronizing two chaotic slave lasers driven by a common master laser. Upon detecting the chaotic emissions from the slave lasers, synchronized and correlated random bit streams are generated at an output bit rate of 1.91 Gbps with a bit error ratio of only 3.6%. In addition to optically injected lasers, a laser with distributed feedback from a fiber Bragg grating (FBG) is also experimentally demonstrated for RBG. The FBG provides distributed feedback to effectively suppress the TDS, enabling the continuous tuning of the bit rate. RBG is experimentally demonstrated at a tunable output bit rate from 0.3 Gbps to 100 Gbps, where randomness is verified by a test suite of the National Institute of Standards and Technology. Besides laser chaos, an extension to discrete-time RBG scheme is also experimentally investigated at 50 Gbps using modulation instability in a highly nonlinear fiber. Collectively, the thesis provides understanding on the fundamental randomness and statistical properties in RBG using chaotic semiconductor lasers as well as nonlinearities associated with fibers. Extension to the potential applications in secure communications such as high-speed key distribution is possible using the techniques developed.

Date of Award	30 Aug 2016
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Sze Chun CHAN (Supervisor)