Dimensional and Randomness Characterization of Chaotic Single-Mode Semiconductor Lasers


Student thesis: Doctoral Thesis

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Award date23 Aug 2023


Single-mode semiconductor lasers have been attracting considerable attention for the generation of optical chaos. Chaotic dynamics, amongst other nonlinear behaviors, is particularly useful in the lasers for applications such as secure communication, ranging, and random bit generation (RBG). The performances in these applications are related to different characteristics about the complexity of the chaos. A number of investigations have been devoted to characterizing the temporal properties of the chaotic waveforms, where recent quantifications were conducted on the coherence time in relation to the signal bandwidths, time-delay signature (TDS) in relation to several feedback mechanisms, and time-dependent exponent (TDE) in relation to the Lyapunov exponents about the diverging trajectories of nearby states. By comparison, characterization of the geometric properties of the chaotic attractors are relatively challenging, especially when large data sizes are required for the reconstruction of high-dimensional state spaces. Of particular interest for efficient evaluation of both experimental and numerical data is the correlation dimension D2, which is based on counting neighboring pairs of states in the reconstructed spaces. For invoking chaotic dynamics, a single-mode semiconductor laser can be perturbed by optical injection from a continuous-wave light source, by optical feedback with a delay, or by a combination of both. The perturbation using optical feedback is often preferred because of the potential in supporting high dimensional dynamics, while inherently containing undesirable TDSs corresponding to the round-trip delay. Recent investigations included optical injection with the capability of suppressing the TDSs, although the influences on the dimensions of the chaotic attractors remain to be explored. Firstly, an enhancement of D2 along with the suppression of TDS is experimentally investigated by injecting the chaotic laser subject to optical feedback. While injecting a solitary laser is known to be low-dimensional, injecting the laser under feedback is found to result in the dimension enhancement. Under a careful selection of the computational parameters with an exceptionally large data size and a very large reconstruction embedding dimension, efficient computation is enabled by averaging over many short segments to carefully estimate D2, which increases from 5.2 to 10.6 under a properly chosen injection in terms of strength and detuning frequency. Such an enhanced value of D2 is amongst the highest reported in the experiments. Since D2 is a fundamental geometric quantifier of chaotic attractors, the results are useful in applications of chaos that require high complexities. Secondly, rate-equation modeling of the laser under both injection and feedback is investigated for capturing the effect of dimension enhancement. The numerical results qualitatively reproduce the suppression of TDS and the enhancement of D2, though with slightly different values from 4.7 to 8.1 subject to probable discrepancies in the modeling parameters. Thirdly, randomness of a low-dimensional chaotic laser under only optical injection is investigated for RBG through simultaneous coherent detection. Originating from the injection without any feedback, the chaos contains no undesirable TDS, but it is limited to a low dimensionality of no more than three. Based on the simultaneous coherent detection, the potential of baseband enhancement is illustrated for effectively utilizing even such a relatively low-dimensional dynamics. The simultaneous coherent detection measures the two dimensions of intensity and phase, where through heterodyning and balanced delayed homodyning yields two signals. The two signals are baseband-enhanced, as compared to a signal from direct detection, for effectively utilizing the low-frequency responses of the detectors. Experimenting on the laser with a relaxation resonance of 5.2 GHz, the two
signals have the basebands enhanced by 8 dB and 12 dB. Through a basic postprocessing by discarding bits, they are digitized for RBG with an output bit rate reaching 280 Gbps. Through an extensive postprocessing by involving pseudo-random contributions, RBG at a boosted output bit rate of 1.28 Tbps is possible while the detection bandwidth is reduced to 3 GHz. Both postprocessings satisfy a set of standardized randomness tests from the National Institute of Standards and Technology. Additionally, the balanced delayed homodyning is found to increase both the dimension D2 and the growth of the TDE, thereby pointing to the possible role of detection in characterizing chaos. Overall, the dimension enhancement in the chaotic semiconductor laser is thoroughly characterized with the associated randomness extracted for future applications.