Ultra-High Complexity Optical VCSEL Chaos Generation Based on Reservoir Computing and Logistic Map Cascade for Multiple Applications

• Published in: Journal of lightwave technology Vol. 43; no. 14; pp. 6495 - 6507
• Main Authors: Zhu, Pengjin, Wang, Hongxiang, Ji, Yuefeng
• Format: Journal Article
• Language: English
• Published: New York IEEE 15.07.2025; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Chaos theory; Chaotic communication; Complexity; Complexity theory; Computation; Controllability; Distributed feedback devices; Entropy; logistic map; Logistics; Optical attenuators; Optical feedback; Optical fibers; Optical polarization; Permutations; Quantum cascade lasers; random number generation; Random numbers; Reservoir computing (RC); secure key distribution; ultra-high complexity chaos; Vertical cavity surface emission lasers; Vertical cavity surface emitting lasers; vertical-cavity surface-emitting laser
• ISSN: 0733-8724; 1558-2213
• DOI: 10.1109/JLT.2025.3563496

In this paper, we propose and numerically investigate an ultra-high complexity vertical-cavity surface emitting laser (VCSEL) optical feedback chaotic (RCLCOF) system based on Reservoir Computing (RC) and logistic map cascade, which is considered for integration into the DSP chip. By simultaneously utilizing the high-dimensional mapping capability of RC and the complex nonlinear transformation of logistic map, the proposed system's complexity is significantly enhanced. Specifically, the maximum Permutation Entropy (PE), Spectral Entropy (SE) and bandwidth are 0.999, 0.915 and 40.491 GHz, respectively. Furthermore, the time delay signatures (TDSs) are effectively concealed. To clarify, the RC model in the proposed system does not require training, and all connection weights (<inline-formula><tex-math notation="LaTeX">W_{in}</tex-math></inline-formula>, <inline-formula><tex-math notation="LaTeX">W_{R}</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">W_{out}</tex-math></inline-formula>) are randomly generated. Meanwhile, the complexity enhancement process is based on post-processing, which is relatively flexible and controllable. These conditions are very beneficial for practical implementation. Subsequently, the effects of different parameters on chaotic complexity are explored in detail and the optimal range is determined. Finally, we investigate the application of the RCLCOF system in random number generation, secure key distribution and optical computing, and all confirmed to achieve satisfactory results. In summary, the proposed RCLCOF system has the advantages of high complexity, high integration and low cost, which is expected to be applied in various fields.