Bitao Shen, Haowen Shu, Weiqiang Xie, Ruixuan Chen, Zhi Liu, Zhangfeng Ge, Xuguang Zhang, Yimeng Wang, Yunhao Zhang, Buwen Cheng, Shaohua Yu, Lin Chang, Xingjun Wang

Nature Communications (2023) 14:4590

Abstract

Optical chaos is vital for various applications such as private communication, encryption, anti-interference sensing, and reinforcement learning. Chaotic microcombs have emerged as promising sources for generating massive optical chaos. However, their inter-channel correlation behavior remains elusive, limiting their potential for on-chip parallel chaotic systems with high throughput. In this study, we present massively parallel chaos based on chaotic microcombs and high-nonlinearity AlGaAsOI platforms. We demonstrate the feasibility of generating parallel chaotic signals with inter-channel correlation <0.04 and a high random number generation rate of 3.84 Tbps. We further show the application of our approach by demonstrating a 15-channel integrated random bit generator with a 20 Gbps channel rate using silicon photonic chips. Additionally, we achieved a scalable decision-making accelerator for up to 256-armed bandit problems. Our work opens new possibilities for chaos-based information processing systems using integrated photonics, and potentially can revolutionize the current architecture of communication, sensing and computations.

Introduction and Methods

Chaos is a fundamental phenomenon in physics that exhibits random behaviors due to its great sensitivity to small changes of conditions. It has been playing key roles behind a wide range of applications for modern society: in communications, the generation of chaos guarantees the integrity of cryptographic protocols for secure networks; in computations, the simulation of Monte Carlo problems and reinforcement learning relies on random numbers6 generated from chaos, which is particularly essential for Artificial Intelligence (AI). Recently, chaos has also been used to enable advanced sensing technologies, such as Multiple Input Multiple Output (MIMO) radar or Random Modulation Continuous Wave (RMCW) lidar, which are immune to interference and thus can overcome the time/frequency congestion in ranging. Conventionally, the chaotic source used in information systems is generated from the electronic chaos (Fig. 1a1) induced by nonlinear circuits such as application specific integrated circuit (ASIC) and field programmable gate array (FPGA). Despite their integration compatibility with CMOS electronics, these chaotic sources suffer from low bandwidth (on the order of hundreds of MHz12) and the combination of several sources is necessary for high throughput rate, which is well behind the electronic processing speed and therefore lagging the system performance. This problem gets further highlighted in nowadays parallel information architectures, where multiple data channels need to be proceeded simultaneously for high system throughput.

Key Results and Conclusions

The bandwidth and the parallelization capability demonstrated here can be further improved by optimizing the design as well as fabrication for the microresonator. Currently the microresonator in this work is critically coupled, and by using an over-coupled structure instead, higher conversion efficiency, wider optical spectrum and higher power per comb line could be obtained without degenerating the chaotic properties. Another factor which limits the chaotic bandwidth currently is the intra-cavity nonlinear loss (discussed in Supplementary Note 8), which mainly comes from the three photon absorption and consequently free carrier absorption, leading to relatively high side lobes. This can be solved by employing an integrated PIN structure for the waveguide or working at a longer-wavelength band51. Combining these strategies, combs with chaotic bandwidth above 10 GHz can be expected with 100 mW pump powers. Furthermore, the spectral coverage of the comb can be further extended through dispersion engineering, accessing much more chaotic comb channels than those at C band in this work. By combining all these strategies, a parallel random number generator with beyond 3 Tbps total rate can be achieved, by using only one comb source (detailed discussions can be found in Supplementary Note 6 and 10), which is even better than the best benchtop chaotic system.

Fig.1：Microcomb based massively parallel chaotic signal generation and applications.

a) Different methods to obtain parallel chaotic sources, (a1) multiple electric chaotic oscillators; (a2)spatiotemporal chaos in free space; (a3) multiple chaotic lasers; (a4) chaotic comb. LUT, look-up table; Disp, dispersion element. b) The principle of the chaotic comb function as the parallel chaotic source. As acontinuous wave injected into the high-quality and high-nonlinear optical microcavity, the intracavity field will evolve into the spatiotemporal chaos. The output consists of multiple comb lines in the frequency domain. Each comb line carries a chaotic signal, whose autocorrelation function is a dirac-like function. The crosscorrelation between different channels is negligible. c) Scalable chaos-based systems empowered by chaotic combs. Using the wavelength division multiplexing technology, hundreds of chaotic sources could be distributed, detected, and processed in parallel, and employed for random number generation, reinforcement learning, lidar, radar and private communication.

Fig. 2：The characterization of chaotic combs.

a) The optical spectrum of the generated chaotic comb. b) Setup for characterizing the chaotic comb. ECL external cavity diode laser, EDFA erbium-doped fiber amplifier, NF notch filter, WSS wavelength selective switch, PD photodetector, OSC oscilloscope, ESA electrical spectrum analyzer, OSA optical spectrum analyzer. c) Radio frequency noise spectrum of chaotic combs pumped by different power levels. The gray line shows the spectra without optical input. d) The time serial of a single comb line recorded by the oscilloscope. e) The amplitude distribution of the time serial shown in (d).  f ) The autocorrelation function (ACF) for all comb lines in C band. g)  The full width at half maximum (FWHM) of the ACF for different comb lines varies with the detuning of the pump laser. h) The correlation between different comb lines. i) The crosscorrelation between symmetric comb lines in experiment (red line) and simulation (blue line).

Fig.3：The parallel random bit generator based on a microresonator and a SOI chip.

a) Optical microscope photograph of the SiPh receiver. b) The set-up scheme for parallel random number generation; AWG arrayed waveguide grating, PD photodetector, OSC oscillator, D delay unit, XOR exclusive-OR, BPF band-pass filter, EDFA erbium-doped fiber amplifier. c) The setup for random bit generation using two chaotic combs. d) The possibility distribution function of the differential data. e) The distribution of the extracted 3 LSBs. f) The ACF of the generated bit sequence. The red line indicates the lower limit determined by 1/pffiffiffi n. The NIST SP800-22 test results for signals detected by SOI PD with setup shown in (b) (g) and commercial InP PD with setup shown in (c) (h).

Fig.4：Multi-armed bandit problem solving based on chaotic combs.

a) The scheme of the optical decision making based on the parallel chaotic source. b) One decision process for 32-armed bandit problem. The left figure shows the hit probability distribution of 32 slots, where the third slot have the highest hit probability 0.9. c) The evolution of corrected decision rate with the increase of cycles. The red dashed line marks the corrected decision rate of 95%. d) The evolution of corrected decision rate under different scales. e The comparation of scalability between chaotic-comb-based decision maker and other methods.

https://doi.org/10.1038/s41467-023-40152-w