Optical chaos is crucial in both fundamental research and practical applications because it leverages the high bandwidth and low latency of optical approach to surpass the limitations of electronic processors^[1,2]. Chaotic lasers, induced generally by external perturbations such as optical injection^[3] or feedback^[4,5], serve as effective random bit generators (RBGs)^[6-8] and are pivotal in Monte Carlo (MC) simulations with widespread wide applications from science to commerce^[9]. However, meeting the escalating demand for MC simulations necessitates large-scale parallel RBG devices, characterized by high integration, scalability, and low correlation.

Most previous parallel schemes were nonintegrated and had a small number of channels^[10–12]. In addition, another scheme based on multiwavelength lasers often exhibits a high correlation between different wavelengths due to the competition between longitudinal modes^[13]. In 2008, Li et al. utilized a mode-locked laser and a discrete highly nonlinear fiber (HNLF) to achieve high-speed parallel RBGs^[14]. Although channels of wavelength for the chaotic sources have greatly increased, the discrete HNLF (typically length: 100 m) results in a large footprint. In 2021, Kim et al. utilized a specially designed laser cavity to excite numerous high-order transverse modes and achieve parallel ultrafast RBGs^[15]. However, this poses high requirements for the design of laser cavities and multiplexers for high-order transverse mode. In 2023, Hu et al. demonstrated parallel 10 Tbit/s physical RBGs with a chaotic microcomb using a chip-scale integrated resonator^[16]. Due to the high requirements for the power, polarization, and isolation of the pump laser for the nonlinear microcavities, it is difficult to integrate pump lasers, erbium-doped fiber amplifiers (EDFAs), and isolators with the nonlinear microcavity, resulting in limited integration of the system.

Here, we propose a large-scale parallel chaotic source for fast RBGs based on a monolithically integrated amplified-feedback laser (AFL) array using the reconstruction-equivalent chirp (REC) technique^[17,18]. First, the integrated AFL provides a single chaotic entropy source with a higher effective bandwidth than a chaotic microcomb^[19–21]. In addition, the REC technology provides an integrated method to produce large-scale parallel chaotic laser channels with accurate wavelength spacings^[22]. This scheme has greater spectral scalability and flexibility than frequency combs, which are affected by spectral ranges. Furthermore, almost all discrete optical components including pump lasers, EDFAs, and isolators could be removed.

In this Letter, we experimentally developed a parallel chaotic source based on a monolithically integrated AFL array using the REC technique. Proof-of-concept experiments demonstrate that using our method, eight independent chaotic lasers with a uniform wavelength spacing of 100 GHz are completed. The obtained high-speed random bit streams, after sampling and postprocessing, represent high autocorrelation and low cross-correlation between different chaotic channels. Our approach allows great scalability to achieve massively parallel chaotic channels, thus giving a potential pathway for high-capacity random bit generation.

The micrograph picture of the fabricated monolithic chaotic laser based on optical amplified feedback is displayed in Fig. 1(a). The intracavity configuration is shown in Fig. 1(b), which consists of a distributed feedback (DFB) section (500 µm), an semiconductor optical amplifier (SOA) section (400 µm), and a tail absorption region (TAR) section (100 µm), coated with antireflection (AR) for both side facets. An electrical isolation is achieved by removing a 20 µm-long ohmic contact layer between two sections. The width of the manufactured laser chip and the ridge waveguide is 250 and 2 µm, respectively.

Compared to conventional electron-beam lithography, the REC technique offers obvious advantages of low cost and precise wavelength control^[23,24]. Typically, in the REC technique, high-order subgratings can be used to obtain equivalent phase shifts, and the +1st order subgrating is used as a resonant laser. The period of the +1st order subgrating Λ+1 can be obtained by 1Λ+1=1Λ0+1P,(1)ΔΛ+1=1(PΛ0+1)2ΔP,(2)where Λ0 is the period of the uniform grating and P is the sampled period. We can use different sampling periods with uniform seed grating to achieve different target lasing wavelengths. Derived from Eq. (1), Eq. (2) shows the relation between the grating phase error ΔΛ+1 and the variation of sampled period ΔP. As a result, the error tolerance of the grating phase can be relaxed by a factor of (P/Λ0+1)2, which is typically 2 orders of magnitude^[24,25]. By utilizing the REC technique, we can precisely control the designed chaotic channels and simplify the grating fabrications^[22,26], which provide a solid foundation for large-scale integrated parallel chaotic sources.

The experimental setup is to characterize the chaotic laser we designed, as shown in Fig. 2. Here, the optical spectrum analyzer (OSA) is used to monitor the spectra of lasers, which is one of the important criteria for judging chaotic signals. Meanwhile, the oscilloscope (OSC) and electronic spectrum analyzer (ESA) are used to detect the time-domain and frequency-domain signals of the laser, respectively. It is worth noting that there is no need for discrete external feedback components, due to the integrated amplified feedback; Commercial EDFA is also not needed as an optical relay amplifier, due to its satisfactory power.

When changing the injection current of the two segments of the DFB-SOA laser, rich spectral dynamics appear. As shown in Fig. 3, when we fix the current of the SOA section to 70 mA and change the current of the DFB section, we find that there are four different states at least. When the ISOA is greater than 110 mA, the spectra exhibit a standard single-mode (SM) state without chaotic phenomena. When the ISOA is around 90–110 mA, many spikes appear in the spectra, exhibiting a P-1 oscillation state. When the ISOA is around 75–90 mA, the small spikes on the spectrum disappear, but the spectral width is greatly increased compared to the SM state, namely, the signal-mode chaos (SMC) state. Moreover, the SMC signal could have certain tuning spacings with the increase of IDFB, approximately 40 GHz. When the ISOA is around 40–75 mA, two chaotic signals simultaneously appear, with a wavelength channel of about 100 GHz. The spectral width of each chaotic wavelength is slightly narrower than that of the SMC state but wider than that of the SM state, which indicates that one of the chaotic channels in the dual-mode chaos (DMC) state has a slightly smaller chaotic bandwidth than the SMC state. To visually represent the spectral dynamics, the four different states are independently shown in Figs. 4(a)–4(d).

In the SMC state mentioned above, we tested the optical spectra and power spectra of the eight chaotic channels we designed. As shown in Fig. 5, the eight chaotic channels are evenly spaced, approximately at 100 GHz, and all exhibit spectral broadening characteristics relative to the SM state. Showcased is the feasibility of using REC technology to achieve large-scale parallel chaotic laser sources.

Their power spectra are shown in the blue curve of Fig. 6, which all denote the typical chaotic laser output, and the black curve represents the noise floor. The orange curve represents the single-mode laser. The small bulge on this orange curve is generated by relaxation oscillation. In this context, the 80% bandwidth refers to the frequency range encompassing 80% of the total power within the power spectrum, extending from DC to a specific frequency^[27]. By calculation, the average value of 80% bandwidth for our parallel chaotic lasers is about 8.7 GHz, higher than the bandwidth of chaotic frequency combs (5.6 GHz)^[28]. The chaotic bandwidth could be greatly improved through mutual injection of on-chip semiconductor lasers^[29], but more difficult to control the channel spacings. Therefore, it could be an advanced version of large-scale parallel chaotic sources. In addition, to achieve better parallel transmission, photonic wire bonding (PWB) technology could be used to externally combine the chaotic laser array^[30], allowing multiple chaotic wavelength channels to output from one port.

In Fig. 7, the chaotic bandwidths and temporal waveforms of the eight chaotic lasers are meticulously measured and compiled. To streamline presentation, solely the temporal waveform signal of the first chaotic channel is depicted in Fig. 7(b). This representation is facilitated by a high-speed OSC boasting a sampling rate of 100 GSa/s. The captured waveform serves as a foundational element for subsequent postprocessing steps aimed at generating physical random numbers.

In Fig. 8, the temporal waveform signals from parallel chaotic lasers are sent to a computer for postprocessing to generate physical random numbers. The postprocessing employs the m-least significant bits (m-LSBs) extraction method, involving three steps: delayed difference, 8-bit quantization, and selection of m-LSBs^[31]. Figure 9(a) illustrates the intensity histogram distribution of the 500 µs-long raw data stream, showing an asymmetric distribution characteristic of chaotic semiconductor lasers. This asymmetry can introduce bias into the generated random sequence. After applying a delayed difference, a significantly improved symmetric distribution is achieved, as depicted in Fig. 9(b). Subsequently, the digitalized differential signal undergoes 8-bit quantization, followed by the adoption of the m-LSBs method to eliminate residual correlations between adjacent bits and enhance the uniformity of bit distributions. Retaining three LSBs yields a nearly uniform probability distribution, as demonstrated in Fig. 9(c). Furthermore, the absolute autocorrelation coefficient of the bit stream is less than 10−3 [Fig. 9(d)], indicating the successful elimination of correlation between successive bits.

To validate the randomness of the generated random bits, we subjected the 1-Gbit data to NIST SP 800-22 statistical tests, dividing them into 1000 sequences of 1-Mbit each^[32]. Specifically, 3-LSBs were extracted for each channel; typical results of the NIST tests for all eight channels are illustrated in Fig. 10. These results confirm that the random bit streams generated across all eight channels can be deemed genuinely random and unpredictable.

Furthermore, we conducted thorough assessments by calculating the cross-correlation functions (CCFs) between any two sequences of these eight parallel temporal subsequences. Figure 11 provides a glimpse into this analysis, showcasing four selected examples. Importantly, none of the computed CCFs reveal any significant correlation, indicating the absence of interchannel correlation. This underscores the robust performance and excellent parallel random bit generation capabilities of our system.

In summary, we developed what we believe is a novel approach utilizing a monolithically integrated AFL array through the REC technique to achieve massive parallel chaotic sources for RBGs. The parallel chaotic sources underwent rigorous testing, successfully passing the NIST standard test. Our proof-of-concept experiments revealed the capability of obtaining eight independent random bit streams with a sample rate of 100 GSa/s and wavelength spacing of 100 GHz, demonstrating low correlation between different chaotic channels. This approach offers a viable solution for ultrafast random bit generation with high parallelism, low correlation, and cost-effectiveness. It holds promise for advancing next-generation high-speed communication systems and high-performance computation, with the potential to increase throughput capacity simply by adding more REC-based AFL channels.