Time delay reservoir computing with a silicon microring resonator and a fiber-based optical feedback loop.

Silicon microring resonators serve as critical components in integrated photonic neural network implementations, owing to their compact footprint, compatibility with CMOS technology, and passive nonlinear dynamics. Recent advancements have leveraged their filtering properties as weighting functions, and their nonlinear dynamics as activation functions with spiking capabilities. In this work, we investigate experimentally the linear and nonlinear dynamics of microring resonators for time delay reservoir computing, by introducing an external optical feedback loop. After effectively mitigating the impact of environmental noise on the fiber-based feedback phase dependencies, we evaluate the computational capacity of this system by assessing its performance across various benchmark tasks at a bit rate of few Mbps. We show that the additional memory provided by the optical feedback is necessary to achieve error-free operation in delayed-boolean tasks that require up to 3 bits of memory. In this case the microring was operated in the linear regime and the photodetection was the nonlinear activation function. We also show that the Santa Fe and Mackey Glass prediction tasks are solved when the microring nonlinearities are activated. Notably, our study reveals competitive outcomes even when employing only 7 virtual nodes within our photonic reservoir. Our findings illustrate the silicon microring's versatile performance in the presence of optical feedback, highlighting its ability to be tailored for various computing applications.

Experimental demonstration of bandwidth enhancement in photonic time delay reservoir computing.

Time delay reservoir computing (TDRC) using semiconductor lasers (SLs) has proven to be a promising photonic analog approach for information processing. One appealing property is that SLs subject to delayed optical feedback and external optical injection, allow for tuning the response bandwidth by changing the level of optical injection. Here we use strong optical injection, thereby expanding the SL's modulation response up to tens of gigahertz. Performing a nonlinear time series prediction task, we demonstrate experimentally that for appropriate operating conditions, our TDRC system can operate with sampling times as small as 11.72 ps, without sacrificing computational performance.

Microring resonators with external optical feedback for time delay reservoir computing.

Microring resonators (MRRs) are a key photonic component in integrated devices, due to their small size, low insertion losses, and passive operation. While the MRRs have been established for optical filtering in wavelength-multiplexed systems, the nonlinear properties that they can exhibit give rise to new perspectives on their use. For instance, they have been recently considered for introducing optical nonlinearity in photonic reservoir computing systems. In this work, we present a detailed numerical investigation of a silicon MRR operation, in the presence of external optical feedback, in a time delay reservoir computing scheme. We demonstrate the versatility of this compact, passive device, by exploiting different operating regimes and solving computing tasks with diverse memory requirements. We show that when large memory is required, as it occurs in the Narma 10 task, the MRR nonlinearity does not play a significant role when the photodetection nonlinearity is involved, while the contribution of the external feedback is significant. On the contrary, for computing tasks such as the Mackey-Glass and the Santa Fe chaotic timeseries prediction, the MRR and the photodetection nonlinearities contribute both to efficient computation. The presence of optical feedback improves the prediction of the Mackey-Glass timeseries while it plays a minor role in the Santa Fe timeseries case.

Fast physical repetitive patterns generation for masking in time-delay reservoir computing.

Albeit the conceptual simplicity of hardware reservoir computing, the various implementation schemes that have been proposed so far still face versatile challenges. The conceptually simplest implementation uses a time delay approach, where one replaces the ensemble of nonlinear nodes with a unique nonlinear node connected to a delayed feedback loop. This simplification comes at a price in other parts of the implementation; repetitive temporal masking sequences are required to map the input information onto the diverse states of the time delay reservoir. These sequences are commonly introduced by arbitrary waveform generators which is an expensive approach when exploring ultra-fast processing speeds. Here we propose the physical generation of clock-free, sub-nanosecond repetitive patterns, with increased intra-pattern diversity and their use as masking sequences. To that end, we investigate numerically a semiconductor laser with a short optical feedback cavity, a well-studied dynamical system that provides a wide diversity of emitted signals. We focus on those operating conditions that lead to a periodic signal generation, with multiple harmonic frequency tones and sub-nanosecond limit cycle dynamics. By tuning the strength of the different frequency tones in the microwave domain, we access a variety of repetitive patterns and sample them in order to obtain the desired masking sequences. Eventually, we apply them in a time delay reservoir computing approach and test them in a nonlinear time-series prediction task. In a performance comparison with masking sequences that originate from random values, we find that only minor compromises are made while significantly reducing the instrumentation requirements of the time delay reservoir computing system.

Photonic machine learning implementation for signal recovery in optical communications.

Machine learning techniques have proven very efficient in assorted classification tasks. Nevertheless, processing time-dependent high-speed signals can turn into an extremely challenging task, especially when these signals have been nonlinearly distorted. Recently, analogue hardware concepts using nonlinear transient responses have been gaining significant interest for fast information processing. Here, we introduce a simplified photonic reservoir computing scheme for data classification of severely distorted optical communication signals after extended fibre transmission. To this end, we convert the direct bit detection process into a pattern recognition problem. Using an experimental implementation of our photonic reservoir computer, we demonstrate an improvement in bit-error-rate by two orders of magnitude, compared to directly classifying the transmitted signal. This improvement corresponds to an extension of the communication range by over 75%. While we do not yet reach full real-time post-processing at telecom rates, we discuss how future designs might close the gap.

Integrated semiconductor laser with optical feedback: transition from short to long cavity regime.

A 4-section semiconductor laser with integrated optical feedback has been shown experimentally to be capable of operating in either the short- or long-cavity regime, by controlling the device relaxation oscillation frequency relative to the external cavity frequency. Systematic increase of the laser injection current, and the resulting increase in relaxation oscillation frequency, allowed the transition between the two regimes of operation to be observed. The system displayed a gradual transition from a dynamic dominated by regular pulse packages in the short-cavity regime to one dominated by broadband chaotic output when operating in the long-cavity regime. This suggests that the "short cavity" regular pulse packages continue to co-exist with the "long cavity" broadband chaotic dynamic in the system studied. It is the relative power associated with each of these dynamics that changes. This may occur more generally in similar systems.

Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit.

In the present work a photonic integrated circuit (PIC) that emits broadband chaotic signals is employed for ultra-fast generation of true random bit sequences. Chaotic dynamics emerge from a DFB laser, accompanied by a monolithic integrated 1-cm long external cavity (EC) that provides controllable optical feedback. The short length minimizes the existence of external cavity modes, so flattened broadband spectra with minimized intrinsic periodicities can emerge. After sampling and quantization--without including optical de-correlation techniques and using most significant bits (MSB) elimination post-processing--truly random bit streams with bit-rates as high as 140 Gb/s can be generated. Finally, the extreme robustness of the random bit generator for adaptive bit-rate operation and for various operating conditions of the PIC is demonstrated.

Chaos-on-a-chip secures data transmission in optical fiber links.

Security in information exchange plays a central role in the deployment of modern communication systems. Besides algorithms, chaos is exploited as a real-time high-speed data encryption technique which enhances the security at the hardware level of optical networks. In this work, compact, fully controllable and stably operating monolithic photonic integrated circuits (PICs) that generate broadband chaotic optical signals are incorporated in chaos-encoded optical transmission systems. Data sequences with rates up to 2.5 Gb/s with small amplitudes are completely encrypted within these chaotic carriers. Only authorized counterparts, supplied with identical chaos generating PICs that are able to synchronize and reproduce the same carriers, can benefit from data exchange with bit-rates up to 2.5Gb/s with error rates below 10(-12). Eavesdroppers with access to the communication link experience a 0.5 probability to detect correctly each bit by direct signal detection, while eavesdroppers supplied with even slightly unmatched hardware receivers are restricted to data extraction error rates well above 10(-3).

Hurst exponents and cyclic scenarios in a photonic integrated circuit.

We experimentally report the cyclic scenario of birth and annihilation of periodic orbits in a photonic integrated circuit as the feedback phase of the electric field varies. The latter is also shown to result in minimal alterations in the statistical properties of the chaotic attractor, with simultaneously transiting the Hurst exponent H , erratically, below and above the critical value of H=0.5 that indicates regular Brownian motion. Consequently there is an indication of the most effective operating regions with minimized predictability, which hinders eavesdropping and the progress of forecasting the development of the chaotic light carrier.

Subcarrier modulation in all-optical chaotic communication systems.

The enhancement of the encryption properties of chaotic signals generated by a semiconductor laser subject to optical feedback is numerically demonstrated by applying subcarrier modulation. The numerical analysis shows that the message can be very efficiently encrypted when the radio frequency carrier is within the frequency range where the chaos power density is maximized. Decoding performance is also numerically assessed considering both open- and closed-loop schemes at the receiver side. The impact of subcarrier modulation on system's performance under the influence of parameter mismatch is highlighted.

Chaos-based communications at high bit rates using commercial fibre-optic links.

Chaotic signals have been proposed as broadband information carriers with the potential of providing a high level of robustness and privacy in data transmission. Laboratory demonstrations of chaos-based optical communications have already shown the potential of this technology, but a field experiment using commercial optical networks has not been undertaken so far. Here we demonstrate high-speed long-distance communication based on chaos synchronization over a commercial fibre-optic channel. An optical carrier wave generated by a chaotic laser is used to encode a message for transmission over 120 km of optical fibre in the metropolitan area network of Athens, Greece. The message is decoded using an appropriate second laser which, by synchronizing with the chaotic carrier, allows for the separation of the carrier and the message. Transmission rates in the gigabit per second range are achieved, with corresponding bit-error rates below 10(-7). The system uses matched pairs of semiconductor lasers as chaotic emitters and receivers, and off-the-shelf fibre-optic telecommunication components. Our results show that information can be transmitted at high bit rates using deterministic chaos in a manner that is robust to perturbations and channel disturbances unavoidable under real-world conditions.