Christophe Peucheret

Directly modulated lasers (DMLs) are an attractive technology for short-reach intensity modulation and direct detection communication systems. However, their complex nonlinear dynamics make the modeling and optimization of DML-based systems challenging. In this paper, we study the end-to-end optimization of DML-based systems based on a data-driven surrogate model trained on experimental data. The end-to-end optimization includes the pulse shaping and equalizer filters, the bias current and the modulation radio-frequency (RF) power applied to the laser. The performance of the end-to-end optimization scheme is tested on the experimental setup and compared to 4 different benchmark schemes based on linear and nonlinear receiver-side equalization. The results show that the proposed end-to-end scheme is able to deliver better performance throughout the studied symbol rates and transmission distances while employing lower modulation RF power, fewer filter taps and utilizing a smaller signal bandwidth.

Silicon microring resonators (MRRs) have shown strong potential in acting as the nonlinear nodes of photonic reservoir computing (RC) schemes. By using nonlinearities within a silicon MRR, such as the ones caused by free-carrier dispersion (FCD) and thermo-optic (TO) effects, it is possible to map the input data of the RC to a higher dimensional space. Furthermore, by adding an external waveguide between the through and add ports of the MRR, it is possible to implement a time-delay RC (TDRC) with enhanced memory. The input from the through port is fed back into the add port of the ring with the delay applied by the external waveguide effectively adding memory. In a TDRC, the nodes (virtual) are multiplexed in time, and their respective time evolutions are detected at the drop port. The performance of MRR-based TDRC is highly dependent on the amount of nonlinearity in the MRR. The nonlinear effects, in turn, are dependent on the physical properties of the MRR as they determine the lifetime of the effects. Another factor to take into account is the stability of the MRR response, as strong time-domain discontinuities at the drop port are known to emerge from FCD nonlinearities due to self-pulsing (high nonlinear behaviour). However, quantifying the right amount of nonlinearity that RC needs for a certain task in order to achieve optimum performance is challenging. Therefore, further analysis is required to fully understand the nonlinear dynamics of this TDRC setup. Here, we quantify the nonlinear and linear memory capacity of the previously described microring-based TDRC scheme, as a function of the time constants of the generated carriers and the thermal of the TO effects. We analyze the properties of the TDRC dynamics that generate the parameter space, in terms of input signal power and frequency detuning range, over which conventional RC tasks can be satisfactorily performed by the TDRC scheme.

The use of directly modulated lasers (DMLs) is attractive in low-power, cost-constrained short-reach optical links. However, their limited modulation bandwidth can induce waveform distortion, undermining their data throughput. Traditional distortion mitigation techniques have relied mainly on the separate training of transmitter-side pre-distortion and receiver-side equalization. This approach overlooks the potential gains obtained by simultaneous optimization of the transmitter (constellation and pulse shaping) and receiver (equalization and symbol demapping). Moreover, in the context of DML operation, the choice of laser-driving configuration parameters such as the bias current and peak-to-peak modulation current has a significant impact on system performance. We propose, to our knowledge, a novel end-to-end optimization approach for DML systems, incorporating the learning of bias and peak-to-peak modulation current to the optimization of constellation points, pulse shaping, and equalization. The simulation of the DML dynamics is based on the use of the laser rate equations at symbol rates between 15 and 25 Gbaud. The resulting output sequences from the rate equations are used to build a differentiable data-driven model, simplifying the calculation of gradients needed for end-to-end optimization. The proposed end-to-end approach is compared to three additional benchmark approaches: the uncompensated system without equalization, a receiver-side finite impulse response equalization approach, and an end-to-end approach with learnable pulse shape and nonlinear Volterra equalization but fixed bias and peak-to-peak modulation current. The numerical simulations on the four approaches show that the joint optimization of bias, peak-to-peak current, constellation points, pulse shaping, and equalization outperforms all other approaches throughout the tested symbol rates.

Among the promising advantages of photonic computing over conventional computing architectures is the potential to increase computing efficiency through massive parallelism by using the many degrees of freedom provided by photonics. Here, we numerically demonstrate the simultaneous use of time and frequency (equivalently wavelength) multiplexing to solve three independent tasks at the same time on the same photonic circuit. In particular, we consider a microring-based time-delay reservoir computing (TDRC) scheme that simultaneously solves three tasks: Time-series prediction, classification, and wireless channel equalization. The scheme relies on time-division multiplexing to avoid the necessity of multiple physical nonlinear nodes, while the tasks are parallelized using wavelength division multiplexing (WDM). The input data modulated on each optical channel is mapped to a higher dimensional space by the nonlinear dynamics of the silicon microring cavity. The carrier wavelength and input power assigned to each optical channel have a high influence on the performance of its respective task. When all tasks operate under the same wavelength/power conditions, our results show that the computing nature of each task is the deciding factor of the level of performance achievable. However, it is possible to achieve good performance for all tasks simultaneously by optimizing the parameters of each optical channel. The variety of applications covered by the tasks shows the versatility of the proposed photonic TDRC scheme. Overall, this work provides insight into the potential of WDM-based schemes for improving the computing capabilities of reservoir computing schemes.

End-to-end learning has become a popular method for joint transmitter and receiver optimization in optical communication systems. Such approach may require a differentiable channel model, thus hindering the optimization of links based on directly modulated lasers (DMLs). This is due to the DML behavior in the large-signal regime, for which no analytical solution is available. In this letter, this problem is addressed by developing and comparing differentiable machine learning-based surrogate models. The models are quantitatively assessed in terms of root mean square error and training/testing time. Once the models are trained, the surrogates are then tested in a numerical equalization setup, resembling a practical end-to-end scenario. Based on the numerical investigation conducted, the convolutional attention transformer is shown to outperform the other models considered.

Microring resonators (MRRs) are promising devices for time-delay photonic reservoir computing, but the impact of the different physical effects taking place in the MRRs on the reservoir computing performance is yet to be fully understood. We numerically analyze the impact of linear losses as well as thermo-optic and free-carrier effects relaxation times on the prediction error of the time-series task NARMA-10. We demonstrate the existence of three regions, defined by the input power and the frequency detuning between the optical source and the microring resonance, that reveal the cavity transition from linear to nonlinear regimes. One of these regions offers very low error in time-series prediction under relatively low input power and number of nodes while the other regions either lack nonlinearity or become unstable. This study provides insight into the design of the MRR and the optimization of its physical properties for improving the prediction performance of time-delay reservoir computing.

The frequency chirping properties of silicon ring resonator modulators (RRMs) are experimentally investigated under sinusoidal modulation. The modulated electric field at the output of an RRM is measured in the time domain thanks to a coherent detection system. The power and phase waveforms are then analyzed in terms of their temporal phase and amplitude for different wavelength detunings between the optical source and the resonance and for different modulation frequencies. The evolution of the frequency chirp, described through a peak-to-peak chirp parameter, is quantified as a function of wavelength detuning and modulation frequency for the first time.

We demonstrate 20-Gb/s 4-level pulse amplitude modulation (PAM-4) signal generation using a silicon Mach-Zehnder modulator (MZM) in the O-band. The modulator is driven by two independent binary streams, and the PAM-4 signal is thus generated directly on the chip, avoiding the use of power-hungry digital-to-analog converters (DACs). With optimized amplitude levels of the binary signals applied to the two arms of the MZM, a pre-forward error correction (FEC) bit-error rate (BER) as low as 7.6 × 10⁻⁷ is obtained. In comparison with a commercially available LiNbO₃ modulator, the penalty is only 2 dB at the KP4 FEC threshold of 2.2 × 10⁻⁴.