Francesco Da Ros

Metodi Plamenov Yankov, Francesco Da Ros, Uiara Celine de Moura et al.

The problem of Raman amplifier optimization is studied. A differentiable interpolation function is obtained for the Raman gain coefficient using machine learning (ML), which allows for the gradient descent optimization of forward-propagating Raman pumps. Both the frequency and power of an arbitrary number of pumps in a forward pumping configuration are then optimized for an arbitrary data channel load and span length. The forward propagation model is combined with an experimentally-trained ML model of a backward-pumping Raman amplifier to jointly optimize the frequency and power of the forward amplifier's pumps and the powers of the backward amplifier's pumps. The joint forward and backward amplifier optimization is demonstrated for an unrepeatered transmission of 250 km. A gain flatness of $<$ 1~dB over 4 THz is achieved. The optimized amplifiers are validated using a numerical simulator.

Ali Cem, Siqi Yan, Yunhong Ding et al.

Photonic integrated circuits are facilitating the development of optical neural networks, which have the potential to be both faster and more energy efficient than their electronic counterparts since optical signals are especially well-suited for implementing matrix multiplications. However, accurate programming of photonic chips for optical matrix multiplication remains a difficult challenge. Here, we describe both simple analytical models and data-driven models for offline training of optical matrix multipliers. We train and evaluate the models using experimental data obtained from a fabricated chip featuring a Mach-Zehnder interferometer mesh implementing 3-by-3 matrix multiplication. The neural network-based models outperform the simple physics-based models in terms of prediction error. Furthermore, the neural network models are also able to predict the spectral variations in the matrix weights for up to 100 frequency channels covering the C-band. The use of neural network models for programming the chip for optical matrix multiplication yields increased performance on multiple machine learning tasks.

Bernard J. Giron Castro, Christophe Peucheret, Darko Zibar et al.

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.

Yevhenii Osadchuk, Ognjen Jovanovic, Darko Zibar et al.

We propose spectrum-sliced reservoir computer-based (RC) multi-symbol equalization for 32-GBd PAM4 transmission. RC with 17 symbols at the output achieves an order of magnitude reduction in multiplications/symbol versus single output case while maintaining simple training.

Mehran Soltani, Francesco Da Ros, Andrea Carena et al.

We experimentally validate a real-time machine learning framework, capable of controlling the pump power values of Raman amplifiers to shape the signal power evolution in two-dimensions (2D): frequency and fiber distance. In our setup, power values of four first-order counter-propagating pumps are optimized to achieve the desired 2D power profile. The pump power optimization framework includes a convolutional neural network (CNN) followed by differential evolution (DE) technique, applied online to the amplifier setup to automatically achieve the target 2D power profiles. The results on achievable 2D profiles show that the framework is able to guarantee very low maximum absolute error (MAE) (<0.5 dB) between the obtained and the target 2D profiles. Moreover, the framework is tested in a multi-objective design scenario where the goal is to achieve the 2D profiles with flat gain levels at the end of the span, jointly with minimum spectral excursion over the entire fiber length. In this case, the experimental results assert that for 2D profiles with the target flat gain levels, the DE obtains less than 1 dB maximum gain deviation, when the setup is not physically limited in the pump power values. The simulation results also prove that with enough pump power available, better gain deviation (less than 0.6 dB) for higher target gain levels is achievable.

Bernard J. Giron Castro, Christophe Peucheret, Darko Zibar et al.

Nowadays, as the ever-increasing demand for more powerful computing resources continues, alternative advanced computing paradigms are under extensive investigation. Significant effort has been made to deviate from conventional Von Neumann architectures. In-memory computing has emerged in the field of electronics as a possible solution to the infamous bottleneck between memory and computing processors, which reduces the effective throughput of data. In photonics, novel schemes attempt to collocate the computing processor and memory in a single device. Photonics offers the flexibility of multiplexing streams of data not only spatially and in time, but also in frequency or, equivalently, in wavelength, which makes it highly suitable for parallel computing. Here, we numerically show the use of time and wavelength division multiplexing (WDM) to solve four independent tasks at the same time in a single photonic chip, serving as a proof of concept for our proposal. The system is a time-delay reservoir computing (TDRC) based on a microring resonator (MRR). The addressed tasks cover different applications: Time-series prediction, waveform signal classification, wireless channel equalization, and radar signal prediction. The system is also tested for simultaneous computing of up to 10 instances of the same task, exhibiting excellent performance. The footprint of the system is reduced by using time-division multiplexing of the nodes that act as the neurons of the studied neural network scheme. WDM is used for the parallelization of wavelength channels, each addressing a single task. By adjusting the input power and frequency of each optical channel, we can achieve levels of performance for each of the tasks that are comparable to those quoted in state-of-the-art reports focusing on single-task operation...

Bernard J. Giron Castro, Christophe Peucheret, Darko Zibar et al.

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.

Bernard J. Giron Castro, Christophe Peucheret, Darko Zibar et al.

We quantify the impact of thermo-optic and free-carrier effects on time-delay reservoir computing using a silicon microring resonator. We identify pump power and frequency detuning ranges with NMSE less than 0.05 for the NARMA-10 task depending on the time constants of the two considered effects.

Ali Cem, Ognjen Jovanovic, Siqi Yan et al.

We demonstrate transfer learning-assisted neural network models for optical matrix multipliers with scarce measurement data. Our approach uses <10\% of experimental data needed for best performance and outperforms analytical models for a Mach-Zehnder interferometer mesh.

Kostas Sozos, Francesco Da Ros, Senior Member Optica et al.

High order modulation formats constitute the most prominent way for increasing spectral efficiency in transmission systems. Coherent transceivers that support such higher order formats require heavy digital signal processing (DSP), which increases the power consumption of coherent pluggables, well above the intensity modulation and direct detection (IM/DD) counterparts. Self-coherent or phase retrieval methods have emerged as potential solutions, trying to combine the merits of coherent technology with the simplicity of direct detection. In this work, we experimentally demonstrate the reception of quadrature amplitude modulation (QAM) modulation formats based on direct detection aided by the recurrent optical spectrum slicing (ROSS) photonic accelerator, utilizing minimal DSP and low modulator driving voltages. We experimentally demonstrate 32 Gbaud QAM-4/16 for 25 km, 50 km and 75 km in the C-band aided by a linear digital equalization and the use of programmable photonics as recurrent optical spectrum slicers. We showcase successful detection with driving swings below Vπ/3 in contrast to the full swing required by conventional coherent transceivers. We further improve the system performance utilizing geometric constellation shaping. Finally, we explore the potential power consumption improvement for the next-generation 1.6T pluggables, showcasing over 40% reduction with respect to the most lightweight state of the art coherent solutions reported in literature

Mehran Soltani, Francesco Da Ros, Andrea Carena et al.

We experimentally validate a machine learning-enabled Raman amplification framework, capable of jointly shaping the signal power evolution in two domains: frequency and fiber distance. The proposed experiment addresses the amplification in the whole C-band, by optimizing four first-order counter-propagating Raman pumps.

Ali Cem, Ognjen Jovanovic, Siqi Yan et al.

We present and experimentally evaluate using transfer learning to address experimental data scarcity when training neural network (NN) models for Mach-Zehnder interferometer mesh-based optical matrix multipliers. Our approach involves pre-training the model using synthetic data generated from a less accurate analytical model and fine-tuning with experimental data. Our investigation demonstrates that this method yields significant reductions in modeling errors compared to using an analytical model, or a standalone NN model when training data is limited. Utilizing regularization techniques and ensemble averaging, we achieve < 1 dB root-mean-square error on the matrix weights implemented by a 3x3 photonic chip while using only 25% of the available data.

Metodi P. Yankov, Mehran Soltani, Andrea Carena et al.

Designing and optimizing optical amplifiers to maximize system performance is becoming increasingly important as optical communication systems strive to increase throughput. Offline optimization of optical amplifiers relies on models ranging from white-box models deeply rooted in physics to black-box data-driven and physics-agnostic models. Here, we compare the capabilities of white-, grey- and black-box models on the challenging test case of optimizing a bidirectional distributed Raman amplifier to achieve a target frequency-distance signal power profile. We show that any of the studied methods can achieve similar frequency and distance flatness of between 1 and 3.6 dB (depending on the definition of flatness) over the C-band in an 80-km span. Then, we discuss the models' applicability, advantages, and drawbacks based on the target application scenario, in particular in terms of flexibility, optimization speed, and access to training data.

Bernard J. Giron Castro, Christophe Peucheret, Francesco Da Ros

We numerically demonstrate a silicon add-drop microring-based reservoir computing scheme that combines parallel delayed inputs and wavelength division multiplexing. The scheme solves memory-demanding tasks like time-series prediction with good performance without requiring external optical feedback.

Sergio Hernandez, Christophe Peucheret, Francesco Da Ros et al.

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.

Bernard J. Giron Castro, Christophe Peucheret, Francesco Da Ros

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 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.

Isidora Teofilovic, Ali Cem, David Sanchez-Jacome et al.

Photonic integrated circuits play an important role in the field of optical computing, promising faster and more energy-efficient operations compared to their digital counterparts. This advantage stems from the inherent suitability of optical signals to carry out matrix multiplication. However, even deterministic phenomena such as thermal crosstalk make precise programming of photonic chips a challenging task. Here, we train and experimentally evaluate three models incorporating varying degrees of physics intuition to predict the effect of thermal crosstalk in different locations of an integrated programmable photonic mesh. We quantify the effect of thermal crosstalk by the resonance wavelength shift in the power spectrum of a microring resonator implemented in the chip, achieving modelling errors <0.5 pm. We experimentally validate the models through compensation of the crosstalk-induced wavelength shift. Finally, we evaluate the generalization capabilities of one of the models by employing it to predict and compensate for the effect of thermal crosstalk for parts of the chip it was not trained on, revealing root-mean-square-errors of <2.0 pm.

Metodi P. Yankov, Francesco Da Ros, Søren Forchhammer et al.

The optical fiber multiple-input multiple-output (MIMO) channel with intensity modulation and direct detection (IM/DD) per spatial path is treated. The spatial dimensions represent the multiple modes employed for transmission and the cross-talk between them originates in the multiplexers and demultiplexers, which are polarization dependent and thus timevarying. The upper bounds from free-space IM/DD MIMO channels are adapted to the fiber case, and the constellation constrained capacity is constructively estimated using the Blahut-Arimoto algorithm. An autoencoder is then proposed to optimize a practical MIMO transmission in terms of pre-coder and detector assuming channel distribution knowledge at the transmitter. The pre-coders are shown to be robust to changes in the channel.

Ali Cem, Siqi Yan, Uiara Celine de Moura et al.

We experimentally compare simple physics-based vs. data-driven neural-network-based models for offline training of programmable photonic chips using Mach-Zehnder interferometer meshes. The neural-network model outperforms physics-based models for a chip with thermal crosstalk, yielding increased testing accuracy.

Metodi Plamenov Yankov, Pawel Marcin Kaminski, Henrik Enggaard Hansen et al.

Throughput optimization of optical communication systems is a key challenge for current optical networks. The use of gain-flattening filters (GFFs) simplifies the problem at the cost of insertion loss, higher power consumption and potentially poorer performance. In this work, we propose a component wise model of a multi-span transmission system for signal-to-noise (SNR) optimization. A machine-learning based model is trained for the gain and noise figure spectral profile of a C-band amplifier without a GFF. The model is combined with the Gaussian noise model for nonlinearities in optical fibers including stimulated Raman scattering and the implementation penalty spectral profile measured in back-to-back in order to predict the SNR in each channel of a multi-span wavelength division multiplexed system. All basic components in the system model are differentiable and allow for the gradient descent-based optimization of a system of arbitrary configuration in terms of number of spans and length per span. When the input power profile is optimized for flat and maximized received SNR per channel, the minimum performance in an arbitrary 3-span experimental system is improved by up to 8 dB w.r.t. a system with flat input power profile. An SNR flatness down to 1.2 dB is simultaneously achieved. The model and optimization methods are used to optimize the performance of an example core network, and 0.2 dB of gain is shown w.r.t. solutions that do not take into account nonlinearities. The method is also shown to be beneficial for systems with ideal gain flattening, achieving up to 0.3 dB of gain w.r.t. a flat input power profile.

Stenio M. Ranzini, Roman Dischler, Francesco da Ros et al.

A receiver with shared complexity between optical and digital domains is experimentally demonstrated. Reservoir computing is used to equalize up to 4 directly-detected optically filtered spectral slices of a 32 GBd OOK signal over up to 80 km of SMF.

Metodi P. Yankov, Uiara Celine de Moura, Francesco Da Ros

Cascades of a machine learning-based EDFA gain model trained on a single physical device and a fully differentiable stimulated Raman scattering fiber model are used to predict and optimize the power profile at the output of an experimental multi-span fully-loaded C-band optical communication system.

Francesco Da Ros, Uiara Celine de Moura, Metodi P. Yankov

We report a neural-network based erbium-doped fiber amplifier (EDFA) gain model built from experimental measurements. The model shows low gain-prediction error for both the same device used for training (MSE $\leq$ 0.04 dB$^2$) and different physical units of the same make (generalization MSE $\leq$ 0.06 dB$^2$).