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We experimentally demonstrate the joint optimization of transmitter and receiver parameters in directly modulated laser systems, showing superior performance compared to nonlinear receiver-only equalization while using fewer memory taps, less bandwidth, and lower radiofrequency power., Comment: submitted to the Optical Fiber Conference (OFC)

This paper investigates the application of end-to-end (E2E) learning for joint optimization of pulse-shaper and receiver filter to reduce intersymbol interference (ISI) in bandwidth-limited communication systems. We investigate this in two numerical simulation models: 1) an additive white Gaussian noise (AWGN) channel with bandwidth limitation and 2) an intensity modulated direct detection (IM/DD) link employing an electro-absorption modulator. For both simulation models, we implement a wavelength division multiplexing (WDM) scheme to ensure that the learned filters adhere to the bandwidth constraints of the WDM channels. Our findings reveal that E2E learning greatly surpasses traditional single-sided transmitter pulse-shaper or receiver filter optimization methods, achieving significant performance gains in terms of symbol error rate with shorter filter lengths. These results suggest that E2E learning can decrease the complexity and enhance the performance of future high-speed optical communication systems., Comment: Under review

A resonant electro-optic (EO) frequency comb is generated through electro-optic modulation of laser light within an optical resonator. Compared to cavity-less EO combs generated in a single pass through a modulator, resonant EO combs can produce broader spectra with lower radio frequency (RF) power and offer a measure of noise filtering beyond the cavity's linewidth. Understanding, measuring, and suppressing the sources of phase noise in resonant EO combs is crucial for their applications in metrology, astrophotonics, optical clock generation, and fiber-optic communication. According to the standard phase noise model of frequency combs, only two variables - the common mode offset and repetition rate phase noise - are needed to fully describe the phase noise of comb lines. However, in this work we demonstrate analytically, numerically, and experimentally that this standard model breaks down for resonant EO combs at short timescales (high frequencies) and under certain comb parameters. Specifically, a third phase noise component emerges. Consequently, resonant EO combs feature qualitatively different phase noise from their cavity-less counterparts and may not exhibit the anticipated noise filtering. A more complete description of the deviations from the standard phase noise model is critical to accurately predict the performance of frequency combs. The description presented here paves the way for improved designs tailored to applications such as super-continuum generation and optical communication.

We present a comprehensive phase noise characterization of a mid-IR Cr:ZnS frequency comb. Despite their emergence as a platform for high-resolution dual-comb spectroscopy, detailed investigations into the phase noise of Cr:ZnS combs have been lacking. To address this, we use a recently proposed phase noise measurement technique that employs multi-heterodyne detection and subspace tracking. This allows for the measurement of the common mode, repetition-rate and high-order phase noise terms, and their corresponding scaling as a function of a comb-line number, using a single measurement set-up. We demonstrate that the comb under test is dominated by the common mode phase noise, while all the other phase noise terms are below the measurement noise floor (~ -120 dB rad^2/Hz), and are thereby not identifiable.

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..., Comment: Main text: 11 figures, 3 tables. Supplementary material: 2 figures, 4 tables. The manuscript presented in this pre-print has been accepted for publication in Frontiers: Advanced Optical Technologies. The abstract is shorter than in the PDF file to comply with arXiv requirements

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., Comment: 12 pages, 12 figures. Proceedings SPIE Europe 2024

We numerically demonstrate that joint optimization of FIR based pulse-shaper and receiver filter results in an improved system performance, and shorter filter lengths (lower complexity), for 4-PAM 100 GBd IM/DD systems., Comment: 4 pages (3 article pages + 1 page for references) and 5 figures. Submitted to European Conference on Optical Communications (ECOC) 2024

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 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 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 3 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., Comment: submitted to journal of optical communications and networking (invited)

The rate and reach of directly-modulated laser links is often limited by the interplay between chirp and fiber chromatic dispersion. We address this by optimizing the transmitter, receiver, bias and peak-to-peak current to the laser jointly. Our approach outperforms Volterra post-equalization at various symbol rates., Comment: submitted to european conference on optical communication

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., Comment: 10 pages, 10 figures. The paper has been submitted to the Journal of Lightwave Technology, a special issue on Photonic Computing, as an invited paper. It is under review

In this paper, we experimentally validate our previous numerical works in recurrent optical spectrum slicing (ROSS) accelerators for dispersion compensation in high-speed IM/DD links. For this, we utilize recurrent filters implemented both through a waveshaper and by exploiting novel integrated programmable photonic platforms. Different recurrent configurations are tested. The ROSS accelerators exploit frequency processing through recurrent optical filter nodes in order to mitigate the power fading effect, which hinders the transmission distance and baudrate scalability of IM/DD systems. By equalizing even 80 km of 64 Gb/s PAM-4 transmission in C-band, we prove that our system can offer an appealing solution in highly dispersive channels., Comment: 8 pages, 6 figures

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., Comment: 2 pages, 2 figures. Submitted to Conference on Lasers and Electro-Optics (CLEO) 2024

In this paper, a rate adaptive geometric constellation shaping (GCS) scheme which is fully backward-compatible with existing state of the art bit-interleaved coded modulation (BICM) systems is proposed and experimentally demonstrated. The system relies on optimization of the positions of the quadrature amplitude modulation (QAM) points on the I/Q plane for maximized achievable information rate, while maintaining quantization and fiber nonlinear noise robustness. Furthermore, `dummy' bits are multiplexed with coded bits before mapping to symbols. Rate adaptivity is achieved by tuning the ratio of coded and `dummy' bits, while maintaining a fixed forward error-correction block and a fixed modulation format size. The points' positions and their labeling are optimized using automatic differentiation. The proposed GCS scheme is compared to a time-sharing hybrid (TH) QAM modulation and the now mainstream probabilistic amplitude shaping (PAS) scheme. The TH without shaping is outperformed for all studied data rates in a simulated linear channel by up to 0.7 dB. In a linear channel, PAS is shown to outperform the proposed GCS scheme, while similar performances are reported for PAS and the proposed GCS in a simulated nonlinear fiber channel. The GCS scheme is experimentally demonstrated in a multi-span recirculating loop coherent optical fiber transmission system with a total distance of up to 3000 km. Near-continuous zero-error flexible throughput is reported as a function of the transmission distance. Up to 1-2 spans of increased reach gains are achieved at the same net data rate w.r.t. conventional QAM. At a given distance, up to 0.79 bits/2D symbol of gain w.r.t. conventional QAM is achieved. In the experiment, similar performance to PAS is demonstrated., Comment: Submitted to Journal of Lightwave Technology as a special extended version of a 'top-scored' paper at the European Conference on Optical Communications (ECOC) 2023

The flatness of electro-optic frequency combs (EOFCs) generated in a single silicon ring resonator modulator (RRM) is optimized by employing harmonic superposition of the radio-frequency driving signal. A differential evolution algorithm is employed in conjunction with a simplified model of the RRM for offline optimization of the amplitudes and phases of harmonic driving signals and the operating point of the RRM. The optimized driving signals are then applied to a silicon RRM. EOFCs containing 7 and 9 lines are synthesized with a power imbalance between the lines of 2.9 dB and 5.4 dB, respectively, compared to 9.4 dB for an optimized 5-line comb generated from a single sinusoidal driving signal., Comment: 4 pages, 5 figures, submitted to Optics Letters

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., Comment: 7 pages, 7 figures, Accepted for presentation at The International Joint Conference on Neural Networks (IJCNN), part of IEEE WCCI 2024

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., Comment: 20 pages, 11 figures, submitted to Optics Express (reviewed version)

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 paper, 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., Comment: final version to Photonics Technology Letters (02/01/2024)

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.

Low-complexity neural networks (NNs) have successfully been applied for digital signal processing (DSP) in short-reach intensity-modulated directly detected optical links, where chromatic dispersion-induced impairments significantly limit the transmission distance. The NN-based equalizers are usually optimized independently from other DSP components, such as matched filtering. This approach may result in lower equalization performance. Alternatively, optimizing a NN equalizer to perform functionalities of multiple DSP blocks may increase transmission reach while keeping the complexity low. In this work, we propose a low-complexity NN that performs samples-to-symbol equalization, meaning that the NN-based equalizer includes match filtering and downsampling. We compare it to a samples-to-sample equalization approach followed by match filtering and downsampling in terms of performance and computational complexity. Both approaches are evaluated using three different types of NNs combined with optical preprocessing. We numerically and experimentally show that the proposed samples-to-symbol equalization approach applied for 32 GBd on-off keying (OOK) signals outperforms the samples-domain alternative keeping the computational complexity low. Additionally, the different types of NN-based equalizers are compared in terms of performance with respect to computational complexity.

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.

A many-to-one mapping geometric constellation shaping scheme is proposed with a fixed modulation format, fixed FEC engine and rate adaptation with an arbitrarily small step. An autoencoder is used to optimize the labelings and constellation points' positions.

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., Comment: 2 pages, 2 figures. Submitted to IEEE Photonics Conference 2023

Advanced digital signal processing techniques in combination with ultra-wideband balanced coherent detection have enabled a new generation of ultra-high speed fiber-optic communication systems, by moving most of the processing functionalities into digital domain. In this paper, we demonstrate how digital signal processing techniques, in combination with ultra-wideband balanced coherent detection can enable optical frequency comb noise characterization techniques with novel functionalities. We propose a measurement method based on subspace tracking, in combination with multi-heterodyne coherent detection, for independent phase noise sources identification, separation and measurement. Our proposed measurement technique offers several benefits. First, it enables the separation of the total phase noise associated with a particular comb-line or -lines into multiple independent phase noise terms associated with different noise sources. Second, it facilitates the determination of the scaling of each independent phase noise term with comb-line number. Our measurement technique can be used to: identify the most dominant source of phase noise; gain a better understanding of the physics behind the phase noise accumulation process; and confirm, already existing, and enable better phase noise models. In general, our measurement technique provides new insights into noise behavior of optical frequency combs.

The end-to-end optimization of links based on directly-modulated lasers may require an analytically differentiable channel. We overcome this problem by developing and comparing differentiable laser models based on machine learning techniques., Comment: 4 pages, 6 figures, submitted to european conference on optical communcations 2023

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., Comment: Conference, 2 pages

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., Comment: 2 pages, 2 figues, submitted to CLEO

An autoencoder is used to optimize bit-to-symbol mappings for geometric constellation shaping. The mappings allow for net rate adaptivity without additional hardware complexity, while achieving up to 300km of transmission distance compared to uniform QAM.

End-to-end learning has become a popular method to optimize a constellation shape of a communication system. When the channel model is differentiable, end-to-end learning can be applied with conventional backpropagation algorithm for optimization of the shape. A variety of optimization algorithms have also been developed for end-to-end learning over a non-differentiable channel model. In this paper, we compare gradient-free optimization method based on the cubature Kalman filter, model-free optimization and backpropagation for end-to-end learning on a fiber-optic channel modeled by the split-step Fourier method. The results indicate that the gradient-free optimization algorithms provide a decent replacement to backpropagation in terms of performance at the expense of computational complexity. Furthermore, the quantization problem of finite bit resolution of the digital-to-analog and analog-to-digital converters is addressed and its impact on geometrically shaped constellations is analysed. Here, the results show that when optimizing a constellation with respect to mutual information, a minimum number of quantization levels is required to achieve shaping gain. For generalized mutual information, the gain is maintained throughout all of the considered quantization levels. Also, the results implied that the autoencoder can adapt the constellation size to the given channel conditions.

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., Comment: 12 pages, 17 figures, submitted to Jorunal of Lightwave Technology

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.

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., Comment: submitted to Journal of Lightwave Technology. Extended version of the previous conference paper M. Yankov, D. Zibar, A. Carena, and F. Da Ros, "Forward Raman amplifier optimization using machine learning-aided physical modeling," accepted, Optoelectronics and Communications Conference (OECC), 2022

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., Comment: 4 pages, 5 figures

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., Comment: International Conference on Communications (ICC) 2022

We present a machine learning (ML) framework for designing desired signal power profiles over the spectral and spatial domains in the fiber span. The proposed framework adjusts the Raman pump power values to obtain the desired two-dimensional (2D) profiles using a convolutional neural network (CNN) followed by the differential evolution (DE) technique. The CNN learns the mapping between the 2D profiles and their corresponding pump power values using a data-set generated by exciting the amplification setup. Nonetheless, its performance is not accurate for designing 2D profiles of practical interest, such as a 2D flat or a 2D symmetric (with respect to the middle point in distance). To adjust the pump power values more accurately, the DE fine-tunes the power values initialized by the CNN to design the proposed 2D profile with a lower cost value. In the fine-tuning process, the DE employs the direct amplification model which consists of 8 bidirectional propagating pumps, including 2 second-order and 6 first order, in an 80 km fiber span. We evaluate the framework to design broadband 2D flat and symmetric power profiles, as two goals for wavelength division multiplexing (WDM) system performing over the whole C-band. Results indicate the framework's ability to achieve maximum power excursion of 2.81 dB for a 2D flat, and maximum asymmetry of 14% for a 2D symmetric profile.

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., Comment: 3 pages, 3 figures

Vendor interoperability is one of the desired future characteristics of optical networks. This means that the transmission system needs to support a variety of hardware with different components, leading to system uncertainties throughout the network. For example, uncertainties in signal-to-noise ratio and laser linewidth can negatively affect the quality of transmission within an optical network due to e.g. mis-parametrization of the transceiver signal processing algorithms. In this paper, we propose to geometrically optimize a constellation shape that is robust to uncertainties in the channel conditions by utilizing end-to-end learning. In the optimization step, the channel model includes additive noise and residual phase noise. In the testing step, the channel model consists of laser phase noise, additive noise and blind phase search as the carrier phase recovery algorithm. Two noise models are considered for the additive noise: white Gaussian noise and nonlinear interference noise model for fiber nonlinearities. The latter models the behavior of an optical fiber channel more accurately because it considers the nonlinear effects of the optical fiber. For this model, the uncertainty in the signal-to-noise ratio can be divided between amplifier noise figures and launch power variations. For both noise models, our results indicate that the learned constellations are more robust to uncertainties in channel conditions compared to a standard constellation scheme such as quadrature amplitude modulation and standard geometric constellation shaping techniques.

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., Comment: submitted to JLT

In fundamental papers from 1962 [1, 2], Heffener and Haus showed that it is not possible to construct a linear noiseless amplifier. The implies that the amplifier intrinsic noise sources induce random perturbations on the phase of the incoming optical signal which translates into spectral broadening. To achieve the minimum (quantum noise limited) induced phase fluctuation, and the corresponding minimum spectral broadening, an optimum phase measurement method is needed. We demonstrate that a measurement method based on the heterodyne detection and the extended Kalman filtering approaches an optimum phase measurement in the presence of amplifier noise. A penalty of 5 dB (numerical) and 15 dB (experimental) compared to the quantum limited spectral broadening is achieved. For comparison, the conventional phase measurement method's penalty exceeds 30 dB for the measurements. Our results reveal new scientific insights by demonstrating that the impact of amplifier noise can be significantly reduced by using the proposed phase measurement method. An impact is envisioned for the phase-based optical sensing system, as optical amplification could increase sensing distance with the minimum impact on the phase.

We propose an autoencoder-based geometric shaping that learns a constellation robust to SNR and laser linewidth estimation errors. This constellation maintains shaping gain in mutual information (up to 0.3 bits/symbol) with respect to QAM over various SNR and laser linewidth values.

We present a Convolutional Neural Network (CNN) architecture for inverse Raman amplifier design. This model aims at finding the pump powers and wavelengths required for a target signal power evolution, both in distance along the fiber and in frequency. Using the proposed framework, the prediction of the pump configuration required to achieve a target power profile is demonstrated numerically with high accuracy in C-band considering both counter-propagating and bidirectional pumping schemes. For a distributed Raman amplifier based on a 100 km single-mode fiber, a low mean set (0.51, 0.54 and 0.64 dB) and standard deviation set (0.62, 0.43 and 0.38 dB) of the maximum test error are obtained numerically employing 2 and 3 counter, and 4 bidirectional propagating pumps, respectively., Comment: 4 pages, 4 figures

We numerically demonstrate an all-optical nonlinearity pre-compensation module for state-of-the-art long-reach Raman-amplified unrepeatered links. The compensator design is optimized in terms of propagation symmetry to maximize the performance gains under WDM transmission, achieving 4.0dB and 2.6dB of SNR improvement for 250-km and 350-km links.

Training of autoencoders using the back-propagation algorithm is challenging for non-differential channel models or in an experimental environment where gradients cannot be computed. In this paper, we study a gradient-free training method based on the cubature Kalman filter. To numerically validate the method, the autoencoder is employed to perform geometric constellation shaping on differentiable communication channels, showing the same performance as the back-propagation algorithm. Further investigation is done on a non-differentiable communication channel that includes: laser phase noise, additive white Gaussian noise and blind phase search-based phase noise compensation. Our results indicate that the autoencoder can be successfully optimized using the proposed training method to achieve better robustness to residual phase noise with respect to standard constellation schemes such as Quadrature Amplitude Modulation and Iterative Polar Modulation for the considered conditions.

A machine learning framework predicting pump powers and noise figure profile for a target distributed Raman amplifier gain profile is experimentally demonstrated. We employ a single-layer neural network to learn the mapping from the gain profiles to the pump powers and noise figures. The obtained results show highly-accurate gain profile designs and noise figure predictions, with a maximum error on average of ~0.3dB. This framework provides the comprehensive characterization of the Raman amplifier and thus is a valuable tool for predicting the performance of the next-generation optical communication systems, expected to employ Raman amplification., Comment: 4 pages, 5 figures

Optical communication systems are always evolving to support the need for ever-increasing transmission rates. This demand is supported by the growth in complexity of communication systems which are moving towards ultra-wideband transmission and space-division multiplexing. Both directions will challenge the design, modeling, and optimization of devices, subsystems, and full systems. Amplification is a key functionality to support this growth and in this context, we recently demonstrated a versatile machine learning framework for designing and modeling Raman amplifiers with arbitrary gains. In this paper, we perform a thorough experimental characterization of such machine learning framework. The applicability of the proposed approach, as well as its ability to accurately provide flat and tilted gain-profiles, are tested on several practical fiber types, showing errors below 0.5~dB. Moreover, as channel power optimization is heavily employed to further enhance the transmission rate, the tolerance of the framework to variations in the input signal spectral profile is investigated. Results show that the inverse design can provide highly accurate gain-profile adjustments for different input signal power profiles even not considering this information during the training phase., Comment: 11 pages, 12 figures

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., Comment: Submitted to ECOC 2020

Optimizing modulation and detection strategies for a given channel is critical to maximize the throughput of a communication system. Such an optimization can be easily carried out analytically for channels that admit closed-form analytical models. However, this task becomes extremely challenging for nonlinear dispersive channels such as the optical fiber. End-to-end optimization through autoencoders (AEs) can be applied to define symbol-to-waveform (modulation) and waveform-to-symbol (detection) mappings, but so far it has been mainly shown for systems relying on approximate channel models. Here, for the first time, we propose an AE scheme applied to the full optical channel described by the nonlinear Schr\{"o}dinger equation (NLSE). Transmitter and receiver are jointly optimized through the split-step Fourier method (SSFM) which accurately models an optical fiber. In this first numerical analysis, the detection is performed by a neural network (NN), whereas the symbol-to-waveform mapping is aided by the nonlinear Fourier transform (NFT) theory in order to simplify and guide the optimization on the modulation side. This proof-of-concept AE scheme is thus benchmarked against a standard NFT-based system and a threefold increase in achievable distance (from 2000 to 6640 km) is demonstrated.

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.

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$^2$).

Optical communication systems, operating in C-band, are reaching their theoretically achievable capacity limits. An attractive and economically viable solution to satisfy the future data rate demands is to employ the transmission across the full low-loss spectrum encompassing O, E, S, C and L band of the single mode fibers (SMF). Utilizing all five bands offers a bandwidth of up to $\sim$53.5THz (365nm) with loss below 0.4dB/km. A key component in realizing multi-band optical communication systems is the optical amplifier. Apart from having an ultra-wide gain profile, the ability of providing arbitrary gain profiles, in a controlled way, will become an essential feature. The latter will allow for signal power spectrum shaping which has a broad range of applications such as the maximization of the achievable information rate X distance product, the elimination of static and lossy gain flattening filters (GFF) enabling a power efficient system design, and the gain equalization of optical frequency combs. In this paper, we experimentally demonstrate a multi-band (S+C+L) programmable gain optical amplifier using only Raman effects and machine learning. The amplifier achieves >1000 programmable gain profiles within the range from 3.5 to 30 dB, in an ultra-fast way and a very low maximum error of 1.6e-2 dB/THz over an ultra-wide bandwidth of 17.6-THz (140.7-nm)., Comment: 10 pages, 8 figures

Probabilistic shaping for intensity modulation and direct detection (IM/DD) links is discussed and a peak power constraint determined by the limited modulation extinction ratio (ER) of optical modulators is introduced. The input distribution of 4-ary unipolar pulse amplitude modulation (PAM) symbols is optimized for short-reach transmission links without optical amplification nor in-line dispersion compensation. The resulting distribution is symmetric around its mean allowing to use probabilistic amplitude shaping (PAS) to generate symbols that are protected by forward error correction (FEC) and that have the optimal input distribution. The numerical analysis is confirmed experimentally for both an additive white Gaussian noise (AWGN) channel and a fiber channel, showing gains in transmission reach and transmission rate, as well as rate adaptability., Comment: accepted for publication in Journal of Lightwave Technology