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Electronic Boolean logic gates, the foundation of current computation and digital information processing, are reaching final limits in processing power. The primary obstacle is energy consumption which becomes impractically large, > 0.1 fJ/bit per gate, for signal speeds just over several GHz. Unfortunately, current solutions offer either high-speed operation or low-energy consumption. We propose a design for Boolean logic that can achieve both simultaneously (high speed and low consumption), here demonstrated for NOT and XNOR gates. Our method works by passively modifying the phase relationships among the different frequencies of an input data signal to redistribute its energy into the desired logical output pattern. We experimentally demonstrate a passive NOT gate with an energy dissipation of ~1 fJ/bit at 640 Gb/s and use it as a building block for an XNOR gate. This approach is applicable to any system that can propagate coherent waves, such as electromagnetic, acoustic, plasmonic, mechanical, or quantum.

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 ~53.5 THz (365 nm) with loss below 0.4 dB/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 × 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 ${1.6\cdot10^{-2}}$ dB/THz over an ultra-wide bandwidth of 17.6-THz (140.7-nm)

We propose a jointly optimized nonlinear Fourier transform (NFT)-based transmitter and neural network-based receiver. More than two orders of magnitude improvement in bit error ratio is numerically reported for 5600-km transmission compared to a standard NFT system.

An optical pre-processing structure is used to reduce the burden of digital equalizers and increase transmission reach for a direct detected system impaired by chromatic dispersion. The optical pre-processing consists of the optical signal being sliced into narrow frequency sub-band by an optical filter. Two distinct filters are numerically investigated: an arbitrary waveguide grating (AWG) filter and a series of cascaded Mach-Zehnder delay interferometers (MZDI). Each signal’s spectral slice is detected by a photodetector and used as input for the digital equalizer. Two options are also considered for equalization: a feedforward neural network (NN) equalizer and a recurrent neural network with reservoir computing (RC). The results are analyzed in simulation in terms of signalto-noise penalty at the KP4 forward error correction threshold. The penalty is calculated with respect to a back-toback transmission without equalization. A 32 GBd on-off transmission shows 0 dB penalty at ≈25 km transmission reach with optoelectronic processing with FNN and at ≈40 km with RC.

The topic of nonlinear Fourier transform (NFT) will be discussed focusing on the results achieved so far, on current open challenges and on an outlook on future prospects, especially focusing on machine-learning aided NFT systems.

A comprehensive discussion about the application of a machine learning tool to design Raman amplifiers is provided. Simulation and experimental results demonstrate its accuracy in achieving the desired gain profiles.

A perspective on how machine learning can aid the next–generation of classical and quantum optical communication systems is given. We focus on the design of Raman amplifiers and phase tracking at the quantum limit.

Chromatic dispersion is one of the key limitations to increasing the transmission distance-rate product for short-reach communication systems relying on intensity modulation and direct detection. The available optical dispersion-compensation techniques have lost favor due to their high impact on the link loss budget. Alternative digital techniques are usually power-hungry and introduce latency. In this work, we compare different digital, optical and joint hybrid approaches to provide equalization and dispersion compensation for short-reach optical transmission links. Reservoir computing is reviewed as a promising technique to provide equalization with memory in an easily trainable fashion, and the properties of the reservoir network are directly linked to system performance. Furthermore, we propose a new hybrid method relying on reservoir computing combined with a simple signal pre-conditioning stage directly in the optical domain. The optical pre-processing uses an arrayed waveguide grating to split the received signal into narrow sub-bands. The performance of the proposed scheme is thoroughly characterized both in terms of reservoir properties and appropriate preprocessing. The benefits are numerically demonstrated for 32-GBd on-off keying signal transmission, and show an increase in reach from 10 km to 40 km, corresponding to 400%, compared with more complex digital-only techniques.

A machine learning framework for Raman amplifier design is experimentally tested. Performance in terms of maximum error over the gain profile is investigated for various fiber types and lengths, demonstrating highly-accurate designs.

In this paper, a rate-adaptive coded modulation (CM) system combining polar codes and many-to-one probabilistic shaping is constructed and experimentally demonstrated. We propose to control the polar codes using a fraction of bits referred to as pre-set bits. This not only allows to offset the puncturing loss of rate-adaptive polar codes but also provides shaping gains compared to the non-punctured polar codes. Pre-set bits and many-to-one shaping are combined to form a rate-adaptive bit-interleaved CM system. We experimentally evaluate the system performance for 10x8-GBd dual polarization 256 quadrature amplitude modulation (QAM) wavelength division multiplexed (WDM) system with various input data rates ranging from 61 Gbps to 91 Gbps per carrier. The experimental results demonstrate a 200 km reach increase over a wide range of distances compared to the non-punctured polar codes and punctured polar codes.

We present a novel approach to designing transmission links with lumped amplification achieving near optimal nonlinearity compensation by inclusion of an inline OPC. SNR gains of 6.0 dB to 7.5 dB are found numerically in WDM multi-span transmission when comparing to standard EDFA-based systems.

In this paper, a machine learning-based tunable optical-digital signal processor is demonstrated for a short-reach optical communication system. The effect of fiber chromatic dispersion after square-law detection is mitigated using a hybrid structure, which shares the complexity between the optical and the digital domain. The optical part mitigates the chromatic dispersion by slicing the signal into small sub-bands and delaying them accordingly, before regrouping the signal again. The optimal delay is calculated in each scenario to minimize the bit error rate. The digital part is a nonlinear equalizer based on a neural network. The results are analyzed in terms of signal-to-noise penalty at the KP4 forward error correction threshold. The penalty is calculated with respect to a back-to-back transmission without equalization. Considering 32 GBd transmission and 0 dB penalty, the proposed hybrid solution shows chromatic dispersion mitigation up to 200 ps/nm (12 km of equivalent standard single-mode fiber length) for stage 1 of the hybrid module and roughly double for the second stage. A simplified version of the optical module is demonstrated with an approximated 1.5 dB penalty compared to the complete two-stage hybrid module. Chromatic dispersion tolerance for a fixed optical structure and a simpler configuration of the nonlinear equalizer is also investigated.

Nonlinear frequency division multiplexing (NFDM) systems have been showing remarkable progress in the past few years. However, the majority of the demonstrations have neglected the impact of laser phase noise by employing narrowlinewidth lasers and self-homodyne receivers. The impact of transmitter laser linewidth on NFDM transmission is here numerically and experimentally investigated for dual-polarization discrete NFDM systems. The scaling of linewidth tolerance is analyzed for different signal symbol rates and the results are validated experimentally at 250 MBd. Numerical and experimental analysis show a limited degradation due to laser phase noise with relevant penalty appearing only for linewidth-symbol duration products (Δv × Ts) above 10-3. The 250-MBd experimental results indeed show limited penalty for laser linewidths up to 750-kHz and 100-kHz, for back-to-back and 2000-km transmission, respectively.

A wide range of highly–relevant problems in programmable and integrated photonics, optical amplification and communication deal with inverse system design. Typically, a desired output (usually a gain profile, a noise profile, a transfer function or a similar continuous function) is given and the goal is to determine the corresponding set of input parameters (usually a set of input voltages, currents, powers and wavelengths). We present a novel method for inverse system design using machine learning and apply it to Raman amplifier design. Inverse system design for Raman amplifiers consists of selecting pump powers and wavelengths that would result in a targeted gain profile. This is a challenging task due to highly–complex interaction between pumps and Raman gain. Using the proposed framework, highly–accurate predictions of the pumping setup for arbitrary Raman gain profiles are demonstrated numerically in C and C+L–band, as well as experimentally in C band, for the first time. A low mean (0.46 and 0.35 dB) and standard deviation (0.20 and 0.17 dB) of the maximum error are obtained for numerical (C+L–band) and experimental (C–band) results, respectively, when employing 4 pumps and 100 km span length. The presented framework is general and can be applied to other inverse problems in optical communication and photonics in general.

A low complexity solution to mitigate chromatic dispersion is proposed for short-reach communications. The technique relies on sharing complexity between optical and electronic domain and shows gains in terms of required receiver SNR for up to 20-km fiber transmission.

Improvements in SNR (1.98 dB), Mutual Information (0.95 bit/symbol) and maximum transmission distance (almost 12%) are demonstrated for dual-polarization WDM 16-QAM unrepeatered transmission using optical-phase-conjugation-based back-propagation at the receiver through power and dispersion engineering.

In this work, we present a comprehensive experimental and numerical investigation of the impact of system parameters on wavelength converters based on four-wave-mixing, with focus on practical system implementations in addition to the interaction within the nonlinear medium. The input signal power optimization is emphasized according to the trade-off between the linear and the nonlinear impairments, and the origin of the limitations at the optimum is studied. The impact of the input signal quality on the converted idler is discussed, and depending on the dominant noise contribution a varying conversion penalty is demonstrated. The penalty is also shown to scale with increasing number of WDM channels due to additional nonlinear cross-talk between them. Finally, by means of numerical simulations we extend the experimental characterization to high pump powers, showing the impact of parametric noise amplification, and different pump laser linewidths, which lead to increased phase-noise transfer. The experimental characterization employs an integrated AlGaAs-on-insulator waveguide, and the numerical simulations accompany the results to make the analysis general for $\chi^{(3)}$ materials that satisfy the assumptions of the split-step Fourier method.

The impact of Wiener phase noise on NFDM transmission is experimentally investigated for dual-polarization discrete NFDM systems. The results show minimal OSNR penalty in back-to-back and limited degradation for 2000-km transmission for 750-kHz and 100-kHz linewidth. respectively

We propose, numerically analyze and experimentally demonstrate a low-complexity, modulation-order independent, non-data-aided (NDA), feed-forward carrier phase recovery (CPR) algorithm. The proposed algorithm enables synchronous decoding of arbitrary square-quadrature amplitude modulation (QAM) constellations and it is suitable for a realistic hardware implementation based on block-wise parallel processing. The proposed method is based on principal component analysis (PCA) and it outperforms the well-known and widely used blind phase search (BPS) algorithm at low signal-to-noise ratio (SNR) values, showing much lower cycle slip rate (CSR) both numerically and experimentally. For operation at higher SNR values, a hybrid two-stage implementation combining the proposed method and BPS is also proposed and their performance are investigated benchmarking them against the two-stage BPS (2S-BPS). The complexity of the proposed simple and hybrid methods are evaluated against 2S-BPS and computational complexity savings of 92% and 40% are expected for the simple and hybrid methods, respectively.

Nonlinear distortion experienced by signals during their propagation through optical fibers strongly limits the throughput of optical communication systems. Recently, a strong research focus has been dedicated to nonlinearity mitigation and compensation techniques. At the same time, a more disruptive approach, the nonlinear Fourier transform (NFT), aims at designing signaling schemes more suited to the nonlinear fiber channel. In a short period, impressive results have been reported by modulating either the continuous spectrum or the discrete spectrum. Additionally, very recent works further introduced the opportunity to modulate both spectra for single polarization transmission. Here, we extend the joint modulation scheme to dual-polarization transmission by introducing the framework to construct a dual-polarization optical signal with the desired continuous and discrete spectra. After a brief analysis of the numerical algorithms used to implement the proposed scheme, the first experimental demonstration of dual-polarization joint nonlinear frequency division multiplexing (NFDM) modulation is reported for up to 3200 km of low-loss transmission fiber. The proposed dual-polarization joint modulation schemes enables to exploit all the degrees of freedom for modulation (both polarizations and both spectra) provided by a single-mode fiber (SMF).

This document provides supplementary information to "Dual polarization nonlinear Fourier transform-based optical communication system," https://doi.org/10.1364/optica.5.000263. We present the mathematical derivation of the forward-backward trapezoidal algorithm for the Manakov system, which allows the efficient computation of the scattering data from the time domain dual polarization signal. We furthermore describe the optimization procedure followed in order to choose the scattering coefficients constellations for the transmission focusing on the approach we applied to minimize the peak-to-average power ratio of the transmitted waveform. Finally we present a brief analysis of the noise affecting the eigenvalue and the scattering coefficients.

We propose a novel scheme with a “time-lens”-based partial optical Fourier transform (OFT) and coherent sampling for high-speed complex orthogonal frequency-division multiplexing (OFDM) signal detection. Compared with all-optical OFDM demultiplexing with a matched optical filter, our proposed method replaces specialized optical filters with commercially available equipment, which relaxes stringent manufacturing and operational requirements. Our simulation shows that even with a partial OFT, theoretically, close to inter-channel interference-free performance is possible. In addition, we performed a proof-of-concept experiment of 16 × 10 Gbaud quadrature phase-shift keying (QPSK) all-optical OFDM detection, with all the bit error rates far below the 7% hard-overhead forward error correction limit.