Chromatic Dispersion Compensation Research Articles

Parallel wavelength-division-multiplexed signal transmission and dispersion compensation enabled by soliton microcombs and microrings

The proliferation of computation-intensive technologies has led to a significant rise in the number of datacenters, posing challenges for high-speed and power-efficient datacenter interconnects (DCIs). Although inter-DCIs based on intensity modulation and direct detection (IM-DD) along with wavelength-division multiplexing technologies exhibit power-efficient and large-capacity properties, the requirement of multiple laser sources leads to high costs and limited scalability, and the chromatic dispersion (CD) restricts the transmission length of optical signals. Here we propose a scalable on-chip parallel IM-DD data transmission system enabled by a single-soliton Kerr microcomb and a reconfigurable microring resonator-based CD compensator. We experimentally demonstrate an aggregate line rate of 1.68 Tbit/s over a 20-km-long SMF. The extrapolated energy consumption for CD compensation of 40-km-SMFs is ~0.3 pJ/bit, which is calculated as being around 6 times less than that of the commercial 400G-ZR coherent transceivers. Our approach holds significant promise for achieving data rates exceeding 10 terabits.

Modified CFBG-based approach for chromatic dispersion compensation in high speed DWDM links.

Chromatic dispersion (CD) is a major concern in high speed fiber optics communication systems. This work presents an efficient optical compensation technique with reduced complexity to mitigate CD effects in single mode fiber (SMF) at high data rates. The proposed method includes a post-dispersion mitigation system using a single linear chirped fiber Bragg grating (CFBG) with tanh apodization. Here, various parameters of CFBG, such as grating length, effective refractive index, and apodization function, are optimized to achieve effective CD compensation. Then, the system is extended to a 16-channel WDM link with each channel carrying data at 25Gbps over 100km. The simulation results show that the proposed model enhances the system performance while minimizing overall system complexity. The proposed system is also compatible with the prevailing fiber optics networks. The results are consistent with the findings published in recent studies.

Joint intra and inter-channel nonlinear compensation scheme based on improved learned digital back propagation for WDM systems.

In this paper, we improve the learned digital back propagation (LDBP) and propose a novel joint intra and inter-channel nonlinearity compensation scheme for polarization division multiplexing wavelength-division multiplexed (PDM-WDM) systems. From the perspective of interpretable neural network, the scheme realizes the alternating compensation of chromatic dispersion (CD) and nonlinearity based on physical models. The chromatic dispersion compensation (CDC) adopts one-dimensional convolution operation in the time domain. Moreover, the pulse-broadening effect is introduced into the overlap-and-save method. For nonlinear compensation, the improved joint model is applied, and the impact of the intra-channel pulse broadening and the walk-off effect between different channels caused by CD on the nonlinear effect is considered. To validate the effectiveness of the proposed scheme, we construct an 11-channel simulation system of 36 GBaud PDM uniform 16 quadrature amplitude modulation (PDM-16QAM) 1600 km and 64 GBaud PDM-64QAM 400 km, as well as a 5-channel experimental system of 28 GBaud PDM-16QAM 806.4 km. The simulation results show that the performance of PDM-16QAM with 0.5 steps per span and PDM-64QAM with 2 steps per span improve the Q-factor by approximately 0.75 dB and 0.54 dB at the optimal launch power, compared with the linear compensation scheme. The transmission performance of PDM-16QAM is higher than that of digital back propagation with 5 steps per span (DBP-5StPS), and the complexity is only 31.36% of that of DBP-5StPS. The performance of PDM-64QAM is higher than that of DBP-10StPS, with a complexity of 62.72%. The experimental results show that the performance of PDM-16QAM with 0.5 steps per span is improved with 0.86 dB Q-factor improvement compared with the linear compensation scheme at the optimal launch power, and the performance of the proposed scheme is higher than that of DBP-5StPS with a complexity of only 23.68%.

Distributed Chromatic Dispersion Compensation Method Based on Mismatch Factor for High Resolution OFDR

Distributed Chromatic Dispersion Compensation Method Based on Mismatch Factor for High Resolution OFDR

Integrated-optic chromatic dispersion compensator with completely passive operation and wide operational bandwidth

I report on a fiber chromatic dispersion compensator comprising an array of 100 fixed delay lines sandwiched by a pair of arrayed-waveguide grating-type wavelength filters. The requisite delay for the dispersion compensation is allocated to each demultiplexed wavelength component after the first wavelength filter, and the wavelength components are again multiplexed at the second filter. The flexible capability of delay pattern arrangement enables us to realize various fixed dispersion compensation characteristics. I show transmittance and relative delay time characteristics of a multichannel dispersion compensator for short-distance wavelength division multiplexing communication, and its application to dispersion compensation for a pulse amplitude modulation four signal. I also demonstrate the realization of a dispersion slope compensator for a dispersion-shifted fiber with this configuration.

Compensating Chromatic Dispersion and Phase Noise using Parallel AFB-MBPS For FBMC-OQAM Optical Communication System

Filter Bank Multi-Carrier Offset-QAM (FBMC-OQAM) is one of the hottest topics in research for 5G multi-carrier methods because of its high efficiency in the spectrum, minimal leakage in the side lobes, zero cyclic prefix (CP), and multiphase filter design. Large-scale subcarrier configurations in optical fiber networks need the use of FBMC-OQAM. Chromatic dispersion is critical in optical fiber transmission because it causes different spectral waves (color beams) to travel at different rates. Laser phase noise, which arises when the phase of the laser output drifts with time, is a major barrier that lowers throughput in fiber-optic communication systems. This deterioration may be closely related among channels that share lasers in multichannel fiber-optic systems using methods like wavelength-division multiplexing with frequency combs or space-division multiplexing. In this research, we use parallel Analysis Filter Bank (AFB) equalizers in the receiver part of the FBMC OQAM Optical Communication system to compensate for chromatic dispersion (CD) and phase noise (PN). Following the equalization of CD compensation, the phase of the carriers in the received signal is tracked and compensated using Modified Blind Phase Search (MBPS). The CD and PN compensation techniques are simulated and analyzed numerically and graphically to determine their efficacy. To evaluate the FBMC's efficiency across various equalizers, 16-OQAM is taken into account. Bit Error Rate (BER), Optical Signal-to-Noise Ratio (OSNR), Q-Factor, and Mean Square Error (MSE) were the primary metrics we utilized to evaluate performance. Single-tap equalizer, multi-tap equalizer (N=3), ISDF equalizer with suggested Parallel Analysis Filter Banks (AFBs) (K=3), and MBPS were all set aside for comparison. When compared to other forms of Nonlinear compensation (NLC), the CD and PN tolerance attained by Parallel AFB equalization with MBPS is the greatest.

Adaptive dispersion compensation using a photonic integrated circuit finite impulse response filter.

Optical equalization can be used for chromatic dispersion compensation in optical communication systems to improve the system performance; however, optical signal processing (OSP) is generally specifically designed for transmission channels, that is non-adaptive to dynamic transmission distortions compared with digital signal processing (DSP). In this contribution, we demonstrate optical equalization using a photonic integrated circuit (PIC) filter for chromatic dispersion compensation, with static and adaptive techniques: (a) the static optical equalizer is calibrated based on the known fiber dispersion and length, by using the fractional delay reference method; (b) the adaptive optical equalizer is updated iteratively to compensate transmission impairments based on a least-mean squares (LMS) algorithm. Experimental results show that both the static optical equalizer and the adaptive optical LMS equalizer can give an 18-dB Q-factor for a 14-Gbd QPSK signal transmitting over 30 km. To highlight the capability of the optical equalizers, we use simulations to show the improvement in dispersion compensating characteristics by implementing additional taps.

Chromatic Dispersion Compensation in Phase-Stabilized Dissemination System of Broadband Signals Based on Phase Conjugation

Chromatic Dispersion Compensation in Phase-Stabilized Dissemination System of Broadband Signals Based on Phase Conjugation

Low-complexity clustered polynomial nonlinear filter-based electrical dispersion pre-compensation scheme in IM/DD transmission systems.

A polynomial nonlinear filter (PNLF)-based electrical dispersion pre-compensation (pre-EDC) scheme assisted with Gerchberg-Saxton (GS) algorithm is proposed to compensate the chromatic dispersion (CD) for intensity-modulation and direct-detection (IM/DD) optical transmission systems, where PNLF is utilized to fit the nonlinear transfer function of the iterative GS algorithm-based pre-EDC scheme to realize a low-complexity non-iterative CD pre-compensation. The capability of PNLF to fit the nonlinear iterative process enables the PNLF-based pre-EDC scheme to compensate for CD-induced linear distortions and address CD-induced nonlinear distortions, which are typically captured through iterative approaches. Additionally, to further reduce the computational complexity, we also introduce the k-means clustering algorithm to eliminate the weight redundancy and propose a lower-complexity clustered PNLF-based pre-EDC scheme. Simulation results show that PNLF-based and clustered PNLF-based pre-EDC schemes save 76.0% and 97.5% complexity with only 0.3 dB receiver sensitivity penalty at 20% forward error correction (FEC) threshold, compared with GS-based pre-EDC scheme in C-band 56 GBaud 80-km on-off keying (OOK) system. Furthermore, the effectiveness of PNLF-based and clustered PNLF-based pre-EDC schemes is also evaluated through the experimental demonstration. Experimental results show that under C-band 32 GBaud 80-km OOK system, bit error ratio (BER) satisfying 20% FEC threshold is achieved by applying PNLF-based and clustered PNLF-based pre-EDC schemes, which save 78.3% and 94.2% complexity with only 0.4 dB receiver sensitivity penalty compared with GS-based pre-EDC scheme, respectively. The research results indicate that the (clustered) PNLF-based pre-EDC scheme has the great application potential for CD compensation in high-performance and low-cost IM/DD optical transmission systems.

Reducing Computational Complexity of Neural Networks in Optical Channel Equalization: From Concepts to Implementation

In this paper, a new methodology is proposed that allows for the low-complexity development of neural network (NN) based equalizers for the mitigation of impairments in high-speed coherent optical transmission systems. In this work, we provide a comprehensive description and comparison of various deep model compression approaches that have been applied to feed-forward and recurrent NN designs. Additionally, we evaluate the influence these strategies have on the performance of each NN equalizer. Quantization, weight clustering, pruning, and other cutting-edge strategies for model compression are taken into consideration. In this work, we propose and evaluate a Bayesian optimization-assisted compression, in which the hyperparameters of the compression are chosen to simultaneously reduce complexity and improve performance. Next, this paper presents four distinct metrics (RMpS, BoP, NABS, and NLGs) that are discussed here that can be used to evaluate the amount of computing complexity required by various compression algorithms. These measurements can serve as a benchmark for evaluating the relative effectiveness of various NN equalizers when compression approaches are used. In conclusion, the trade-off between the complexity of each compression approach and its performance is evaluated by utilizing both simulated and experimental data in order to complete the analysis. By utilizing optimal compression approaches, we show that it is possible to design an NN-based equalizer that is simpler to implement and has better performance than the conventional digital back-propagation (DBP) equalizer with only one step per span. This is accomplished by reducing the number of multipliers used in the NN equalizer after applying the weighted clustering and pruning algorithms. Furthermore, we demonstrate that an equalizer based on NN can also achieve superior performance while still maintaining the same degree of complexity as the full electronic chromatic dispersion compensation block. We conclude our analysis by highlighting open questions and existing challenges, as well as possible future research directions.

High-performance end-to-end deep learning IM/DD link using optics-informed neural networks.

In this paper, we introduce optics-informed Neural Networks and demonstrate experimentally how they can improve performance of End-to-End deep learning models for IM/DD optical transmission links. Optics-informed or optics-inspired NNs are defined as the type of DL models that rely on linear and/or nonlinear building blocks whose mathematical description stems directly from the respective response of photonic devices, drawing their mathematical framework from neuromorphic photonic hardware developments and properly adapting their DL training algorithms. We investigate the application of an optics-inspired activation function that can be obtained by a semiconductor-based nonlinear optical module and is a variant of the logistic sigmoid, referred to as the Photonic Sigmoid, in End-to-End Deep Learning configurations for fiber communication links. Compared to state-of-the-art ReLU-based configurations used in End-to-End DL fiber link demonstrations, optics-informed models based on the Photonic Sigmoid show improved noise- and chromatic dispersion compensation properties in fiber-optic IM/DD links. An extensive simulation and experimental analysis revealed significant performance benefits for the Photonic Sigmoid NNs that can reach below BER HD FEC limit for fiber lengths up to 42 km, at an effective bit transmission rate of 48 Gb/s.

Power-Efficient Voronoi Constellations for Fiber-Optic Communication Systems

Voronoi constellations (VCs) are considered as an effective geometric shaping method due to their high power efficiencies and low complexity. In this paper, the performance of 16- and 32-dimensional VCs with a variety of spectral efficiencies transmitted in the nonlinear fiber channel are investigated. Both single-channel and wavelength-division multiplexing systems are considered for the transmission of the VCs, as well as different signal processing schemes, including chromatic dispersion compensation and digital backpropagation. Multiple performance metrics including the uncoded bit error rate, mutual information (MI), and generalized mutual information (GMI) of VCs are evaluated. Compared with quadrature amplitude modulation (QAM) formats, the VCs provide 1.0–2.4 dB launch power gains, up to 0.50 bits/symbol/dimension-pair MI gains, up to around 30% potential reach increase at the same MI, and up to 0.30 bits/symbol/dimension-pair GMI gains in a limited launch power range. The observed performance gains over QAM are found higher than in the back-to-back case. Moreover, a general GMI estimation method for very large constellations using importance sampling is proposed for the first time.

Receiver IQ Imbalance and Skew Compensation for High Order Modulation Formats by Frequency Domain 4 × 2 MIMO

A typical coherent front-end may encounter imperfections, such as amplitude imbalance, phase imbalance and skew, between four sampling channels. These receiver (Rx) imperfections, together with traditional chromatic dispersion (CD) compensation, would induce in-phase (I) and quadrature (Q) mixing, which greatly degrades the system performance. In this work, we propose a modulation format independent frequency domain (FD) 4 × 2 multi-inputs and multi-outputs (MIMO) based on decision directed least mean square (DD-LMS) algorithm to solve this problem. Compared with traditional 2 × 2 MIMO, it enables to compensate for all of Rx imperfections. Compared with 4 × 4 MIMO, it can eliminate performance penalty induced by the IQ mixing after optical fiber transmission. Compared with traditional time domain 4 × 2 MIMO, the proposed FD 4 × 2 MIMO has advantages in terms of complexity and parallel processing. We also evaluate the Rx imperfections compensation capability, noise tolerance tolerance, polarization tracking capability, residual CD and transmitter imperfections tolerance of the proposed equalizers. The proposed FD 4 × 2 MIMO algorithms are verified by numerical simulation with different modulation formats and experimentally validated with 40 Gbaud polarization division multiplexed 16-ary quadrature amplitude modulation signal.

Surface-emitting THz quantum cascade laser frequency comb with tunable external mirror dispersion compensation

We present a surface emitting THz quantum cascade laser frequency comb with an adjustable chromatic dispersion compensation via a mechanically tunable GTI cavity. Surface emission and high optical feedback into the laser cavity are achieved by a planarized ridge waveguide design with low reflectivity facets and two broadband patch array antennas for coupling to an external mirror (back side) and for power extraction (front side). We demonstrate direct and reproducible manipulation of the frequency comb state, specifically the comb stability and beatnote frequency tuning, by controlling the position of an external movable mirror.

Enhanced dispersion reduction using apodized uniform fiber Bragg grating for optical MTDM transmission systems

The aim of this work is to propose a model for enhancing chromatic dispersion compensation in standard single mode optical fibers (SSMFs). The proposed model consists of a single stage Apodized Uniform Fiber Bragg Gratings (AUFBG) in a post-compensation scheme. It is based on the Maximum Time Division Multiplexing (MTDM) technique. The performance of the proposed model is evaluated through the quality factor (Q-factor) and Bit Error Rate (BER) in four cases, in a comparative study. In case one, the system performance is evaluated without using UFBG. The other cases study the effect of the proposed model with using different connections schemes and the most common apodization functions. For simulation, the proposed model is connected in a 10 Gbps WDM 70 km link under ordinary operating parameters. The simulation and evaluation process is conducted by Optisystem 7.0. In the pre-compensation scheme, the best results are obtained as a maximum Q-factor of 9.2 and a minimum BER of 3.25 × 10–20, using a tanh apodization function. The proposed model realizes an improvement over the related work by at least ~ 68%.

Continuous entanglement distribution over a transnational 248 km fiber link

Reliable long-distance distribution of entanglement is a key technique for many quantum applications, most notably quantum key distribution. Here, we present a continuously working, trusted-node free international link between Austria and Slovakia, directly distributing polarization-entangled photon pairs via 248 km of deployed telecommunication fiber. Despite 79 dB loss, we observe stable detected pair rates of 9 s−1 over 110 h. We mitigate multi-pair detections with strict temporal filtering, enabled by nonlocal compensation of chromatic dispersion and superconducting nanowire detectors. Fully automatized active polarization stabilization keeps the entangled state’s visibility at 86% for altogether 82 h. In a quantum cryptography context, this corresponds to an asymptotic secure key rate of 1.4 bits/s and 258 kbit of total key, considering finite-key effects. Our work paves the way for low-maintenance, ultra-stable quantum communication over long distances, independent of weather conditions and time of day, thus constituting an important step towards the quantum internet.

Complexity reduction over Bi-RNN-based nonlinearity mitigation in dual-pol fiber-optic communications via a CRNN-based approach

Bidirectional recurrent neural networks (bi-RNNs), in particular bidirectional long short term memory (bi-LSTM), bidirectional gated recurrent unit, and convolutional bi-LSTM models, have recently attracted attention for nonlinearity mitigation in fiber-optic communication. The recently adopted approaches based on these models, however, incur a high computational complexity which may impede their real-time functioning. In this paper, by addressing the sources of complexity in these methods, we propose a more efficient network architecture, where a convolutional neural network encoder and a unidirectional many-to-one vanilla RNN operate in tandem, each best capturing one set of channel impairments while compensating for the shortcomings of the other. We deploy this model in two different receiver configurations. In one, the neural network is placed after a linear equalization chain and is merely responsible for nonlinearity mitigation; in the other, the neural network is directly placed after the chromatic dispersion compensation and is responsible for joint nonlinearity and polarization mode dispersion compensation. For a 16-QAM 64 GBd dual-polarization optical transmission over 14×80km standard single-mode fiber, we demonstrate that the proposed hybrid model achieves the bit error probability of the state-of-the-art bi-RNN-based methods with greater than 50% lower complexity, in both receiver configurations.

Chromatic dispersion compensation by cascaded FBG with duobinary modulation scheme

In this paper, we propose a dispersion compensation model to minimize the chromatic dispersion to enhance system performance. The proposed model is based on applying the duobinary modulation scheme on 4-stages of cascaded identical apodized uniform fiber Bragg grating. Different apodization functions are tested to determine the one that provides the best performance. The proposed model is connected in three different connection schemes: pre, post and symmetrical, to get the best connection. To evaluate the performance of the proposed system, a comparative study is conducted using non-return to zero (NRZ) and modified duobinary (MDB) modulation schemes. For evaluation, a 10 Gbps WDM link is simulated at a distance of 100 km under a set of predefined operating parameters. Optisystem 17.0 is used for simulation and evaluation. Both quality factor (Q-factor) and bit error rate (BER) are used as performance indices. All cases of NRZ modulation scheme do not meet the minimum operational requirements in terms of Q-factor and BER. Only in the case of MDB modulation scheme, the symmetrical compensation with tanh apodization meets the minimum operational requirements with a Q-factor of 6.39 and BER of 8.44 × 10–11. The proposed model achieves better results as compared to the other modulation schemes: a maximum Q-factor values of 8.964 and a BER of 1.3 × 10–19 with tanh apodization in the pre-compensation scheme. As compared to related work, the system performance achieves ~ 99% improvement.

Bi-Directional Self-Homodyne Transmission With MIMO-Free DSP for Next-Generation Data Center Interconnects

We propose and demonstrate bi-directional (BiDi) self-homodyne coherent detection (SHCD) system experimentally, in which the multiple input multiple output free (MIMO-free) digital signal processing (DSP) is achieved with the help of BiDi-operated adaptive polarization controller (APC). Since the polarization wandering of the local oscillator (LO) is relevant to that of the counter-propagating signal within the same fiber, the APC can realize the polarization tracking and compensation for LO and the counter-propagating signal simultaneously. The power-consuming 2x2 MIMO DSP, can be eliminated in our proposed BiDi SHCD system. The frequency offset compensation (FOC), carrier phase recovery (CPR) are also omitted thanks to the SHCD. Besides, the dedicated chromatic dispersion compensation (CDC) is no longer needed due to short-reach transmission of data center interconnect (DCI). We validate in experiment the proposed system using 23GBaud DP-32QAM signal delivering 230Gb/s over 2 km of single mode fibers (SMFs) with the laser-linewidth tolerance of 1MHz. The parameters of polarization tracking algorithm are optimized to attain the polarization rotation tolerance up to 850 rad/s under the FEC threshold of 2x10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−2</sup> . The proposed BiDi SHCD system achieves the coherent-lite DSP without MIMO, FOC, CPR and dedicated CDC algorithm in dynamic state of polarization (SOP) rotation while maintaining the full spectral efficiency (SE) of traditional coherent system.

Design of fully interpretable neural networks for digital coherent demodulation.

In this paper, we propose a digital coherent demodulation architecture using fully interpretable deep neural networks (NNs). We show that all the conventional coherent digital signal processing (DSP) is deeply unfolded into a well-structured NN so that the established training algorithms in machine learning can be applied. In contrast to adding or replacing certain algorithms of existing DSP in coherent receivers, we replace all the coherent demodulation algorithms with a fully interpretable NN (FINN), making the whole NN interpretable. The FINN is modular and flexible to add or drop modules, including chromatic dispersion compensation (CDC), the digital back-propagation (DBP) algorithm for fiber nonlinearity compensation, carrier recovery and residual impairments. The resulted FINN can be quickly initialized by straightforwardly referring to the conventional DSP, and can also enjoy further performance enhancement in the nonlinear fiber transmissions by NN. We conduct a 132-Gb/s polarization multiplexed (PM)-16QAM transmission experiment over 600-km standard single mode fiber. The experimental results show that without fiber nonlinearity compensation, FINN-CDC obtains less than 0.06-dB SNR gain than chromatic dispersion compensation (CDC). However, with fiber nonlinearity compensation, 2-steps per span FINN-DBP (FINN-2sps-DBP) and FINN-1sps-DBP bring about 0.59-dB and 0.53-dB SNR improvement compared with the conventional 2sps-DBP and 1sps-DBP, respectively.