Performance limits in optical communications due to fiber nonlinearity

In this paper, we review the historical evolution of predictions of the performance of optical communication systems. We will describe how such predictions were made from the outset of research in laser based optical communications and how they have evolved to their present form, accurately predicting the performance of coherently detected communication systems.

[1]  Nori Shibata,et al.  A NOVEL OPTICAL DUOBINARY TRANSMISSION SYSTEM WITH NO RECEIVER SENSITIVITY DEGRADATION , 1995 .

[2]  Zabih Ghassemlooy,et al.  Artificial Neural Network Nonlinear Equalizer for Coherent Optical OFDM , 2015, IEEE Photonics Technology Letters.

[3]  Andrew R. Chraplyvy.  Optical power limits in multi-channel wavelength-division-multiplexed systems due to stimulated Raman scattering , 1984 .

[4]  Masataka Nakazawa,et al.  400 Gbit/s 256 QAM-OFDM transmission over 720 km with a 14 bit/s/Hz spectral efficiency by using high-resolution FDE. , 2013, Optics express.

[5]  Giuseppe Durisi,et al.  Capacity of a Nonlinear Optical Channel With Finite Memory , 2014, Journal of Lightwave Technology.

[6]  Xiang Zhou,et al.  Performance limitation due to statistical Raman crosstalk in a WDM system with multiple-wavelength bidirectionally pumped Raman amplification , 2003 .

[7]  Sergei K. Turitsyn,et al.  Phase-Conjugated Pilots for Fibre Nonlinearity Compensation in CO-OFDM Transmission , 2015, Journal of Lightwave Technology.

[8]  N. Olsson.  Lightwave systems with optical amplifiers , 1989 .

[9]  F. Derr,et al.  Coherent optical QPSK intradyne system: concept and digital receiver realization , 1992 .

[10]  Andrew Lord,et al.  The impact of capacity growth in national telecommunications networks , 2016, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[11]  S. Radic,et al.  Two-fold transmission reach enhancement enabled by transmitter-side digital backpropagation and optical frequency comb-derived information carriers. , 2015, Optics express.

[12]  I. Fair,et al.  On Four-Wave Mixing Suppression in Dispersion-Managed Fiber-Optic OFDM Systems With an Optical Phase Conjugation Module , 2011, Journal of Lightwave Technology.

[13]  Xiang Liu,et al.  Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit , 2013, Nature Photonics.

[14]  T. Okoshi,et al.  Suppression of beat noise from optical amplifiers using coherent receivers , 1994 .

[15]  Polina Bayvel,et al.  4 Tb/s Transmission Reach Enhancement Using 10 × 400 Gb/s Super-Channels and Polarization Insensitive Dual Band Optical Phase Conjugation , 2016, Journal of Lightwave Technology.

[16]  K. Kikuchi,et al.  Parametric instability of optical amplifier noise in long-distance optical transmission systems , 1997 .

[17]  Cristian B. Czegledi,et al.  On the limits of digital back-propagation in the presence of transceiver noise. , 2017, Optics express.

[18]  Rakefet Weidenfeld,et al.  Phased-array cancellation of nonlinear FWM in coherent OFDM dispersive multi-span links. , 2008, Optics express.

[19]  Yu-Ting Hsueh,et al.  System Performance Prediction With the Gaussian Noise Model in 100G PDM-QPSK Coherent Optical Networks , 2013, Journal of Lightwave Technology.

[20]  C. Kurtzke,et al.  Suppression of fiber nonlinearities by appropriate dispersion management , 1993, IEEE Photonics Technology Letters.

[21]  Nobuhiko Kikuchi,et al.  High-spectral efficiency DWDM transmission of 100-Gbit/s/lambda IM/DD single sideband-baseband-Nyquist-PAM8 signals , 2017, 2017 Optical Fiber Communications Conference and Exhibition (OFC).

[22]  E.S.R. Sikora,et al.  Catastrophic damage and accelerated ageing in bent fibres caused by high optical powers , 2000 .

[23]  D. Rafique,et al.  Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems. , 2011, Optics express.

[24]  Wenjun Zhou,et al.  Transmission of a 120-GBd PM-NRZ Signal Using a Monolithic Double-Side EML , 2016, IEEE Photonics Technology Letters.

[25]  Idelfonso Tafur Monroy,et al.  Real-time 200 Gb/s (4×56.25 Gb/s) PAM-4 transmission over 80 km SSMF using quantum-dot laser and silicon ring-modulator , 2017, 2017 Optical Fiber Communications Conference and Exhibition (OFC).

[26]  Sergei K. Turitsyn,et al.  Optical rogue waves in telecommunication data streams , 2011 .

[27]  John D. Downie,et al.  Capacity-approaching transmission over 6375 km at spectral efficiency of 8.3 bit/s/Hz , 2016, 2016 Optical Fiber Communications Conference and Exhibition (OFC).

[28]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[29]  N. Hanik,et al.  RZ versus NRZ modulation format for dispersion compensated SMF-based 10-Gb/s transmission with more than 100-km amplifier spacing , 1999, IEEE Photonics Technology Letters.

[30]  Frank R. Kschischang,et al.  Implications of information theory in optical fibre communications , 2016, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[31]  Alexei N. Pilipetskii,et al.  SDM for power efficient transmission , 2017, 2017 Optical Fiber Communications Conference and Exhibition (OFC).

[32]  René-Jean Essiambre,et al.  Capacity Trends and Limits of Optical Communication Networks , 2012, Proceedings of the IEEE.

[33]  Behrouz Farhang-Boroujeny,et al.  OFDM Versus Filter Bank Multicarrier , 2011, IEEE Signal Processing Magazine.

[34]  Kenneth O. Hill,et al.  cw three-wave mixing in single-mode optical fibers , 1978 .

[35]  Rameez Asif,et al.  Logarithmic step-size based digital backward propagation in N-channel 112Gbit/s/ch DP-QPSK transmission , 2011, 2011 13th International Conference on Transparent Optical Networks.

[36]  Polina Bayvel,et al.  Replacing the Soft FEC Limit Paradigm in the Design of Optical Communication Systems , 2015, ArXiv.

[37]  P. Bayvel,et al.  Prediction of transmission penalties due to cross-phase modulation in WDM systems using a simplified technique , 2000, IEEE Photonics Technology Letters.

[38]  Tetsuya Miki,et al.  High-speed digital-signal transmission experiments by optical wavelength-division multiplexing , 1977 .

[39]  Geert Morthier,et al.  69 Gb/s DMT direct modulation of a heterogeneously integrated InP-on-Si DFB laser , 2017, 2017 Optical Fiber Communications Conference and Exhibition (OFC).

[40]  T. Sugie.  Impact of SBS on CPFSK coherent transmission systems using dispersion-shifted fiber , 1993, IEEE Photonics Technology Letters.

[41]  S. G. Evangelides,et al.  Reduction of the nonlinear impairment in ultralong lightwave systems by tailoring the fibre dispersion , 1994 .

[42]  Paolo Serena.  Nonlinear Signal–Noise Interaction in Optical Links With Nonlinear Equalization , 2016, Journal of Lightwave Technology.

[43]  Polina Bayvel,et al.  Experimental characterisation of digital Nyquist pulse-shaped dual-polarisation 16QAM WDM transmission and comparison with the Gaussian noise model of nonlinear propagation , 2014, 2014 16th International Conference on Transparent Optical Networks (ICTON).

[44]  B R Suydam,et al.  Optical phase conjugation for time-domain undoing of dispersive self-phase-modulation effects. , 1983, Optics letters.

[45]  N. J. Doran.  Soliton communications systems: the concept is alive , 2001, LEOS 2001. 14th Annual Meeting of the IEEE Lasers and Electro-Optics Society (Cat. No.01CH37242).

[46]  Hung Nguyen Tan,et al.  Approaching Complete Cancellation of Nonlinearity in WDM Transmission Through Optical Phase Conjugation , 2015 .

[47]  Stylianos Sygletos,et al.  Injection locking-based pump recovery for phase-sensitive amplified links. , 2013, Optics express.

[48]  D. Christodoulides,et al.  Evolution of stimulated Raman crosstalk in wavelength division multiplexed systems , 1996, IEEE Photonics Technology Letters.

[49]  Rameez Asif,et al.  Nonlinear mitigation using carrier phase estimation and digital backward propagation in coherent QAM transmission , 2012, 2012 38th European Conference and Exhibition on Optical Communications.

[50]  N. Rossi,et al.  Nonlinear interference noise statistics in unmanaged coherent networks with channels propagating over different lightpaths , 2014, 2014 The European Conference on Optical Communication (ECOC).

[51]  Yojiro Mori,et al.  Novel Polarization-diversity Scheme Based on Mutual Phase Conjugation for Fiber-nonlinearity Mitigation in Ultra-long Coherent Optical Transmission Systems , 2013 .

[52]  Munehiko Nagatani,et al.  Discrete Multitone Transmission at Net Data Rate of 250 ${\text{Gb/s}}$ Using Digital-Preprocessed Analog-Multiplexed DAC With Halved Clock Frequency and Suppressed Image , 2017, Journal of Lightwave Technology.

[53]  Peter A. Andrekson,et al.  Mitigation of nonlinear impairments on QPSK data in phase-sensitive amplified links , 2013 .

[54]  Polina Bayvel,et al.  High spectral density transmission emulation using amplified spontaneous emission noise. , 2016, Optics letters.

[55]  Francesco Da Ros,et al.  Multichannel nonlinear distortion compensation using optical phase conjugation in a silicon nanowire. , 2015, Optics express.

[56]  J. Conradi,et al.  Multilevel signaling for increasing the reach of 10 Gb/s lightwave systems , 1999 .

[57]  Gabriella Bosco,et al.  GN-Model Validation Over Seven Fiber Types in Uncompensated PM-16QAM Nyquist-WDM Links , 2014, IEEE Photonics Technology Letters.

[58]  Sethumadhavan Chandrasekhar,et al.  Multi-channel nonlinearity compensation of 128-Gb/s PDM-QPSK signals in dispersion-managed transmission using dispersion-folded digital backward propagation , 2014, OFC.

[59]  A. D. Ellis,et al.  Four wave mixing in ultra long transmission systems incorporating linear amplifiers , 1990 .

[60]  A D Ellis,et al.  Timing and phase jitter suppression in coherent soliton transmission. , 2014, Optics letters.

[61]  T. S. Kinsel,et al.  Wide-band optical communication systems: Part I—Time division multiplexing , 1970 .

[62]  K J Blow,et al.  Suppression of soliton interactions by periodic phase modulation. , 1994, Optics letters.

[63]  A. Ellis,et al.  Capacity limits of systems employing multiple optical phase conjugators. , 2015, Optics express.

[64]  K. Kao,et al.  Dielectric-fibre surface waveguides for optical frequencies , 1966 .

[65]  F. Kapron,et al.  RADIATION LOSSES IN GLASS OPTICAL WAVEGUIDES , 1970 .

[66]  K. Inoue,et al.  Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion , 1995 .

[67]  T. Sugie.  Maximum repeaterless transmission of lightwave systems imposed by stimulated Brillouin scattering in fibres , 1995 .

[68]  S. Bigo,et al.  Pitfalls of error estimation from measured non-Gaussian nonlinear noise statistics over dispersion-unmanaged systems , 2014, 2014 The European Conference on Optical Communication (ECOC).

[69]  Morteza H. Shoreh,et al.  Compensation of nonlinearity impairments in coherent optical OFDM systems using multiple optical phase conjugate modules , 2014, IEEE/OSA Journal of Optical Communications and Networking.

[70]  A D Ellis,et al.  Minimising total energy requirements in amplified links by optimising amplifier spacing. , 2014, Optics express.

[71]  Darko Zibar,et al.  Machine Learning Techniques for Optical Performance Monitoring From Directly Detected PDM-QAM Signals , 2017, Journal of Lightwave Technology.

[72]  William Shieh,et al.  Analytical Expressions for Nonlinear Transmission Performance of Coherent Optical OFDM Systems With Frequency Guard Band , 2012, Journal of Lightwave Technology.

[73]  Ronen Dar,et al.  Inter-Channel Nonlinear Interference Noise in WDM Systems: Modeling and Mitigation , 2015, Journal of Lightwave Technology.

[74]  Erwan Pincemin,et al.  1,200 km SMF (100 km spans) 280 Gbit/s Coherent WDM Transmission using Hybrid Raman/EDFA Amplification , 2007 .

[75]  Andrew D. Ellis,et al.  5 Gbit/s soliton propagation over 350 km with large periodic dispersion coefficient perturbations using erbium doped fibre amplifier repeaters , 1991 .

[76]  S. Bigo,et al.  On nonlinear distortions of highly dispersive optical coherent systems. , 2012, Optics express.

[77]  S. T. Le,et al.  Optical and Digital Phase Conjugation Techniques for Fiber Nonlinearity Compensation , 2015, 2015 Opto-Electronics and Communications Conference (OECC).

[78]  Mohammed Y. S. Sowailem,et al.  168-Gb/s Single Carrier PAM4 Transmission for Intra-Data Center Optical Interconnects , 2017, IEEE Photonics Technology Letters.

[79]  David V. Plant,et al.  224-Gb/s 10-km Transmission of PDM PAM-4 at 1.3 μm Using a Single Intensity-Modulated Laser and a Direct-Detection MIMO DSP-Based Receiver , 2015, Journal of Lightwave Technology.

[80]  H. Haus,et al.  Random walk of coherently amplified solitons in optical fiber transmission. , 1986, Optics letters.

[81]  R. Olshansky,et al.  Optical polarization division multiplexing at 4 Gb/s , 1992, IEEE Photonics Technology Letters.

[82]  Francesco Da Ros,et al.  Kerr Nonlinearity Mitigation: Mid-Link Spectral Inversion Versus Digital Backpropagation in 5×28-GBd PDM 16-QAM Signal Transmission , 2015, Journal of Lightwave Technology.

[83]  Magnus Karlsson,et al.  Mitigation of nonlinearities using conjugate data repetition. , 2015, Optics express.

[84]  David J. Ives,et al.  The Benefit of Split Nonlinearity Compensation for Single-Channel Optical Fiber Communications , 2015, IEEE Photonics Technology Letters.

[85]  Paolo Minzioni,et al.  Nonlinearity Compensation in a Fiber-Optic Link by Optical Phase Conjugation , 2009 .

[86]  R S Tucker,et al.  Green Optical Communications—Part I: Energy Limitations in Transport , 2011, IEEE Journal of Selected Topics in Quantum Electronics.

[87]  N J Doran,et al.  Compensating for dispersion and the nonlinear Kerr effect without phase conjugation. , 1996, Optics letters.

[88]  Jake Bromage,et al.  Scaling of the Raman gain coefficient: applications to germanosilicate fibers , 2003 .

[89]  D. Rafique,et al.  Digital back-propagation for spectrally efficient WDM 112 Gbit/s PM m-ary QAM transmission. , 2011, Optics express.

[90]  J. Ania-Castañón.  Quasi-lossless transmission using second-order Raman amplification and fibre Bragg gratings. , 2004, Optics express.

[91]  M. Karlsson,et al.  Perturbation Analysis of Nonlinear Propagation in a Strongly Dispersive Optical Communication System , 2012, Journal of Lightwave Technology.

[92]  Adam Lender.  Correlative level coding for binary-data transmission , 1966, IEEE Spectrum.

[93]  Danish Rafique,et al.  Compensation of intra-channel nonlinear fibre impairments using simplified digital back-propagation algorithm. , 2011, Optics express.

[94]  P. Bayvel,et al.  Modeling of four-wave mixing and gain peaking in amplified WDM optical communication systems and networks , 1996 .

[95]  Peter A. Andrekson,et al.  Phase-sensitive amplified optical link operating in the nonlinear transmission regime , 2012, 2012 38th European Conference and Exhibition on Optical Communications.

[96]  Andrew D. Ellis,et al.  WDM Orthogonal Subcarrier Multiplexing , 2016, Journal of Lightwave Technology.

[97]  A. N. Pinto,et al.  Statistical model for link lengths in optical transport networks , 2013, IEEE/OSA Journal of Optical Communications and Networking.

[98]  K. Goroshko,et al.  Fundamental Limitations of Digital Back Propagation due to Polarization Mode Dispersion , 2015 .

[99]  Andrew Lord,et al.  Optical-phase conjugation nonlinearity compensation in Flexi-Grid optical networks , 2015 .

[100]  K. Inoue.  Phase-mismatching characteristic of four-wave mixing in fiber lines with multistage optical amplifiers. , 1992, Optics letters.

[101]  Frank R. Kschischang,et al.  Upper bound on the capacity of a cascade of nonlinear and noisy channels , 2015, 2015 IEEE Information Theory Workshop (ITW).

[102]  Hussam G. Batshon,et al.  49.3 Tb/s Transmission Over 9100 km Using C+L EDFA and 54 Tb/s Transmission Over 9150 km Using Hybrid-Raman EDFA , 2015, Journal of Lightwave Technology.

[103]  I. Jacobs,et al.  Optical preamplifier receiver for spectrum-sliced WDM , 1997 .

[104]  M. Secondini,et al.  A Combined Regular-Logarithmic Perturbation Method for Signal-Noise Interaction in Amplified Optical Systems , 2009, Journal of Lightwave Technology.

[105]  Keang-Po Ho,et al.  Spectral efficiency limits and modulation/detection techniques for DWDM systems , 2004, IEEE Journal of Selected Topics in Quantum Electronics.

[106]  S. Sygletos,et al.  Exceeding the nonlinear-shannon limit using raman laser based amplification and optical phase conjugation , 2014, OFC 2014.

[107]  D. Schadt,et al.  Effect of amplifier spacing on four-wave mixing in multichannel coherent communications , 1991 .

[108]  P. Poggiolini.  The GN Model of Non-Linear Propagation in Uncompensated Coherent Optical Systems , 2012, Journal of Lightwave Technology.

[109]  Marco Secondini,et al.  Scope and Limitations of the Nonlinear Shannon Limit , 2017, Journal of Lightwave Technology.

[110]  Jaroslaw E Prilepsky,et al.  Capacity estimates for optical transmission based on the nonlinear Fourier transform , 2016, Nature Communications.

[111]  Yanhe Li,et al.  Optimizing the bandwidth and noise performance of distributed multi-pump Raman amplifiers , 2004 .

[112]  Thomas Richter,et al.  Coherent reception and 126 GHz bandwidth digital signal processing of CO-OFDM superchannel generated by fiber frequency conversion , 2014, OFC 2014.

[113]  Oskars Ozolins,et al.  1.55-μm EML-based DMT transmission with nonlinearity-aware time domain super-Nyquist image induced aliasing , 2017, 2017 Optical Fiber Communications Conference and Exhibition (OFC).

[114]  Seb J Savory,et al.  Digital filters for coherent optical receivers. , 2008, Optics express.

[115]  M. Tan,et al.  Evaluation of 100G DP-QPSK long-haul transmission performance using second order co-pumped Raman laser based amplification. , 2015, Optics express.

[116]  Polina Bayvel,et al.  On the performance of multichannel digital backpropagation in high-capacity long-haul optical transmission. , 2014, Optics express.

[117]  S. Chandrasekhar,et al.  Fiber nonlinearity compensation of an 8-channel WDM PDM-QPSK signal using multiple phase conjugations , 2014, OFC 2014.

[118]  Nick Doran,et al.  Energy enhancement of dispersion-managed solitons and WDM , 1998 .

[119]  N. Kagi,et al.  Optimizing the location of dispersion compensators in periodically amplified fiber links in the presence of third-order nonlinear effects , 1996, IEEE Photonics Technology Letters.

[120]  Weisheng Hu,et al.  Upstream dispersion management supporting 100 km differential reach in TWDM-PON. , 2015, Optics express.

[121]  Xi Chen,et al.  Influence of PMD on fiber nonlinearity compensation using digital back propagation. , 2012, Optics express.

[122]  P. Winzer,et al.  On the Limits of Digital Back-Propagation in Fully Loaded WDM Systems , 2016, IEEE Photonics Technology Letters.

[123]  J. Gordon,et al.  Phase noise in photonic communications systems using linear amplifiers. , 1990, Optics letters.

[124]  David J. Ives,et al.  Throughput Gains From Adaptive Transceivers in Nonlinear Elastic Optical Networks , 2017, Journal of Lightwave Technology.

[125]  Seung-Hyun Cho,et al.  1.25 Gb/s operation of ASE injected RSOA with 50 GHz channel spacing by using injection current adjustment, dispersion management and receiver with decision threshold level control , 2010, 2010 12th International Conference on Transparent Optical Networks.

[126]  Masaharu Ohashi,et al.  Four-wave mixing suppression effect of dispersion distributed fibers , 1999 .

[127]  Stylianos Sygletos,et al.  Optical fibre limits:an approach using ASE channel estimation , 2015 .

[128]  Jian Zhao,et al.  Approaching the Non-Linear Shannon Limit , 2010, Journal of Lightwave Technology.

[129]  M. Nakazawa,et al.  1.28 Tbit/s-70 km OTDM transmission using third- and fourth-order simultaneous dispersion compensation with a phase modulator , 2000 .

[130]  D. Cotter.  Observation of stimulated Brillouin scattering in low-loss silica fibre at 1.3 μm , 1982 .

[131]  Takushi Kazama,et al.  Simultaneous nonlinearity mitigation in 92 × 180-Gbit/s PDM-16QAM transmission over 3840 km using PPLN-based guard-band-less optical phase conjugation. , 2016, Optics express.

[132]  D. Saad,et al.  Communication networks beyond the capacity crunch , 2016, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[133]  Takeshi Hoshida,et al.  Implementation efficient nonlinear equalizer based on correlated digital backpropagation , 2011, 2011 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference.

[134]  W. Forysiak,et al.  Reduction of Gordon-Haus jitter in soliton transmission systems by optical phase conjugation , 1995 .

[135]  T. Sugihara,et al.  Spectrally-efficient dual phase-conjugate twin waves with orthogonally multiplexed quadrature pulse-shaped signals , 2014, OFC 2014.

[136]  Ting Wang,et al.  112-Gb/s DP-QPSK transmission over 7,860-km DMF using phase-conjugated copy and digital phase-sensitive boosting with enhanced noise and nonlinearity tolerance , 2013, 2013 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference (OFC/NFOEC).

[137]  L. Nelson,et al.  Space-division multiplexing in optical fibres , 2013, Nature Photonics.

[138]  M. O'Sullivan,et al.  5120 km RZ-DPSK transmission over G652 fiber at 10 Gb/s with no optical dispersion compensation , 2005, OFC/NFOEC Technical Digest. Optical Fiber Communication Conference, 2005..

[139]  Hung Nguyen Tan,et al.  Signal-transparent wavelength conversion and light-speed back propagation through fiber , 2016, 2016 Optical Fiber Communications Conference and Exhibition (OFC).

[140]  Leif Katsuo Oxenløwe,et al.  Experimental Comparison of Gains in Achievable Information Rates from Probabilistic Shaping and Digital Backpropagation for DP-256QAM/1024QAM WDM Systems , 2016 .

[141]  R. Cigliutti,et al.  The LOGON strategy for low-complexity control plane implementation in new-generation flexible networks , 2013, 2013 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference (OFC/NFOEC).

[142]  T. Miya,et al.  Ultimate low-loss single-mode fibre at 1.55 μm , 1979 .

[143]  Takehiro Tsuritani,et al.  Super-Nyquist-WDM transmission over 7,326-km seven-core fiber with capacity-distance product of 1.03 Exabit/s · km. , 2014, Optics express.

[144]  P. Winzer,et al.  Capacity Limits of Optical Fiber Networks , 2010, Journal of Lightwave Technology.

[145]  R.A. Shafik,et al.  On the Extended Relationships Among EVM, BER and SNR as Performance Metrics , 2006, 2006 International Conference on Electrical and Computer Engineering.

[146]  Paparao Palacharla,et al.  The impact of spectral inversion placement for nonlinear phase noise mitigation in non-uniform transmission links , 2014, 2014 IEEE Photonics Conference.

[147]  P. Mitra,et al.  The channel capacity of a fiber optics communication system: perturbation theory , 2000, physics/0007033.

[148]  M. O'sullivan,et al.  Modulation instability and its impact in multispan optical amplified IMDD systems: theory and experiments , 1997 .

[149]  M. Feder,et al.  New bounds on the capacity of the nonlinear fiber-optic channel. , 2014, Optics letters.

[150]  R. Chang.  Synthesis of band-limited orthogonal signals for multichannel data transmission , 1966 .

[151]  Keang-Po Ho,et al.  Electronic compensation technique to mitigate nonlinear phase noise , 2004, Journal of Lightwave Technology.

[152]  E. Forestieri,et al.  Achievable Information Rate in Nonlinear WDM Fiber-Optic Systems With Arbitrary Modulation Formats and Dispersion Maps , 2013, Journal of Lightwave Technology.

[153]  Xi Chen,et al.  Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems. , 2010, Optics express.

[154]  David V. Plant,et al.  504 and 462 Gb/s direct detect transceiver for single carrier short-reach data center applications , 2017, 2017 Optical Fiber Communications Conference and Exhibition (OFC).

[155]  G. E. Bodeep,et al.  Laser mode partition noise in lightwave systems using dispersive optical fiber , 1992 .

[156]  Andrew D. Ellis,et al.  Limitations of WDM transmission over 560 km due to degenerate four wave mixing , 1992 .

[157]  D. Wood.  Constraints on the bit rates in direct detection optical communication systems using linear or soliton pulses , 1990 .

[158]  I. S. Amiri,et al.  W-Band OFDM for Radio-over-Fiber Direct-Detection Link Enabled by Frequency Nonupling Optical Up-Conversion , 2014, IEEE Photonics Journal.

[159]  Philippe Ciblat,et al.  Inter-Subcarrier Nonlinear Interference Canceler for Long-Haul Nyquist-WDM Transmission , 2016, IEEE Photonics Technology Letters.

[160]  Shigeki Watanabe,et al.  Optical coherent broad-band transmission for long-haul and distribution systems using subcarrier multiplexing , 1993 .

[161]  Danish Rafique,et al.  Intra-channel nonlinearity compensation for PM-16 QAM traffic co-propagating with 28 Gbaud m-ary QAM neighbours. , 2013, Optics express.

[162]  A. Mecozzi.  On the optimization of the gain distribution of transmission lines with unequal amplifier spacing , 1998, IEEE Photonics Technology Letters.

[163]  Guifang Li,et al.  Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing. , 2008, Optics express.

[164]  H. Steinberg.  The use of a laser amplifier in a laser communication system , 1963 .

[165]  Liang Zhang,et al.  Single-lane 180 Gb/s SSB-duobinary-PAM-4 signal transmission over 13 km SSMF , 2017, 2017 Optical Fiber Communications Conference and Exhibition (OFC).

[166]  J. Bromage.  Raman amplification for fiber communications systems , 2003, Journal of Lightwave Technology.

[167]  N. S. Kapany,et al.  Fiber Optics. IX. Waveguide Effects , 1961 .

[168]  P. Kaewplung,et al.  Complete analysis of sideband instability in chain of periodic dispersion-managed fiber link and its effect on higher order dispersion-managed long-haul wavelength-division multiplexed systems , 2002 .

[169]  V N Treshchikov,et al.  100 Gb s−1 coherent dense wavelength division multiplexing system reach extension beyond the limit of electronic dispersion compensation using optical dispersion management , 2014 .

[170]  Seb J. Savory,et al.  Linear and nonlinear impairment mitigation in a Nyquist spaced DP-16QAM WDM transmission system with full-field DBP , 2014, 2014 The European Conference on Optical Communication (ECOC).

[171]  I. Morita,et al.  Reduction of Gordon-Haus timing jitter by periodic dispersion compensation in soliton transmission , 1995 .

[172]  Benjamin Foo,et al.  Experimental demonstrations of dual polarization CO-OFDM using mid-span spectral inversion for nonlinearity compensation. , 2014, Optics express.

[173]  Mariia Sorokina,et al.  Sparse identification for nonlinear optical communication systems: SINO method. , 2016, Optics express.

[174]  Chao Lu,et al.  Amplifier-less transmission of 56Gbit/s PAM4 over 60km using 25Gbps EML and APD , 2017, 2017 Optical Fiber Communications Conference and Exhibition (OFC).

[175]  Guifang Li,et al.  Polarization Diversity Transmitter and Optical Nonlinearity Mitigation using Polarization-Time Coding , 2006 .

[176]  Hoon Kim,et al.  Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise , 2003, IEEE Photonics Technology Letters.

[177]  David V. Plant,et al.  XPM Model-Based Digital Backpropagation for Subcarrier-Multiplexing Systems , 2015, Journal of Lightwave Technology.

[178]  K. Kikuchi,et al.  Coherent demodulation of 40-Gbit/s polarization-multiplexed QPSK signals with 16-GHz spacing after 200-km transmission , 2005, OFC/NFOEC Technical Digest. Optical Fiber Communication Conference, 2005..

[179]  Andrew D. Ellis,et al.  The effect of high optical power on modern fibre at 1.5 µm , 2016, 2016 18th International Conference on Transparent Optical Networks (ICTON).

[180]  R. Smith.  Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and brillouin scattering. , 1972, Applied optics.

[181]  Danish Rafique,et al.  Polarization multiplexed 224 Gb/s 16QAM transmission employing digital back-propagation , 2011, 2011 37th European Conference and Exhibition on Optical Communication.

[182]  P. Bayvel,et al.  Electronic dispersion compensation by signal predistortion using digital Processing and a dual-drive Mach-Zehnder Modulator , 2005, IEEE Photonics Technology Letters.

[183]  Luca Barletta,et al.  Experimental Study of Nonlinear Phase Noise and its Impact on WDM Systems with DP-256QAM , 2016 .

[184]  Telmo R Cunha,et al.  Nonlinear compensation with DBP aided by a memory polynomial. , 2016, Optics express.

[185]  Masataka Nakazawa,et al.  42.3-Tbit/s, 18-Gbaud 64QAM WDM coherent transmission of 160 km over full C-band using an injection locking technique with a spectral efficiency of 9 bit/s/Hz , 2017, 2017 Optical Fiber Communications Conference and Exhibition (OFC).

[186]  Liang Du,et al.  Efficient digital backpropagation for PDM-CO-OFDM optical transmission systems , 2010, 2010 Conference on Optical Fiber Communication (OFC/NFOEC), collocated National Fiber Optic Engineers Conference.

[187]  Hung Nguyen Tan,et al.  Optimized WDM Transmission Impairment Mitigation by Multiple Phase Conjugations , 2016, Journal of Lightwave Technology.

[188]  Andrew Sinclair,et al.  High Capacity Transport—100G and Beyond , 2015, Journal of Lightwave Technology.

[189]  M. O'Sullivan,et al.  Characterization of electrostriction nonlinearity in a standard single-mode fiber based on cross-phase modulation , 2015, 2015 Optical Fiber Communications Conference and Exhibition (OFC).

[190]  Patrick P. Iannone,et al.  Transmission of two wavelength-multiplexed 10 Gbit/s channels over 560 km of dispersive fibre , 1994 .

[191]  Keang-Po Ho,et al.  Statistical properties of stimulated Raman crosstalk in WDM systems , 2000, Journal of Lightwave Technology.

[192]  Masatoyo Sumida,et al.  2.5 Gbit/s-9720 km, 10 Gbit/s-6480 km transmission in the FSA commercial system with 90 km spaced optical amplifier repeaters and dispersion-managed cables , 1995 .

[193]  Jacklyn D. Reis,et al.  Single wavelength 100G real-time transmission for high-speed data center communications , 2017, 2017 Optical Fiber Communications Conference and Exhibition (OFC).

[194]  L. Potí,et al.  Impact of Optical and Electrical Narrowband Spectral Shaping in Faster Than Nyquist Tb Superchannel , 2013, IEEE Photonics Technology Letters.

[195]  D. Marcuse.  Single-channel operation in very long nonlinear fibers with optical amplifiers at zero dispersion , 1991 .

[196]  Xuefeng Tang,et al.  WDM transmissions exploiting optical phase conjugation , 2007, Ann. des Télécommunications.

[197]  Paul H. Siegel,et al.  On the Multiuser Capacity of WDM in a Nonlinear Optical Fiber: Coherent Communication , 2006, IEEE Transactions on Information Theory.

[198]  A D Ellis,et al.  PMD tolerant nonlinear compensation using in-line phase conjugation. , 2016, Optics express.

[199]  Gerard Lachs,et al.  Information rates for photocount detection systems , 1969, IEEE Trans. Inf. Theory.

[200]  M. E. McCarthy,et al.  Impact of Optical Phase Conjugation on the Nonlinear Shannon Limit , 2016, Journal of Lightwave Technology.

[201]  M. Chagnon,et al.  Experimental study of 112 Gb/s short reach transmission employing PAM formats and SiP intensity modulator at 1.3 μm. , 2014, Optics express.

[202]  C. Menyuk,et al.  10-Gb/s transmission of NRZ over 10000 km and solitons over 13500 km error-free in the same dispersion-managed system , 1997, IEEE Photonics Technology Letters.

[203]  Shigeki Watanabe,et al.  Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation , 1996 .

[204]  D. Cotter,et al.  Stimulated Raman crosstalk in optical transmission: effects of group velocity dispersion , 1984 .

[205]  A. V. Luchnikov,et al.  Long-range interaction of picosecond solitons through excitation of acoustic waves in optical fibers , 1992 .

[206]  D. Rafique,et al.  Various Nonlinearity Mitigation Techniques Employing Optical and Electronic Approaches , 2011, IEEE Photonics Technology Letters.

[207]  Andrew D. Ellis,et al.  Unrepeatered 2.4 Gbit/s transmission experiment over 250 km of step-index fibre using erbium power amplifier , 1990 .

[208]  M. Winter,et al.  Error Vector Magnitude as a Performance Measure for Advanced Modulation Formats , 2012, IEEE Photonics Technology Letters.

[209]  Roland Ryf,et al.  Fiber nonlinearity compensation by digital backpropagation of an entire 1.2-Tb/s superchannel using a full-field spectrally-sliced receiver , 2013 .

[210]  Dong Pan,et al.  Cost-effective 25G APD TO-can/ROSA for 100G applications , 2017, 2017 Optical Fiber Communications Conference and Exhibition (OFC).

[211]  Eduward Tangdiongga,et al.  Demonstration and application of 37.5 Gb/s duobinary-PAM3 in PONs , 2017, 2017 Optical Fiber Communications Conference and Exhibition (OFC).

[212]  F. Hauske,et al.  Intrachannel Nonlinearity Compensation by Inverse Volterra Series Transfer Function , 2012, Journal of Lightwave Technology.

[213]  A. Chraplyvy.  Limitations on lightwave communications imposed by optical-fiber nonlinearities , 1990 .

[214]  N R Das,et al.  Probability of Power Depletion in SRS Cross-Talk and Optimum Detection Threshold for Minimum BER in a WDM Receiver , 2011, IEEE Journal of Quantum Electronics.

[215]  J. C. Cartledge,et al.  Signal processing techniques for reducing the impact of fiber nonlinearities on system performance , 2016, 2016 Optical Fiber Communications Conference and Exhibition (OFC).

[216]  Gabriella Bosco,et al.  Performance Limits of Nyquist-WDM and CO-OFDM in High-Speed PM-QPSK Systems , 2010, IEEE Photonics Technology Letters.

[217]  S. T. Le,et al.  The impact of phase conjugation on the nonlinear-Shannon limit: The difference between optical and electrical phase conjugation , 2015, 2015 IEEE Summer Topicals Meeting Series (SUM).

[218]  Andrew Ellis,et al.  Effect of second order signal-noise interactions in nonlinearity compensated optical transmission systems. , 2016, Optics letters.

[219]  T. Widdowson,et al.  2.5 Gbit/s NRZ system aspects for transoceanic distances , 1992 .

[220]  A. Naka,et al.  In-line amplifier transmission distance determined by self-phase modulation and group-velocity dispersion , 1994 .

[221]  M. Manna,et al.  FWM resonances in dispersion slope-matched and nonzero-dispersion fiber maps , 2002, IEEE Photonics Technology Letters.

[222]  Masatoshi Suzuki,et al.  10 Gbit/s, 4500km Transmission Experiment Using 138 Cascaded Er-doped Fiber Amplifiers , 1992 .

[223]  David J Richardson,et al.  Filling the Light Pipe , 2010, Science.

[224]  A. Yariv,et al.  Compensation for phase distortions in nonlinear media by phase conjugation. , 1980, Optics letters.

[225]  Mark D. Pelusi.  Fiber looped phase conjugation of polarization multiplexed signals for pre-compensation of fiber nonlinearity effect. , 2013, Optics express.

[226]  K. Turitsyn,et al.  Information capacity of optical fiber channels with zero average dispersion. , 2003, Physical review letters.

[227]  N. S. Bergano,et al.  Circulating loop transmission experiments for the study of long-haul transmission systems using erbium-doped fiber amplifiers , 1995 .

[228]  B. Zhu,et al.  Transmission of a 1.2-Tb/s 24-carrier no-guard-interval coherent OFDM superchannel over 7200-km of ultra-large-area fiber , 2009, 2009 35th European Conference on Optical Communication.

[229]  Gaurav Garg,et al.  Path Averaged Soliton Systems for Long-Haul Communication , 2017 .

[230]  Mark D Pelusi,et al.  Optically tunable compensation of nonlinear signal distortion in optical fiber by end-span optical phase conjugation. , 2012, Optics express.

[231]  H. Nyquist,et al.  Certain Topics in Telegraph Transmission Theory , 1928, Transactions of the American Institute of Electrical Engineers.

[232]  M. Chagnon,et al.  Four-Dimensional Modulation and Stokes Direct Detection of Polarization Division Multiplexed Intensities, Inter Polarization Phase and Inter Polarization Differential Phase , 2016, Journal of Lightwave Technology.

[233]  Kazuo Hagimoto,et al.  10 Gbit/s, 280 km nonrepeatered transmission with suppression of modulation instability , 1994 .

[234]  Mariia Sorokina,et al.  Ripple Distribution for Nonlinear Fibre-Optic Channels , 2017, Optics express.

[235]  Hung Nguyen Tan,et al.  Transmission optimized impairment mitigation by 12 stage phase conjugation of WDM 24×48 Gb/s DP-QPSK signals , 2015, 2015 Optical Fiber Communications Conference and Exhibition (OFC).

[236]  J. L. Gimlett,et al.  Performance of directly modulated DFB lasers in 10-Gb/s ASK, FSK, and DPSK lightwave systems , 1990 .

[237]  Stylianos Sygletos,et al.  The Potential for Networks with Capacities Exceeding the Nonlinear-Shannon Limit , 2015 .

[238]  Francesca Parmigiani,et al.  Nonlinearity mitigation for multi-channel 64-QAM signals in a deployed fiber link through optical phase conjugation , 2016, 2016 Optical Fiber Communications Conference and Exhibition (OFC).

[239]  Donald D. Matulka.  Application of LASERS to Digital Communications , 1962, IRE Transactions on Aerospace and Navigational Electronics.

[240]  Takashi Inoue,et al.  Nearly-ideal optical phase conjugation based nonlinear compensation system , 2014, OFC 2014.

[241]  Lihui Pang,et al.  Study on the control technology of optical solitons in optical fibers , 2016 .

[242]  Partha P. Mitra,et al.  Nonlinear limits to the information capacity of optical fibre communications , 2000, Nature.

[243]  Akira Naka,et al.  Inline amplifier transmission experiments over 4500 km at 2.5 Gb/s , 1992 .

[244]  Leonid G. Kazovsky,et al.  Phase- and polarization-diversity coherent optical techniques , 1989 .

[245]  H. Louchet,et al.  Analytical model for the performance evaluation of DWDM transmission systems , 2003, IEEE Photonics Technology Letters.

[246]  Md Asif Iqbal,et al.  Four wave mixing in distributed Raman amplified optical transmission systems , 2016, 2016 IEEE Photonics Conference (IPC).

[247]  Naoki Fujiwara,et al.  28-Gbit/s 80-km transmission using SOA-assisted extended-reach EADFB laser (AXEL) , 2017, 2017 Optical Fiber Communications Conference and Exhibition (OFC).

[248]  Keith Willox.  Q factor: the wrong answer for service providers and equipment manufacturers , 2003, IEEE Commun. Mag..

[249]  C. Menyuk,et al.  Optimization of the split-step Fourier method in modeling optical-fiber communications systems , 2003 .

[250]  E. Yamada,et al.  10 Gbit/s soliton data transmission over one million kilometres , 1991 .

[251]  O. E. DeLange.  Wide-band optical communication systems: Part II—Frequency-division multiplexing , 1970 .

[252]  Nori Shibata,et al.  Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber , 1987 .

[253]  E.A. Golovchenko,et al.  Four-wave mixing in multispan dispersion-managed transmission links , 1998, IEEE Photonics Technology Letters.

[254]  Ikuo Mito,et al.  Input power limits of single-mode optical fibers due to stimulated Brillouin scattering in optical communication systems , 1988 .

[255]  M. A. Iqbal,et al.  Transmission performance improvement using random DFB laser based Raman amplification and bidirectional second-order pumping. , 2016, Optics express.

[256]  Fan Zhang,et al.  800 Gb/s (8 × 100 Gb/s) Nyquist Half-Cycle Single-Sideband Modulation Direct-Detection Transmission Over 320 km SSMF at C-band , 2017, Journal of Lightwave Technology.

[257]  Nikola Alic,et al.  Beating the Nonlinear Capacity Limit , 2016 .

[258]  Wei Chen,et al.  140-Gb/s 20-km Transmission of PAM-4 Signal at 1.3 $\mu \text{m}$ for Short Reach Communications , 2015, IEEE Photonics Technology Letters.

[259]  R. S. Asha,et al.  A Survey on Dispersion Management Using Optical Solitons in Optical Communication System , 2016 .

[260]  A. Hasegawa,et al.  Generation of asymptotically stable optical solitons and suppression of the Gordon-Haus effect. , 1992, Optics letters.

[261]  Gregory Raybon,et al.  Unrepeatered transmission over 150 km of nonzero-dispersion fibre at 100 Gbit/s with semiconductor based pulse source, demultiplexer and clock recovery , 1999 .

[262]  Andrew D. Ellis,et al.  40 Gbit/s transmission over 406 km of NDSF using mid-span spectral inversion by four-wave-mixing in a 2 mm long semiconductor optical amplifier , 1997 .

[263]  D. M. Spirit,et al.  Effect of fibre dispersion on four-wave mixing in multichannel coherent optical transmission system , 1992 .

[264]  Maxim Kuschnerov,et al.  Digital Fiber Nonlinearity Compensation: Toward 1-Tb/s transport , 2014, IEEE Signal Processing Magazine.

[265]  Jau Tang.  The channel capacity of a multispan DWDM system employing dispersive nonlinear optical fibers and an ideal coherent optical receiver , 2002 .

[266]  I. S. Amiri,et al.  All-Optical OFDM Generation for IEEE802.11a Based on Soliton Carriers Using Microring Resonators , 2014, IEEE Photonics Journal.

[267]  B. Spinnler,et al.  Optical phase conjugation for ultra long-haul phase-shift-keyed transmission , 2006, Journal of Lightwave Technology.

[268]  Francesca Parmigiani,et al.  26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing , 2011 .

[269]  M.G. Taylor,et al.  Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments , 2004, IEEE Photonics Technology Letters.

[270]  Peter J. Winzer,et al.  Scaling Optical Fiber Networks: Challenges and Solutions , 2015 .

[271]  B. Jalali,et al.  Optical rogue waves , 2007, Nature.

[272]  Polina Bayvel,et al.  Reach enhancement of 100% for a DP-64QAM super-channel using MC-DBP , 2015, 2015 Optical Fiber Communications Conference and Exhibition (OFC).