Capacity Trends and Limits of Optical Communication Networks

Since the first deployments of fiber-optic communication systems three decades ago, the capacity carried by a single-mode optical fiber has increased by a staggering 10 000 times. Most of the growth occurred in the first two decades with growth slowing to ten times in the last decade. Over the same three decades, network traffic has increased by a much smaller factor of 100, but with most of the growth occurring in the last few years, when data started dominating network traffic. At the current growth rate, the next factor of 100 in network traffic growth will occur within a decade. The large difference in growth rates between the delivered fiber capacity and the traffic demand is expected to create a capacity shortage within a decade. The first part of the paper recounts the history of traffic and capacity growth and extrapolations for the future. The second part looks into the technological challenges of growing the capacity of single-mode fibers by presenting a capacity limit estimate of standard and advanced single-mode optical fibers. The third part presents elementary capacity considerations for transmission over multiple transmission modes and how it compares to a single-mode transmission. Finally, the last part of the paper discusses fibers supporting multiple spatial modes, including multimode and multicore fibers, and the role of digital processing techniques. Spatial multiplexing in fibers is expected to enable system capacity growth to match traffic growth in the next decades.

[1]  Ting Wang,et al.  64-Tb/s (640×107-Gb/s) PDM-36QAM transmission over 320km using both pre- and post-transmission digital equalization , 2010, 2010 Conference on Optical Fiber Communication (OFC/NFOEC), collocated National Fiber Optic Engineers Conference.

[2]  Henning Bülow Coherent Multi Channel Transmission over Multimode-Fiber and Related Signal Processing , 2010 .

[3]  Stuart,et al.  Dispersive multiplexing in multimode optical fiber , 2000, Science.

[4]  S. Miller,et al.  Some Coupled-Wave Theory and Application to Waveguides (Abstract) , 1953 .

[5]  E. A. J. Marcatili,et al.  Multimode theory of graded-core fibers , 1973 .

[6]  H. Sunak Optical fiber communications , 1985, Proceedings of the IEEE.

[7]  G. V. Chester,et al.  Solid-State Physics , 1962, Nature.

[8]  R. Hartley Transmission of information , 1928 .

[9]  B. Zhu,et al.  Space-, wavelength-, polarization-division multiplexed transmission of 56-Tb/s over a 76.8-km seven-core fiber , 2011, 2011 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference.

[10]  Antonia Maria Tulino,et al.  Multiple-antenna capacity in the low-power regime , 2003, IEEE Trans. Inf. Theory.

[11]  A. Yariv Coupled-mode theory for guided-wave optics , 1973 .

[12]  S. Bigo,et al.  Nonlinear Effects in Mode-Division-Multiplexed Transmission Over Few-Mode Optical Fiber , 2011, IEEE Photonics Technology Letters.

[13]  Ivan B. Djordjevic Ultimate information capacity of fiber-optic networks , 2010, OPTO.

[14]  Govind P. Agrawal,et al.  Nonlinear Fiber Optics , 1989 .

[15]  J.E. Mazo,et al.  Digital communications , 1985, Proceedings of the IEEE.

[16]  E. Desurvire A Common Quantum Noise Model for Optical Amplification and Nonlinearity in WDM Transmission , 2002, 2002 28TH European Conference on Optical Communication.

[17]  S. Shamai,et al.  Capacity of a pulse amplitude modulated direct detection photon channel , 1990 .

[18]  T F Taunay,et al.  Silicon Photonics Core-, Wavelength-, and Polarization-Diversity Receiver , 2011, IEEE Photonics Technology Letters.

[19]  Francesco Poletti,et al.  Description of ultrashort pulse propagation in multimode optical fibers , 2008 .

[20]  Claude Oestges,et al.  MIMO Wireless Communications: From Real-World Propagation to Space-Time Code Design , 2007 .

[21]  S. Shambayati,et al.  Deep-space optical communications , 2011, 2011 International Conference on Space Optical Systems and Applications (ICSOS).

[22]  Mark Shtaif,et al.  Capacity limitations in fiber-optic communication systems as a result of polarization-dependent loss. , 2009, Optics letters.

[23]  S Mumtaz,et al.  PDL mitigation in PolMux OFDM systems using Golden and Silver Polarization-Time codes , 2010, 2010 Conference on Optical Fiber Communication (OFC/NFOEC), collocated National Fiber Optic Engineers Conference.

[24]  J. Gordon,et al.  Quantum Effects in Communications Systems , 1962, Proceedings of the IRE.

[25]  M. Gagnaire,et al.  An overview of broad-band access technologies , 1997, Proc. IEEE.

[26]  Herbert Haunstein,et al.  OFDM spectral efficiency limits from fiber and system non-linearities , 2010, 2010 Conference on Optical Fiber Communication (OFC/NFOEC), collocated National Fiber Optic Engineers Conference.

[27]  Peter J. Winzer,et al.  Capacity limits of information transmission in optically-routed fiber networks , 2010 .

[28]  P. Mitra,et al.  The channel capacity of a fiber optics communication system , 2002, Optical Fiber Communication Conference and Exhibit.

[29]  J. L. Massey,et al.  Capacity, Cutoff Rate, and Coding for a Direct-Detection Optical Channel , 1981, IEEE Trans. Commun..

[30]  P. Littlewood,et al.  The effect of propagation nonlinearities on the information capacity of WDM optical fiber systems: cross-phase modulation and four-wave mixing , 2004 .

[31]  Andrew Sendonaris,et al.  Joint signaling strategies for approaching the capacity of twisted-pair channels , 1998, IEEE Trans. Commun..

[32]  J. N. Kutz,et al.  Mode mixing and power diffusion in multimode optical fibers , 1998 .

[33]  Jerry D. Gibson,et al.  The Communications Handbook , 2002 .

[34]  Toshio Morioka,et al.  1 Tbit/s (100 Gbit/s × 10 channel) OTDM/WDM transmission using a single supercontinuum WDM source , 1996 .

[35]  R. D. Standley,et al.  Pulse dispersion and refractive-index profiles of some low-noise multimode optical fibers , 1973 .

[36]  P. J. Winzer,et al.  Fibre nonlinearities in electronically pre-distorted transmission , 2005 .

[37]  Ajoy Ghatak,et al.  The fiber optic essentials , 2007 .

[38]  Masanori Koshiba,et al.  Novel multi-core fibers for mode division multiplexing: proposal and design principle , 2009, IEICE Electron. Express.

[39]  Peter J. Winzer,et al.  Capacity limits of information transmission in optically-routed fiber networks , 2010, Bell Labs Technical Journal.

[40]  A. Andrusier,et al.  Increasing the PDL tolerance of systems by use of the Golden-code , 2010, 36th European Conference and Exhibition on Optical Communication.

[41]  W. B. Gardner Microbending loss in optical fibers , 1975, The Bell System Technical Journal.

[42]  Gerhard Kramer,et al.  Capacity limits of information transport in fiber-optic networks. , 2008, Physical review letters.

[43]  D. Gloge,et al.  Bending loss in multimode fibers with graded and ungraded core index. , 1972, Applied optics.

[44]  A. Hardy,et al.  Coupled modes of multiwaveguide systems and phased arrays , 1986 .

[45]  Lei Xu,et al.  Spatial-domain-based multidimensional modulation for multi-Tb/s serial optical transmission. , 2011, Optics express.

[46]  A. Sano,et al.  100 × 120-Gb/s PDM 64-QAM transmission over 160 km using linewidth-tolerant pilotless digital coherent detection , 2010, 36th European Conference and Exhibition on Optical Communication.

[47]  D. A. Bell,et al.  Information Theory and Reliable Communication , 1969 .

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

[49]  Kazunori Mukasa,et al.  Investigation on multi-core fibers with large Aeff and low micro bending loss , 2010 .

[50]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

[51]  Claude E. Shannon,et al.  The Mathematical Theory of Communication , 1950 .

[52]  Kunimasa Saitoh,et al.  Heterogeneous multi-core fibers: proposal and design principle , 2009, IEICE Electron. Express.

[53]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[54]  Robert W. Tkach Scaling optical communications for the next decade and beyond , 2010 .

[55]  Ali H. Sayed,et al.  Capacity enhancement in coherent optical MIMO (COMIMO) multimode fiber links , 2006, IEEE Communications Letters.

[56]  Andrea J. Goldsmith,et al.  Energy-efficiency of MIMO and cooperative MIMO techniques in sensor networks , 2004, IEEE Journal on Selected Areas in Communications.

[57]  Gerhard Kramer,et al.  The Capacity of Fiber-Optic Communication Systems , 2008, OFC/NFOEC 2008 - 2008 Conference on Optical Fiber Communication/National Fiber Optic Engineers Conference.

[58]  J. R. Pierce,et al.  Coupling of Modes of Propagation , 1954 .

[59]  Kin Seng Chiang,et al.  Microbend-induced mode coupling in a graded-index multimode fiber. , 2005, Applied optics.

[60]  John M. Cioffi,et al.  Increase in capacity of multiuser OFDM system using dynamic subchannel allocation , 2000, VTC2000-Spring. 2000 IEEE 51st Vehicular Technology Conference Proceedings (Cat. No.00CH37026).

[61]  E. Ip,et al.  101.7-Tb/s (370×294-Gb/s) PDM-128QAM-OFDM transmission over 3×55-km SSMF using pilot-based phase noise mitigation , 2011, 2011 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference.

[62]  Bane V. Vasic,et al.  Calculation of Achievable Information Rates of Long-Haul Optical Transmission Systems Using Instanton Approach , 2007, Journal of Lightwave Technology.

[63]  N. Olsson,et al.  Erbium-Doped Fiber Amplifiers: Fundamentals and Technology , 1999 .

[64]  Dietrich Marcuse,et al.  Coupled mode theory of optical resonant cavities , 1985 .

[65]  A. Snyder Coupled-Mode Theory for Optical Fibers , 1972 .

[66]  B. Zhu,et al.  Statistics of crosstalk in bent multicore fibers. , 2010, Optics express.

[67]  D. Marcuse Theory of dielectric optical waveguides , 1974 .

[68]  Takashi Sasaki,et al.  Low-crosstalk and low-loss multi-core fiber utilizing fiber bend , 2011, 2011 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference.

[69]  Shlomo Shamai,et al.  On the capacity of a twisted-wire pair: Gaussian model , 1990, IEEE Trans. Commun..

[70]  Gerard J. Foschini,et al.  Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas , 1996, Bell Labs Technical Journal.

[71]  L. Goddard Information Theory , 1962, Nature.

[72]  R. J. Black,et al.  Optical Waveguide Modes: Polarization, Coupling and Symmetry , 2010 .

[73]  Steve Hranilovic,et al.  Wireless optical communication systems , 2004 .

[74]  Sergio Verdú,et al.  Spectral efficiency in the wideband regime , 2002, IEEE Trans. Inf. Theory.

[75]  Massimiliano Salsi,et al.  Transmission at 2×100Gb/s, over two modes of 40km-long prototype few-mode fiber, using LCOS-based mode multiplexer and demultiplexer , 2011, 2011 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference.

[76]  H. Kogelnik Theory of Optical Waveguides , 1988 .

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

[78]  Sergio Benedetto,et al.  Principles of Digital Transmission: With Wireless Applications , 1999 .

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

[80]  M. Mayrock,et al.  Capacity loss due to polarization effects in coherent optical systems , 2010, 36th European Conference and Exhibition on Optical Communication.

[81]  R. M. Derosier,et al.  Four-photon mixing and high-speed WDM systems , 1995 .

[82]  Harry Nyquist Certain Topics in Telegraph Transmission Theory , 1928 .

[83]  C Jacobsen,et al.  Low-loss photonic crystal fibers for transmission systems and their dispersion properties. , 2004, Optics express.

[84]  J. von Hoyningen-Huene,et al.  Optical coupling components for spatial multiplexing in multi-mode fibers , 2011, 2011 37th European Conference and Exhibition on Optical Communication.

[85]  P. Winzer Energy-Efficient Optical Transport Capacity Scaling Through Spatial Multiplexing , 2011, IEEE Photonics Technology Letters.

[86]  Emre Telatar,et al.  Capacity of Multi-antenna Gaussian Channels , 1999, Eur. Trans. Telecommun..

[87]  Thomas C. Hales Sphere packings, I , 1997, Discret. Comput. Geom..

[88]  Itsuro Morita,et al.  DWDM transmission with 7.0-bit/s/Hz spectral efficiency using 8×65.1-Gbit/s coherent PDM-OFDM signals , 2009, 2009 Conference on Optical Fiber Communication - incudes post deadline papers.

[89]  S. Miller Coupled wave theory and waveguide applications , 1954 .

[90]  Eikichi Yamashita,et al.  Modal and coupling field analysis of optical fibers with circularly distributed multiple cores and a central core , 1986 .

[91]  D. Marcuse,et al.  Coupled mode theory of round optical fibers , 1973 .

[92]  Yves Jaouën,et al.  Space-Time Codes for Optical Fiber Communication with Polarization Multiplexing , 2010, 2010 IEEE International Conference on Communications.

[93]  J. Pocholle,et al.  Mode coupling in a multimode optical fiber with microbends. , 1975, Applied optics.

[94]  Ali H. Sayed,et al.  Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links [Topics in Optical Communications] , 2007, IEEE Communications Magazine.

[95]  M. J. Gans,et al.  On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas , 1998, Wirel. Pers. Commun..

[96]  Aaron D. Wyner,et al.  Capacity and error-exponent for the direct detection photon channel-Part II , 1988, IEEE Trans. Inf. Theory.

[97]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[98]  Sugizaki Ryuichi,et al.  Investigation on Multi-Core Fibers with Large Aeff and Low Micro Bending Loss , 2010 .

[99]  B. Vasic,et al.  Calculation of Achievable Information Rates of Long-Haul Optical Transmission Systems using Instanton Approach , 2006, 2006 IEEE International Symposium on Information Theory.

[100]  A. Gnauck,et al.  Space-division multiplexing over 10 km of three-mode fiber using coherent 6 × 6 MIMO processing , 2011, 2011 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference.

[101]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[102]  J. Gordon,et al.  Quantum Statistics of Masers and Attenuators , 1963 .

[103]  G. Raybon,et al.  Pseudo-Linear Transmission of High-Speed TDM Signals , 2002 .

[104]  B. Zhu,et al.  Seven-core multicore fiber transmissions for passive optical network. , 2010, Optics express.

[105]  R. Olshansky,et al.  Mode Coupling Effects in Graded-index Optical Fibers. , 1975, Applied optics.

[106]  J.-J. Werner,et al.  The HDSL environment (high bit rate digital subscriber line) , 1991 .

[107]  Amos A. Hardy,et al.  Coupled mode solutions of multiwaveguide systems , 1986 .

[108]  T. Kobayashi,et al.  69.1-Tb/s (432 × 171-Gb/s) C- and extended L-band transmission over 240 km Using PDM-16-QAM modulation and digital coherent detection , 2010, 2010 Conference on Optical Fiber Communication (OFC/NFOEC), collocated National Fiber Optic Engineers Conference.

[109]  C. Boisrobert,et al.  Fiber Optic Communication Systems , 1979 .

[110]  Andrea J. Goldsmith,et al.  Energy-constrained modulation optimization , 2005, IEEE Transactions on Wireless Communications.

[111]  Theodore S. Rappaport,et al.  Wireless communications - principles and practice , 1996 .

[112]  Benyuan Zhu,et al.  Low cross-talk design of multi-core fibers , 2010, CLEO/QELS: 2010 Laser Science to Photonic Applications.

[113]  R.-J. Essiambre,et al.  Impact of fiber nonlinearities on advanced modulation formats using electronic pre-distortion , 2006, 2006 Optical Fiber Communication Conference and the National Fiber Optic Engineers Conference.

[114]  J. Mckenna,et al.  Coupled line equations with random coupling , 1972 .

[115]  D. Marinescu,et al.  Classical and Quantum Information Theory , 2011 .

[116]  Gregory Raybon,et al.  Chapter 6 – Pseudo-Linear Transmission of High-Speed TDM Signals: 40 and 160 Gb/s , 2002 .

[117]  B. Crosignani,et al.  Soliton propagation in multimode optical fibers. , 1981, Optics letters.

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

[119]  Emmanuel Desurvire,et al.  Erbium-Doped Fiber Amplifiers, Device and System Developments , 2002 .

[120]  S. Swain Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences , 1984 .

[121]  H. Haus,et al.  Coupled-mode theory , 1991, Proc. IEEE.

[122]  Anton A. Huurdeman Optical Fiber Transmission , 2003 .

[123]  P. J. Winzer,et al.  10 × 112-Gb/s PDM 16-QAM transmission over 630 km of fiber with 6.2-b/s/Hz spectral efficiency , 2009, 2009 Conference on Optical Fiber Communication - incudes post deadline papers.

[124]  Casimer M. DeCusatis,et al.  Fiber Optic Essentials , 2005 .

[125]  Agrawal,et al.  Instability due to cross-phase modulation in the normal-dispersion regime. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[126]  E Kapon,et al.  Supermode analysis of phase-locked arrays of semiconductor lasers. , 1984, Optics letters.

[127]  Sudharman K. Jayaweera,et al.  An energy-efficient virtual MIMO architecture based on V-BLAST processing for distributed wireless sensor networks , 2004, 2004 First Annual IEEE Communications Society Conference on Sensor and Ad Hoc Communications and Networks, 2004. IEEE SECON 2004..

[128]  J. Gordon,et al.  Solitons in Optical Fibers: Fundamentals and Applications , 2006 .

[129]  Ivan B Djordjevic Energy-efficient spatial-domain-based hybrid multidimensional coded-modulations enabling multi-Tb/s optical transport. , 2011, Optics express.

[130]  E. Yamashita,et al.  Modal analysis method for optical fibers with symmetrically distributed multiple cores , 1985 .

[131]  J. A. Buck,et al.  Fundamentals of optical fibers , 1995 .

[132]  H. E. Rowe,et al.  Transmission Distortion in Multimode Random Waveguides , 1972 .

[133]  Jau Tang The Shannon channel capacity of dispersion-free nonlinear optical fiber transmission , 2001 .

[134]  Ting Wang,et al.  On the channel capacity of multilevel modulation schemes with coherent detection , 2009, 2009 Asia Communications and Photonics conference and Exhibition (ACP).

[135]  Robert B. Ash,et al.  Information Theory , 2020, The SAGE International Encyclopedia of Mass Media and Society.

[136]  David Tse,et al.  Fundamentals of Wireless Communication , 2005 .

[137]  D. Gloge,et al.  Optical power flow in multimode fibers , 1972 .

[138]  D. Marcuse,et al.  Effect of fiber nonlinearity on long-distance transmission , 1991 .

[139]  Agrawal,et al.  Modulation instability induced by cross-phase modulation. , 1987, Physical review letters.

[140]  Jun Wang,et al.  On the channel capacity of MIMO-OFDM systems , 2005, IEEE International Symposium on Communications and Information Technology, 2005. ISCIT 2005..

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

[142]  David O. Caplan Laser communication transmitter and receiver design , 2007 .

[143]  H. Kogelnik High-capacity optical communications: personal recollections , 2000, IEEE Journal of Selected Topics in Quantum Electronics.

[144]  Francesco Poletti,et al.  Dynamics of femtosecond supercontinuum generation in multimode fibers. , 2009, Optics express.

[145]  P. Winzer,et al.  High spectral efficiency modulation for high capacity transmission , 2008, 2008 Digest of the IEEE/LEOS Summer Topical Meetings.

[146]  Knight,et al.  Single-Mode Photonic Band Gap Guidance of Light in Air. , 1999, Science.

[147]  Albert G. Greenberg,et al.  Experience in measuring backbone traffic variability: models, metrics, measurements and meaning , 2002, IMW '02.

[148]  Antonello Cutolo,et al.  Coupled-mode theory of nonlinear propagation in multimode and single-mode fibers: envelope solitons and self-confinement , 1982 .

[149]  Helmut Bölcskei,et al.  On the capacity of OFDM-based spatial multiplexing systems , 2002, IEEE Trans. Commun..

[150]  Yanming Huo,et al.  Analysis of transverse mode competition and selection in multicore fiber lasers , 2005 .

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

[152]  John D. Love,et al.  Vector modes of six-port couplers , 1987 .

[153]  Peter J. Winzer,et al.  Outage calculations for spatially multiplexed fiber links , 2011, 2011 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference.

[154]  E. Desurvire A quantum model for optically amplified nonlinear transmission systems , 2002 .

[155]  Hermann A. Haus,et al.  Coupled-mode theory of optical waveguides , 1987 .

[156]  Ajoy Ghatak,et al.  Fiber Optic Essentials: Thyagarajan/Fiber Optic , 2007 .

[157]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[158]  D. Marcuse Derivation of coupled power equations , 1972 .

[159]  Verzekeren Naar Sparen,et al.  Cambridge , 1969, Humphrey Burton: In My Own Time.

[160]  Dirk Müller,et al.  Generation of Megawatt Optical Solitons in Hollow-Core Photonic Band-Gap Fibers , 2003, Science.

[161]  Joseph M. Kahn,et al.  Channel capacity of WDM systems using constant-intensity modulation formats , 2002, Optical Fiber Communication Conference and Exhibit.

[162]  M. Kakui,et al.  Ultra-low-loss (0.1484 dB/km) pure silica core fibre and extension of transmission distance , 2002 .

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

[164]  Peter J. Winzer,et al.  MIMO capacities and outage probabilities in spatially multiplexed optical transport systems. , 2011, Optics express.

[165]  A. Mecozzi Limits to long-haul coherent transmission set by the Kerr nonlinearity and noise of the in-line amplifiers , 1994 .

[166]  P. Roberts,et al.  Ultimate low loss of hollow-core photonic crystal fibres. , 2005, Optics express.

[167]  G. Agrawal Fiber-Optic Communication Systems: Agrawal/Fiber-Optic , 2010 .

[168]  S. Bigo,et al.  Nonlinear effects in long-haul transmission over bimodal optical fibre , 2010, 36th European Conference and Exhibition on Optical Communication.

[169]  Francis T. S. Yu Entropy and information optics , 2000, SPIE Defense + Commercial Sensing.

[170]  C. Gardiner,et al.  Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics , 2004 .

[171]  R. Stolen,et al.  Nonlinearity in fiber transmission , 1980, Proceedings of the IEEE.

[172]  Yanming Huo,et al.  Fundamental mode operation of a 19-core phase-locked Yb-doped fiber amplifier. , 2004, Optics express.

[173]  C. Gardiner Handbook of Stochastic Methods , 1983 .

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

[175]  Peter J. Winzer,et al.  Capacity Limits of Fiber-Optic Communication Systems , 2009, OFC 2009.

[176]  A. Robert Calderbank,et al.  MIMO Wireless Communications , 2007 .

[177]  Peter J. Winzer,et al.  Exploring capacity limits of fibre-optic mommunication systems , 2008, 2008 34th European Conference on Optical Communication.

[178]  Bernhard Schmauss,et al.  Stable coherent MIMO transport over few mode fiber enabled by an adiabatic mode splitter , 2010, 36th European Conference and Exhibition on Optical Communication.

[179]  E. Yamashita,et al.  A simple coupled-mode analysis method for multiple-core optical fiber and coupled dielectric waveguide structures , 1988, 1988., IEEE MTT-S International Microwave Symposium Digest.

[180]  A. Gnauck,et al.  MIMO-Based Crosstalk Suppression in Spatially Multiplexed 3$\,\times \,$56-Gb/s PDM-QPSK Signals for Strongly Coupled Three-Core Fiber , 2011, IEEE Photonics Technology Letters.

[181]  P. K. Chaturvedi,et al.  Communication Systems , 2002, IFIP — The International Federation for Information Processing.

[182]  J. Pierce,et al.  Optical Channels: Practical Limits with Photon Counting , 1978, IEEE Trans. Commun..

[183]  Robert W. Tkach,et al.  Scaling optical communications for the next decade and beyond , 2010, Bell Labs Technical Journal.

[184]  R.W. Tkach,et al.  High-Capacity Optical Transmission Systems , 2008, Journal of Lightwave Technology.

[185]  Ivan B. Djordjevic,et al.  On the channel capacity of multilevel modulation schemes with coherent detection , 2009 .

[186]  W. Fischer,et al.  Sphere Packings, Lattices and Groups , 1990 .

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

[188]  F. Forghieri,et al.  One Terabit/s Transmission Experiment , 1996 .

[189]  P. Winzer,et al.  Electronic predistortion and fiber nonlinearity , 2006, IEEE Photonics Technology Letters.

[190]  John Kerr Ll.D. XLIII. On rotation of the plane of polarization by reflection from the pole of a magnet , 1877 .

[191]  W. Ryan,et al.  Optical Channel Capacity , 2010 .

[192]  H. Nyquist,et al.  Certain factors affecting telegraph speed , 1924, Journal of the A.I.E.E..

[193]  Dietrich Marcuse,et al.  Curvature loss formula for optical fibers , 1976 .

[194]  Alexander L Gaeta,et al.  Nonlinear optics in hollow-core photonic bandgap fibers. , 2008, Optics express.

[195]  A. Yariv,et al.  Quantum Fluctuations and Noise in Parametric Processes. I. , 1961 .

[196]  Andrew M. Odlyzko,et al.  Bubbles, Gullibility, and Other Challenges for Economics, Psychology, Sociology, and Information Sciences , 2010, First Monday.

[197]  Meir Feder,et al.  Use of space-time coding in coherent polarization-multiplexed systems suffering from polarization-dependent loss. , 2010, Optics letters.

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

[199]  Wei-Ping Huang Coupled-mode theory for optical waveguides: an overview , 1994 .

[200]  Abbas Jamalipour,et al.  Wireless communications , 2005, GLOBECOM '05. IEEE Global Telecommunications Conference, 2005..

[201]  Toshio Morioka,et al.  100 Gbit/s x 10 channel OTDM/WDM Transmission using a Single Supercontinuum WDM Source , 1996 .

[202]  I. Djordjevic,et al.  Achievable information rates for high-speed long-haul optical transmission , 2005, Journal of Lightwave Technology.

[203]  Osamu Shimakawa,et al.  Ultra-low-crosstalk multi-core fiber feasible to ultra-long-haul transmission , 2011, 2011 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference.