COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
René-Jean Essiambre
Bell Laboratories, Alcatel-Lucent, Holmdel, NJ, ...
3
COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
Acknowledgment
Jerry Foschini
Gerhard Kramer
Roland Ryf
Sebastian ...
4
COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
Outline
1. Basic Information Theory
2. The “Fiber Channel”
3. Capa...
5
COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
Historical Evolution of Fiber-Optic Systems Capacity
What is the u...
Basic Information Theory
7
COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
The Birth of Information Theory
One paper by C. E. Shannon in two ...
8
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Shannon’s Formula for Bandlimited Channels
C: Channel capacity (bi...
9
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Three Elements Necessary to Achieve the Shannon Limit
-5 -4 -3 -2 ...
The “Fiber Channel”
11
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Dependence of Fiber Loss Coefficient on Wavelength for
Silica Fib...
12
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Optical Spectrum Layout in Wavelength-Division
Multiplexing
Frequ...
13
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Propagation for Distributed Amplification
Generalized Nonlinear S...
Capacity of Standard Single-
Mode Fiber
15
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Nonlinear Shannon Fiber Capacity Limit Estimate
 Modulation
 Co...
16
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Nonlinear Shannon Limit (Single Polarization) and
Record Experime...
17
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Nature of Nonlinear Capacity Limitations in Single-Mode Fiber
WDM...
18
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Nonlinear Shannon Limit versus Distance
Nonlinear capacity limit ...
Capacity of Advanced Single-
Mode Fibers
20
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Nonlinear Shannon Limit versus Fiber Loss Coefficient
Nonlinear c...
21
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Nonlinear Shannon Limit versus Fiber Nonlinear Coefficient
A very...
22
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Nonlinear Shannon Limit versus Fiber Dispersion
The weakest depen...
Polarization-Division
Multiplexing in Fibers
24
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Propagation Equations for Dual Polarization in Single-
Mode Fiber...
25
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Nonlinear Shannon Limit (PDM) and Record Experiments
We are appro...
Space-Division Multiplexing in
Fibers
27
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Various Types of Optical Fibers
‘‘Single-mode’’ fibers
7-core 19 ...
28
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Examples of Spatial Modes Profiles
Single-mode fiber Few-mode fib...
29
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Schematic of Coherent MIMO-based Coherent Crosstalk
Suppression f...
30
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Spectral Efficiency and Energy Gain from Spatial
Multiplexing
Lar...
31
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4,200 km Transmission Experiment with Coupled-Core 3-
Core Fiber ...
COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
Example of Spatial-Mode Multiplexers
(PHASE-PLATE-BASED COUPLERS)
In...
COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
Set-up of 6x6 MIMO Transmission Experiment
over 65 km
FEW-MODE FIBER...
COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
Q-FACTOR FOR 12 x 12 MIMO TRANSMISSION
59 km FMF SPAN AND 20-Gbaud 1...
COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
Historical Capacity Evolution by Multiplexing Types
1980 1985 1990 1...
Nonlinear Propagation Modeling
in Multimode/Multicore Fibers
37
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Nonlinear Equations of Propagation for Multicore and
Multimode Fi...
38
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Explicit Nonlinear Equations of Propagation for Two Spatial Modes...
39
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Random Linear Mode Coupling and Averaged Nonlinear
Equations of P...
40
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Nonlinear Equations of Propagation for Multicore and
Multimode Fi...
41
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Generalized Manakov Equations for Random Linear Mode
Coupling bet...
42
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Generalized Manakov Equations for Random Linear Mode
Coupling bet...
Intermodal Nonlinearities in
Multimode/Multicore Fibers
COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
Experimental Set-Up to Measure Inter-modal
Four-Wave Mixing
• Probe ...
COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
Measured Relative Group Velocities and Chromatic
Dispersions of the ...
COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
Schematic of the Experiment on Inter-Modal FWM
•All pumps and probe ...
COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
Experimental Observations of IM-FWM
IM-FWM was observed over the ent...
Summary and Outlook
49
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Summary and Outlook
• There appears to be a limit to single-mode ...
COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
The Capacity Limit of Single-Mode Fibers and Technologies Enabling High Capacities in Multimode and Multicore Fibers
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The Capacity Limit of Single-Mode Fibers and Technologies Enabling High Capacities in Multimode and Multicore Fibers

  1. 1. COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
  2. 2. COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED. René-Jean Essiambre Bell Laboratories, Alcatel-Lucent, Holmdel, NJ, USA The Upcoming Capacity Limit of Single-Mode Fibers and Increasing Optical Network Capacity using Multimode and Multicore Fibers Presentation at III WCOM on May 28, 2014
  3. 3. 3 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Acknowledgment Jerry Foschini Gerhard Kramer Roland Ryf Sebastian Randel Peter Winzer Nick Fontaine Bob Tkach Andy Chraplyvy and many others … Jim Gordon Xiang Liu S. Chandrasekhar Bert Basch Antonia Tulino Maurizio Magarini Herwig Kogelnik
  4. 4. 4 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Outline 1. Basic Information Theory 2. The “Fiber Channel” 3. Capacity of Standard Single-Mode Fiber 4. Capacity of Advanced Single-Mode Fibers 5. Polarization-Division Multiplexing in Fibers 6. Space-Division Multiplexing in Fibers 7. Nonlinear Propagation Modeling in Multimode/Multicore Fibers 8. Intermodal Nonlinearities in Multimode/Multicore Fibers 9. Summary and Outlook
  5. 5. 5 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Historical Evolution of Fiber-Optic Systems Capacity What is the ultimate capacity that an optical fiber can carry? Record Capacities 10 100 1 10 100 Systemcapacity Gbits/sTbits/s 1986 1990 1994 1998 2002 2006 2010 0.01 0.1 1 10Spectralefficiency (bits/s/Hz) WDMchannels 0.5 dB/year (12%/year) 2.5 dB/year (78%/year) from Essiambre et al., J. Lightwave Technol., pp. 662-701 (2010)
  6. 6. Basic Information Theory
  7. 7. 7 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. The Birth of Information Theory One paper by C. E. Shannon in two separate issues of the Bell System Technical Journal (1948) Mathematical theory that calculates the asymptote of the rates that information can be transmitted at an arbitrarily low error rate through an additive noise channel Claude E. Shannon (1955) “Copyright 1955 Alcatel-Lucent USA, Inc.”
  8. 8. 8 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Shannon’s Formula for Bandlimited Channels C: Channel capacity (bits/s) , B: Channel bandwidth (Hz) SNR: Signal-to-noise ratio  Signal energy / noise energy C / B  Capacity per unit bandwidth or spectral efficiency (SE) SE = C/B = log2 (1 + SNR)Shannon capacity limit: Increasing the SNR by 3 dB increases the capacity by 1 bit/s/Hz per polarization state SNR (dB) Spectralefficiency (bits/s/Hz) -5 0 5 10 15 20 25 30 0 1 2 3 4 5 6 7 8 9 10 + 3 dB SNR + 1 bit/s/Hz
  9. 9. 9 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Three Elements Necessary to Achieve the Shannon Limit -5 -4 -3 -2 -1 0 1 2 3 4 5 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Time (symbol period) Amplitude(n.u.) One pulse Adjacent pulse Sampling instant 1) Modulation:Nyquist pulses  sin(t)/t Darker area  larger density of symbols 2) Constellation: bi-dim. Gaussian 3) Coding (an example illustrating the principle here) 1 0 1 1 0 0 0 1 0 0 1 0 Uncoded data Information bits Information bits Detection of bit sequences is no different than detection bit per bit 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1 Coded data Information bits Information bits Redundant bits Redundant bits Detection of bit sequences can correct errors
  10. 10. The “Fiber Channel”
  11. 11. 11 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Dependence of Fiber Loss Coefficient on Wavelength for Silica Fibers Wavelength (nm) Fiberlosscoefficient(dB/km) 1200 1250 1300 1350 1400 1450 1500 1550 1600 1650 1700 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 EDFA Allwave SSMF C-band L-bandS-band U-bandE-bandO-band OH absorption Silica-based optical fibers have a large wavelength band having loss below 0.35 dB/km Wavelength Wavelength-division multiplexed (WDM) channels …… ~ 50GHz ~ 10 THz Essiambre et al. “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol., pp. 662-701(2010)
  12. 12. 12 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Optical Spectrum Layout in Wavelength-Division Multiplexing Frequency RS WDM channel of interest Noise Power WDM frequency band Neighboring WDM channels Neighboring WDM channels Guardband In-band Out-of-bandOut-of-band B • WDM channel spacing is limited by signal bandwidth • The ‘in-band’ fields (signal and noise) travel from the transmitter to the receiver • The ‘out-of-band’ fields (signal and noise) are generally not available to the transmitter or the receiver
  13. 13. 13 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Propagation for Distributed Amplification Generalized Nonlinear Schrodinger Equation (GNSE): Amplified spontaneous emission (additive white Gaussian noise) : Electrical field : Fiber dispersion : Nonlinear coefficient : Spontaneous emission factor : = 1 –  where  is the photon occupancy factor : Photon energy at signal wavelength : Fiber loss coefficient or
  14. 14. Capacity of Standard Single- Mode Fiber
  15. 15. 15 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Nonlinear Shannon Fiber Capacity Limit Estimate  Modulation  Constellations  Coding  Electronic digital signal processing (DSP)  Optical amplification • An array of advanced technologies is included  Regeneration (optical and electronic)  Optical phase conjugation  Polarization-mode dispersion (PMD)  Polarization-dependent loss (PDL) or gain (PDG) • What is not included  Fiber loss coefficient  Fiber nonlinear coefficient  Chromatic dispersion • What fiber properties are studied
  16. 16. 16 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Nonlinear Shannon Limit (Single Polarization) and Record Experiments We are closely approaching the capacity limit of SSMF Nonlinear Shannon limit for SSMF and record experimental demonstrations 0 5 10 15 20 25 30 35 40 0 1 2 3 4 5 6 7 8 9 10 SNR (dB) Spectralefficiency(bits/s/Hz) NL Shannon PSCF: 500 km (1) NTT at OFC’10: 240 km (2) AT&T at OFC’10: 320 km (3) NTT at ECOC’10: 160 km (4) NEC at OFC’11: 165 km NL Shannon SSMF: 500 km Standard single-mode fiber (SSMF) Essiambre et al. “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol., pp. 662-701(2010)
  17. 17. 17 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Nature of Nonlinear Capacity Limitations in Single-Mode Fiber WDM signal-signal nonlinear interactions dominate over signal- noise nonlinear interactions Origin of Capacity Limitations 0 5 10 15 20 25 30 35 40 0 1 2 3 4 5 6 7 8 9 10 SNR (dB) Spectralefficiency (bits/s/Hz) (1) WDM, ASE, OFs (2) WDM , w/o ASE, OFs (3) 1 ch, ASE, OFs (4) 1 ch, ASE, w/o OFs -25 -20 -15 -10 -5 0 5 10Pin (dBm) 10 15 20 25 30 35 40 45OSNR (dB) Nonlinear signal-noise interactions Nonlinear signal-signal interactions Fig. 36 of Essiambre et al. “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol., pp. 662-701(2010)
  18. 18. 18 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Nonlinear Shannon Limit versus Distance Nonlinear capacity limit increases slowly with decreasing system length Standard single-mode fiber 10 0 10 1 10 2 10 3 10 4 4 6 8 10 12 14 16 Distance (km) Spectralefficiency(bits/s/Hz) Linear fit Capacity estimate data FTTH Access Metro LH ULH SM FTTH: Fiber-to-the-home LH: Long-haul ULH: Ultra-long-haul SM: Submarine from Essiambre and Tkach, “Capacity Trends and Limits of Optical Communication Networks,” Proc. IEEE, pp. 1035-1055 (2012)
  19. 19. Capacity of Advanced Single- Mode Fibers
  20. 20. 20 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Nonlinear Shannon Limit versus Fiber Loss Coefficient Nonlinear capacity limit increases surprinsingly slowly with a reduction of the fiber loss coefficient SSMF fiber parameters except loss (distance = 1000 km) 10 -3 10 -2 10 -1 10 0 10 1 4 6 8 10 12 14 Loss coefficient, dB(dB/km) Spectralefficiency(bits/s/Hz) Conjectured fibers with ultra-low loss coefficient SSMF Lowest achieved fiber loss coefficient Linear extrapolation Capacity estimate data from Essiambre and Tkach, “Capacity Trends and Limits of Optical Communication Networks,” Proc. IEEE, pp. 1035-1055 (2012)
  21. 21. 21 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Nonlinear Shannon Limit versus Fiber Nonlinear Coefficient A very large decrease in the fiber nonlinear coefficient does not dramatically increase the nonlinear Shannon limit 10 -4 10 -3 10 -2 10 -1 10 0 10 1 6 8 10 12 14 16 Nonlinear coefficient,  (W - km)-1 Spectralefficiency(bits/s/Hz) Linear extrapolation Capacity estimate data Projected  for hollow-core fibers SSMF SSMF fiber parameters except loss (distance = 500 km, dB = 0.15 dB/km) from Essiambre and Tkach, “Capacity Trends and Limits of Optical Communication Networks,” Proc. IEEE, pp. 1035-1055 (2012)
  22. 22. 22 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Nonlinear Shannon Limit versus Fiber Dispersion The weakest dependence of the nonlinear Shannon limit on fiber parameters is for dispersion 10 0 10 1 10 2 6 7 8 9 10 11 12 Dispersion, D (ps/(nm - km)) Spectralefficiency(bits/s/Hz) Linear extrapolation Capacity estimate data SSMF fiber parameters except loss (distance = 500 km) from Essiambre and Tkach, “Capacity Trends and Limits of Optical Communication Networks,” Proc. IEEE, pp. 1035-1055 (2012)
  23. 23. Polarization-Division Multiplexing in Fibers
  24. 24. 24 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Propagation Equations for Dual Polarization in Single- Mode Fibers Equations describing propagation of two polarization modes in single-mode fibers (refered to as Manakov Equations): This set of two coupled equations can be used to model: • Polarization-division multiplexed (PDM) signals • Combined effect of nonlinearity in both polarization states • Nonlinear interactions between signal and noise in different polarizations Cross-polarization modulation (XpolM) XpolM nonlinearly couples the two polarization states of the light
  25. 25. 25 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Nonlinear Shannon Limit (PDM) and Record Experiments We are approaching the capacity limit of SSMF Nonlinear Shannon limit for SSMF and record experimental demonstrations Standard single-mode fiber (SSMF) 0 5 10 15 20 25 30 35 40 0 2 4 6 8 10 12 14 16 18 20 SNR (dB) Spectralefficiency(bits/s/Hz) NL Shannon PDM NL Shannon Single Pol. 2 x NL Shannon Single Pol. SSMF 500 km (1) AT&T at OFC’10: 320 km (2) NTT at ECOC’10: 160 km (3) NEC at OFC’11: 165 km (4) NTT at OFC’12: 240 km From Essiambre, Tkach and Ryf, upcoming book chapter in Optical Fiber Telecommunication VI (2013)
  26. 26. Space-Division Multiplexing in Fibers
  27. 27. 27 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Various Types of Optical Fibers ‘‘Single-mode’’ fibers 7-core 19 -core3-core Few-mode fiber Multimode fiber Multicore fibers Multimode fibers Hollow-core fibers Optical fibers can support from two to hundreds of spatial modes • One spatial mode but supports two modes (two polarization states) • Only fiber used for distances > 1km • Can support a few or many spatial modes • Traditionally for short reach (~ 100 meters) • Can exhibit coupling or not between cores • Coupled-core fibers support ‘‘supermodes’’ • Core made of air • Only short lengths (a few hundred meters) with high loss have been fabricated Air Holes
  28. 28. 28 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Examples of Spatial Modes Profiles Single-mode fiber Few-mode fiber Spatial overlap of modes leads to nonlinear interactions between modes Three-core fibers 3 spatial modes x 2 polarizations = 6 modes 1 spatial mode x 2 pol. = 2 modes 3 spatial modes x 2 polarizations = 6 modes 0° 0° 0° 0° 240° 120° 0° 120° 240° Fiber cross-sections:
  29. 29. 29 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Schematic of Coherent MIMO-based Coherent Crosstalk Suppression for Space-Division Multiplexing (SDM) • All guided modes of the SDM fiber are selectively launched • All guided modes are linearly coupled during propagation in the SDM fiber • All guided modes are simultaneously detected with coherent receivers • Multiple-input multiple-output (MIMO) digital signal processing decouples the received signals to recover the transmitted signal Represents a single spatial mode and a single polarization state Crosstalk from spatial multiplexing can be nearly completely removed by MIMO digital signal processing SDEMUX SMUX h11 h12 h13 h1N h21 h22 h23 h2N h31 h32 h33 h3N hN1 hN2 hN3 hNN SDM fiber Ch3 Ch1 Ch2 ChN MIMO DSP Out1 Out2 Out3 OutN SDM fiber SDM amplifier Coh-Rx3 Coh-Rx1 Coh-Rx2 Coh-RxN Adapted from Morioka et al., IEEE Commun. Mag., pp. S31-S42 (2012)
  30. 30. 30 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Spectral Efficiency and Energy Gain from Spatial Multiplexing Large gains in spectral efficiency and energy per bit can be obtained using spatial multiplexing • Gain in spectral efficiency: • Gain in energy per bit: See also Winzer, “Energy-Efficient Optical Transport Capacity Scaling Through Spatial Multiplexing,” PTL, pp. 851-853 (2011) from Essiambre and Tkach, “Capacity Trends and Limits of Optical Communication Networks,” Proc. IEEE, pp. 1035-1055 (2012)
  31. 31. 31 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. 4,200 km Transmission Experiment with Coupled-Core 3- Core Fiber (proto-photonic crystal fiber?) 4,200 km - Single-channel signals are launched into each core - Linear coupling between cores is very large - Use of multiple-input multiple output (MIMO) to “uncouple” the mixed signals - Longest transmission with multiple spatial modes from Ryf et al., Proc. OFC, paper PDP5C (2012)
  32. 32. COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Example of Spatial-Mode Multiplexers (PHASE-PLATE-BASED COUPLERS) Insertion loss 8.3 dB, 9.0 dB, 10.6 dB for LP01, LP11a, LP11b respectively Crosstalk rejection > 28dB SMF port 2 SMF port 1 SMF port 0 Phase Plates Beam Splitters f1 f2 Lenses Mirror MMUX FMF LP01 X-pol LP11a X-pol LP11b X-pol IntensityPhase LP01 Y-pol LP11a Y-pol LP11b Y-pol From Ryf et.al., J. Lighwave Technol. pp. 521-531 (2013)
  33. 33. COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Set-up of 6x6 MIMO Transmission Experiment over 65 km FEW-MODE FIBER SPAN WITH 6 SPATIAL MODES Test signal: 12 x 20Gbd 16QAM on 32 WDM wavelength (25 GHz spacing) 59 km FMF 400 ns Q 0..5x49 ns 3DW-SMUX 3DW-SMUX 1 3 5 I Q I 2ch – DAC 30 GS/s Inter- leaver O E DFB DFB DFB ECL DN-MZM DN-MZM DFB 2 4 6 PD-CRX 5 PD-CRX 3 LO ECL LeCroy 24 ch, 20 GHz, 40 GS/s DSO PD-CRX 2 PD-CRX 1 PD-CRX 6 PD-CRX 4 PBS 1 3 5 2 4 6 6 x Loop Switch 6xBlocker …… Load Switch Blocker 6 x Blocker MZM 12.5 GHz Inter- leaver O E 50 GHz 100 GHz 25 GHz See Ryf et al., Proc. of OFC, Post-deadline paper PDP5A.1 (2013)
  34. 34. COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Q-FACTOR FOR 12 x 12 MIMO TRANSMISSION 59 km FMF SPAN AND 20-Gbaud 16QAM SIGNALS • All 32 WDM channels clearly above FEC limit after 177 km transmission from Ryf et al., Proc. of OFC, Post-deadline paper PDP5A.1 (2013)
  35. 35. COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Historical Capacity Evolution by Multiplexing Types 1980 1985 1990 1995 2000 2005 2010 2015 2020 Year Systemcapacity(Tb/s) 0.001 0.01 0.1 10 100 1000 1 TDM Research WDM Research SDM Research Space-division multiplexing has already exceeded the nonlinear Shannon capacity limit of single-mode fibers TDM: Time-division multiplexing WDM: Wavelength-division multiplexing SDM: Space-division multiplexing Nonlinear Shannon capacity limit of single-mode fibers from Essiambre et al., Photon. J., Vol. 5, No. 2, paper 0701307 (2013)
  36. 36. Nonlinear Propagation Modeling in Multimode/Multicore Fibers
  37. 37. 37 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Nonlinear Equations of Propagation for Multicore and Multimode Fibers For each spatial mode p , the equation of propagation is given by: This set of p vector equations models nonlinear interactions between signal and noise in all spatial modes Inverse group velocity Group velocity dispersion Linear mode coupling Nonlinear mode coupling (involves a large number of individual mode fields) Noise : Overlap integral between modes p, l, m and n : Linear coupling coefficient between mode p and m T : Transpose, H : Hermitian conjugate Phase velocity
  38. 38. 38 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Explicit Nonlinear Equations of Propagation for Two Spatial Modes Equation of propagation for mode 1 polarization x: Inverse group velocity Group velocity dispersion Linear mode coupling Nonlinearmodecoupling Noise Phase velocity The number of nonlinear terms becomes very large, even for only 2 spatial modes
  39. 39. 39 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Random Linear Mode Coupling and Averaged Nonlinear Equations of Propagation for Multicore and Multimode Fibers Averaging over random mode coupling matrix should provide physical insights and decrease computation time by a few orders of magnitudes Stochastic nonlinear terms  average effect? • We represent the fields for all modes as the field vector • Realistic SDM fibers introduce random linear mode coupling represented by a random coupling matrix • The propagation equations in the new frame • Simplifying equations involves random matrix theory • Result of averaging depend on the structure of the linear coupling matrix
  40. 40. 40 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Nonlinear Equations of Propagation for Multicore and Multimode Fibers For each spatial mode p , the equation of propagation is given by: This set of p vector equations models nonlinear interactions between signal and noise in all spatial modes Inverse group velocity Group velocity dispersion Linear mode coupling Nonlinear mode coupling (involves a large number of individual mode fields) Noise : Overlap integral between modes p, l, m and n : Linear coupling coefficient between mode p and m T : Transpose, H : Hermitian conjugate Phase velocity From Mumtaz et al., J. Lightwave Technol., pp. 398-406 (2013)
  41. 41. 41 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Generalized Manakov Equations for Random Linear Mode Coupling between Two Polarizations of Same Mode There is significant reduction in the number of nonlinear terms but still more complicated dynamics than single-mode fibers From Mumtaz et al., J. Lightwave Technol., pp. 398-406 (2013) Nonlinear Equations of Propagation:
  42. 42. 42 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Generalized Manakov Equations for Random Linear Mode Coupling between All Modes If all modes randomly couple, the nonlinear propagation equations behave like a “super single-mode fibers” From Mumtaz et al., J. Lightwave Technol., pp. 398-406 (2013) Nonlinear Equations of Propagation:
  43. 43. Intermodal Nonlinearities in Multimode/Multicore Fibers
  44. 44. COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Experimental Set-Up to Measure Inter-modal Four-Wave Mixing • Probe is continuous wave (CW) and is always in the LP01 mode • Pump is modulated at 10 Gb/s On-Off Keying (OOK) and launched in either the LP11 or the LP01 mode • Pump is polarization scrambled SBS: Stimulated Brillouin scattering NRZ: Non-return-to-zero ECL: External-cavity laser MZM: Mach-Zehnder modulator PPG: Pulse-pattern generator MMUX: Spatial mode multiplexer MDMUX: Spatial mode demultiplexer OSA: Optical spectrum analyzer π 0 MDEMUX LP11 LP01 SBS suppressor NRZ modulator 70MHz 245MHz + MMUX π 0 LP11 LP01 (c) LP01 LP01 (a) GI-FMF 4.7 km OSA ECLs PM MZM PPG PS LP11 LP11 (b) π 0 π 0 0 1 Pump Probe See Essiambre et al., Photon. Technol. Lett., pp. 535-538 (2013) and Essiambre et al., Photon. Technol. Lett., pp. 539-542 (2013) GI-FMF: Graded-index few-mode fiber Supports 3 spatial modes (6 true modes)
  45. 45. COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Measured Relative Group Velocities and Chromatic Dispersions of the LP01 and LP11 Modes GI-FMF • Two waves belonging to two spatial modes have the same group velocity for a wavelength separation of ~16.2 nm between the LP11 and the LP01 modes • Chromatic dispersion of the LP11 mode is slightly larger than that of the LP01 mode 1525 1530 1535 1540 1545 1550 1555 1560 1565 -800 -600 -400 -200 0 200 400Relativeinversegroupvelocity(ps/km) 1525 1530 1535 1540 1545 1550 1555 1560 1565 16 17 18 19 20 21 22 Chromaticdispersion[ps/(km-nm)] Wavelength (nm) LP11 dispersion LP01 dispersion LP11 rel. vg -1 LP11 rel. vg -1 (fit) LP01 rel. vg -1 LP01 rel. vg -1 (fit) from Essiambre et al., Photon. Technol. Lett., pp. 539-542 (2013)
  46. 46. COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Schematic of the Experiment on Inter-Modal FWM •All pumps and probe are continuous waves (CWs) •The first pump (P1) is in the LP11 mode •The second pump (P2) and the probe (B) are in the LP01 mode •The wavelength of the probe is swept across the entire C-band •The pump wavelengths are kept fixed •One observes the idler(s) generated When and where will an idler be generated? Wavelength Power LP11 Pump (P1) LP01 Pump (P2) LP01 Probe (B) LP11 Idler (I) IM-FWM pump and probe waves arrangements 40 nm from Essiambre et al., Photon. Technol. Lett., pp. 539-542 (2013)
  47. 47. COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Experimental Observations of IM-FWM IM-FWM was observed over the entire 40-nm EDFA bandwidth • Figure a: Process 1 (PROC1) can be dominant • Figure b: Process 2 (PROC2) can be dominant • Both PROC1 and PROC2 can be present simultaneously 1530 1535 1540 1545 1550 1555 -60 -50 -40 -30 -20 -10 0 Power(dBm) Wavelength (nm) probe = 1546 nm probe = 1547 nm probe = 1548 nm 1530 1535 1540 1545 1550 1555 Wavelength (nm) probe = 1552 nm probe = 1553 nm probe = 1554 nm 1,530 1,535 1,540 1,545 1,550 Wavelength (nm) probe = 1547 nm probe = 1548 nm probe = 1549 nm a) PROC1 (LP01 Pump P2 : 1554 nm) b) PROC2 (LP01 Pump P2: 1546 nm) c) PROC1 & 2 (LP01 Pump P2: 1546 nm) LP01 Probe (B) LP11 Idler (I) LP11 Idler (I) (PROC2) LP11 Idler (I) (PROC1) LP11 Pump (P1) LP01 Pump (P2) LP11 Idler (I) LP01 Pump (P2) LP01 Pump (P2) LP01 Probe (B) LP01 Probe (B) LP11 Pump (P1) LP11 Pump (P1) 1 2 3 1 2 3 1 2 3 1 2 3 123 1231 2 3 1530 15501535 1540 1545 One can experimentally observe that depending on the position of the probe from Essiambre et al., Photon. Technol. Lett., pp. 539-542 (2013)
  48. 48. Summary and Outlook
  49. 49. 49 COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED. Summary and Outlook • There appears to be a limit to single-mode fiber capacity in transparent optically-routed fiber networks due to fiber Kerr nonlinearity • Laboratory experiments are about a factor of 2 from such a limit • Commercial systems are about a factor of 6 from such a limit • Advanced single-mode fibers produce limited increase in capacity Single-Mode Fiber Capacity Limit Space-Division Multiplexing in Multimode and Multicore Fibers • Multimode and/or multicore fibers are needed to perform space-division multiplexing in fibers • Multimode and multicore fibers should provide a dramatic increase in capacity per fiber strand • Multimode and/or multicore fibers are new laboratories for nonlinear optics • No definitive model of nonlinear transmission equations available yet • Unclear which fiber type maximizes capacity and/or is most suitable for implementation See Essiambre and Tkach, “Capacity Trends and Limits of Optical Communication Networks,” Proc. IEEE, pp. 1035-1055 (2012) See Essiambre et al. “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol., pp. 662-701(2010)
  50. 50. COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
  51. 51. COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED.

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