The Capacity Limit of Single-Mode Fibers and Technologies Enabling High Capacities in Multimode and Multicore Fibers

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
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
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
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)

7
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
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
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

11
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
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
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

Capacity of Standard Single-
Mode Fiber

15
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
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
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
Nonlinear Shannon Limit versus Distance
Nonlinear capacity limit increases slowly with decreasing system length
10
0
10
1
10
2
10
3
10
4
4
6
8
10
12
14
16
Distance (km)
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)

Capacity of Advanced Single-
Mode Fibers

20
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)
Conjectured fibers with
ultra-low loss coefficient
SSMF
Lowest achieved
fiber loss coefficient
Linear extrapolation

21
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
Projected  for
hollow-core fibers
SSMF
SSMF fiber parameters except loss (distance = 500 km, dB = 0.15 dB/km)

22
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))
SSMF fiber parameters except loss (distance = 500 km)

Polarization-Division
Multiplexing in Fibers

24
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
Nonlinear Shannon Limit (PDM) and Record Experiments
We are approaching the capacity limit of SSMF
Nonlinear Shannon limit for SSMF and record experimental
demonstrations
(SSMF)
0 5 10 15 20 25 30 35 40
0
2
4
6
8
10
12
14
16
18
20
SNR (dB)
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)

Space-Division Multiplexing in
Fibers

27
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
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
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
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)

31
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)

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)

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)

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)

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)

Nonlinear Propagation Modeling
in Multimode/Multicore Fibers

37
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
Explicit Nonlinear Equations of Propagation for Two Spatial Modes
Equation of propagation for mode 1 polarization x:
Nonlinearmodecoupling
Noise
Phase velocity
The number of nonlinear terms becomes very
large, even for only 2 spatial modes

39
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
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
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
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
Nonlinear Equations of Propagation:

42
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”
Nonlinear Equations of Propagation:

Intermodal Nonlinearities in
Multimode/Multicore Fibers

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)

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)

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

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

49
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)

The Capacity Limit of Single-Mode Fibers and Technologies Enabling High Capacities in Multimode and Multicore Fibers

The Capacity Limit of Single-Mode Fibers and Technologies Enabling High Capacities in Multimode and Multicore Fibers

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