COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
The Capacity Limit of Single-Mode Fibers:
opportunity for multimode and multicore fibers?
René-Jean Essiambre
Crawford Hill Laboratory, Bell Laboratories, Alcatel-Lucent, Holmdel, NJ, USA
Presentation at the IEEE NJ Coast, Women in Engineering Meeting on April 9, 2014
COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
Acknowledgment
Jerry Foschini
Gerhard Kramer
Roland Ryf
Sebastian Randel
Bob Tkach
Peter Winzer
Nick Fontaine
Andy Chraplyvy
Jim Gordon
Xiang Liu
S. Chandrasekhar
Greg Raybon
Bert Basch
Antonia Tulino
Maurizio Magarini
Herwig Kogelnik
and many others …
3
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Outline
1.
2.
3.
4.
Basic Information Theory
The “Fiber Channel”
Capacity of Single-Mode Fiber
Space-Division Multiplexing in Few-Mode,
Multimode and Multicore Fibers
5. Summary and Outlook
4
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Historical Evolution of Fiber-Optic Systems Capacity
What is the ultimate
capacity that an optical
fiber can carry?
10
WDM channels
Tbits/s
Gbits/s
Spectral efficiency
(bits/s/Hz)
Record Capacities
System capacity
100
2.5 dB/year
1 (78%/year)
100
10
1986
10
0.5 dB/year
(12%/year)
1990
1
0.1
0.01
from Essiambre et al., J. Lightwave Technol., pp. 662-701 (2010)
5
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1994
1998
2002
2006 2010
Basic Information Theory
The Birth of Information Theory
One paper by C. E. Shannon in two separate issues
of the Bell System Technical Journal (1948)
“Copyright 1955 Alcatel-Lucent USA, Inc.”
Claude E. Shannon (1955)
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
7
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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)
Spectral efficiency
(bits/s/Hz)
Shannon capacity limit:
10
9
8
7
6
5
4
3
2
1
0
-5
SE = C/B = log2 (1 + SNR)
+ 1 bit/s/Hz
+ 3 dB SNR
0
5
10
15
20
25
30
SNR (dB)
Increasing the SNR by 3 dB increases the capacity by 1 bit/s/Hz
per polarization state
8
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Three Elements Necessary to Achieve the Shannon Limit
Modulation:Nyquist pulses  sin(t)/t
1)
2)
Constellation: bi-dim. Gaussian
Darker area
 larger
density of
symbols
Amplitude (n.u.)
One pulse
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-5 -4 -3 -2 -1
0
1
2
3
4
5
Time (symbol period)
3)
Coding (a simple example here for illustrative puposes)
Coded data
Uncoded data
Information bits
Redundant
Redundant
Information bits bits Information bits bits
Information bits
101100010010
1011001101001001
Detection of bit sequences is no
different than detection bit per bit
Detection of bit sequences can
correct errors
9
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10
Optical spectrum
(dBm/symbol rate)
Nyquist pulse
e.g. Sinc  sin(x)/x
Sinc pulse
1.2
1
0.8
0
-10
-20
RS = 1/TS
-30
-40
-1
0.6
TS
0.4
0.2
0
-0.2
Sampling instant
-0.4
-5 -4 -3 -2 -1
0
1
2
3
Time (symbol period)
-0.5
0
0.5
1
Frequency (units of symbol rate)
4
5
Field amplitude ( mW1/2 )
Amplitude (n.u.)
1.4
Imag part of field ( mW1/2 )
Modulation and Constellations for Spectral Packing
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
5
10
15
1.5
1
0.5
0
-0.5
-1
-1.5
-1.5 -1 -0.5 0
0.5 1
1.5
Real part of field ( mW1/2 )
20
25
30
Symbol number
• Spectrally compact modulation (Nyquist signaling  “sin(x)/x” shaped pulses)
• Arbitrary constellations can be generated (example above: 2 rings)
An arbitrary waveform generator is necessary to generate a
spectrally compact input signal
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The “Fiber Channel”
Fiber Loss Coefficient for Silica Fibers
Wavelength-division multiplexed (WDM) channels
…
…
Wavelength
Fiber loss coefficient (dB/km)
0.5
O-band
E-band
~ 50GHz
S-band C-band L-band U-band
0.45
EDFA
0.4
OH absorption
~ 10 THz
0.35
0.3
0.25
SSMF
Allwave
0.2
0.15
1200
1250
1300
1350
1400
1450
1500
1550
1600
1650
1700
Wavelength (nm)
Silica-based optical fibers have a large wavelength band of
~400 nm (~55 THz) having loss below 0.35 dB/km
Essiambre et al. “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol., pp. 662-701(2010)
12
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Optically-Routed Networks
Mesh Networks
WDM channels
…
…
Wavelength
~ 50GHz
Tx
Rx
Rx
Reconfigurable
optical add-drop
multiplexer
(ROADM)
Tx
In optically-routed networks, neighboring WDM channels
waveforms are generally not known to a user but can be
transported over the same optical fiber!
13
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The “Fiber Channel”
The “fiber channel” is defined as a point-to-point connection in
an optically-routed network
Electrical
domain
Optical path
…
Data DSP E/O
Electrical
domain
O/E DSP Data’
Tx
Rx
fiber type 1
fiber type 2
ROADM
• Arbitrary complex digital signal processing (DSP) is allowed at either
ends (transmitter and receiver) of the optical path
• The optical path incorporates nearly square optical filters from
reconfigurable optical add-drop multiplexers (ROADMs) and long
segments of optical fibers
No other optical elements than optical fibers and
optical filters (ROADMs) are present in the optical path
14
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Nonlinear Equation of Propagation (Distributed Amplification)
Generalized Nonlinear Schroedinger Equation (GNSE):
: Electrical field
: Fiber dispersion
: Nonlinear coefficient
where,
Amplified spontaneous emission
(additive white Gaussian noise)
: Spontaneous emission factor
: = 1 –  where  is the photon occupancy factor
: Photon energy at signal wavelength
: Fiber loss coefficient
The GNSE is very accurate in describing propagation in
optical fibers but has no solution with arbitrary input field
15
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Amplified Spontaneous Emission Accumulation and Fiber
Loss Coefficient
• Erbium-doped fiber amplified (EDFA) systems
• Ideal distributed Raman amplified (IDRA) systems
For ideal distributed Raman amplification, reducing the loss coefficient 
by a factor of 2 reduces the noise spectral density by the same factor
16
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Capacity of Single-Mode Fiber
Nonlinear Shannon Fiber Capacity Limit Estimate
• An array of advanced technologies is included





Modulation
Constellations
Coding
Electronic digital signal processing (DSP)
Optical amplification
• What fiber properties are studied
 Fiber loss coefficient
 Fiber nonlinear coefficient
 Chromatic dispersion
• What is not considered
 Regeneration (optical and electronic)
 Polarization-mode dispersion (PMD)
 Polarization-dependent loss (PDL) or gain (PDG)
18
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Nonlinear Shannon Limit (Single Polarization) and
Record Experiments
Nonlinear Shannon limit for SSMF and record experimental
demonstrations
Spectral efficiency (bits/s/Hz)
10
NL Shannon SSMF: 500 km
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
9
8
7
Standard single-mode fiber
(SSMF)
6
5
4
3
2
1
0
0
5
10
15
20
25
SNR (dB)
30
35
40
We are closely approaching the capacity limit of SSMF
Essiambre et al. “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol., pp. 662-701(2010)
19
COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
Nonlinear Shannon Limit versus Distance
Standard single-mode fiber
Spectral efficiency (bits/s/Hz)
16
Linear fit
Capacity estimate data
14
12
FTTH: Fiber-to-the-home
LH: Long-haul
ULH: Ultra-long-haul
SM: Submarine
10
8
6
4
0
10
ULH
FTTH
Access
10
1
Metro
10
LH
2
10
3
SM 10
4
Distance (km)
Nonlinear capacity limit increases slowly with decreasing system length
from Essiambre and Tkach, “Capacity Trends and Limits of Optical Communication Networks,” Proc. IEEE, pp. 1035-1055 (2012)
20
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Nonlinear Shannon Limit versus Fiber Loss Coefficient
SSMF fiber parameters except loss (distance = 1000 km)
Spectral efficiency (bits/s/Hz)
14
Capacity estimate data
Linear extrapolation
12
Conjectured fibers with
ultra-low loss coefficient
10
8
Lowest achieved
fiber loss coefficient
SSMF
6
4 -3
10
10
-2
10
-1
10
0
Loss coefficient,  dB(dB/km)
10
1
Nonlinear capacity limit increases surprinsingly slowly with a
reduction of the fiber loss coefficient
from Essiambre and Tkach, “Capacity Trends and Limits of Optical Communication Networks,” Proc. IEEE, pp. 1035-1055 (2012)
21
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Nonlinear Shannon Limit versus Fiber Nonlinear Coefficient
SSMF fiber parameters except loss (distance = 500 km, dB = 0.15 dB/km)
Spectral efficiency (bits/s/Hz)
16
Linear extrapolation
Capacity estimate data
14
12
Projected  for
hollow-core fibers
10
8
6 -4
10
SSMF
10
-3
10
-2
10
-1
10
0
10
1
Nonlinear coefficient,  (W - km)-1
A very large decrease in the fiber nonlinear coefficient does not
dramatically increase the nonlinear Shannon limit
from Essiambre and Tkach, “Capacity Trends and Limits of Optical Communication Networks,” Proc. IEEE, pp. 1035-1055 (2012)
22
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Nonlinear Shannon Limit versus Fiber Dispersion
SSMF fiber parameters except loss (distance = 500 km)
Spectral efficiency (bits/s/Hz)
12
Linear extrapolation
Capacity estimate data
11
10
9
8
7
6 0
10
10
1
10
2
Dispersion, D (ps/(nm - km))
The weakest dependence of the nonlinear Shannon limit
on fiber parameters is for dispersion
from Essiambre and Tkach, “Capacity Trends and Limits of Optical Communication Networks,” Proc. IEEE, pp. 1035-1055 (2012)
23
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Nonlinear Propagation Equations for Polarization-Division
Multiplexing (PDM)
Equations describing nonlinear propagation of two polarization
states in single-mode fibers (refered to as Manakov Equations):
Cross-polarization
modulation (XpolM)
XpolM is an additional term that nonlinearly couples the
signals in both polarization
24
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Nonlinear Shannon Limit (PDM) and Record Experiments
Nonlinear Shannon limit for SSMF and record experimental
demonstrations
Spectral efficiency (bits/s/Hz)
20
NL Shannon PDM
NL Shannon Single Pol.
2 x NL Shannon Single Pol.
18
16
Standard single-mode fiber
(SSMF)
SSMF 500 km
14
12
10
8
6
4
(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
2
0
0
5
10
15
20
25
30
35
40
SNR (dB)
We are closely approaching the capacity limit of SSMF
From Essiambre, Tkach and Ryf, upcoming book chapter in Optical Fiber Telecommunication VI (2013)
25
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Capacity per Amplification Bandwidth
Fiber loss coefficient (dB/km)
0.5
O-band
E-band
S-band C-band L-band U-band
0.45
0.4
OH absorption
0.35
0.3
0.25
SSMF
Allwave
0.2
0.15
1200
1250
1300
1350
1400
1450
1500
1550
1600
1650
1700
Wavelength (nm)
Bandwidth
Capacity
C band EDFA
~ 5 THz
~ 85 Tb/s
C+L band EDFA
10 THz
170 Tb/s
Full optical window
50 THz
0.85 Pb/s
The capacity of a C+L band EDFA system is about 10 millions times
the average bandwidth of internet access to costumers (20 Mb/s)
Essiambre et al. “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol., pp. 662-701(2010)
26
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Space-Division Multiplexing in
in Few-Mode, Multimode and
Multicore Fibers
Various Types of Optical Fibers
‘‘Single-mode’’ fibers
Multimode fibers
• 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)
Few-mode fiber
Multicore fibers
Hollow-core fibers
• Can exhibit coupling or not between cores
• Coupled-core fibers support ‘‘supermodes’’
3-core
Multimode fiber
7-core
• Core made of air
• Only short lengths (a few hundred meters)
with high loss have been fabricated
19 -core
Air
Holes
Optical fibers can support from two to hundreds of modes
28
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Examples of Spatial Modes Profiles
Fiber cross-sections:
Single-mode fiber
Few-mode fiber
Three-core fibers
0°
0°
0°
0°
0°
240°
120°
120°
240°
1 spatial mode x 2 pol.
3 spatial modes x 2 polarizations
3 spatial modes x 2 polarizations
= 2 modes
= 6 modes
= 6 modes
Spatial overlap of modes leads to nonlinear
interactions between modes
29
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Schematic of Coherent MIMO-based Coherent Crosstalk
Suppression for Space-Division Multiplexing (SDM)
Ch1
SDM
amplifier
SDM fiber
h11
h12
h13
h1N
h21
h22
h23
h2N
h31
h32
h33
h3N
Coh-Rx2
SDM fiber
SDEMUX
SMUX
Ch2
Ch3
Coh-Rx1
Coh-Rx3
MIMO DSP
Coh-RxN
•
•
•
•
hNN
OutN
hN3
Out3
Represents a single spatial mode and a single polarization state
hN2
Out1
hN1
Out2
ChN
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
Crosstalk from spatial multiplexing can be nearly completely
removed by MIMO digital signal processing
Adapted from Morioka et al., IEEE Commun. Mag., pp. S31-S42 (2012)
30
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Example of Spatial-Mode Multiplexers
(PHASE-PLATE-BASED COUPLERS)
SMF
port 0
MMUX
SMF
port 1
Beam
Splitters
f1
f2
FMF
LP01 X-pol
LP01 Y-pol
LP11a X-pol LP11a Y-pol LP11b X-pol LP11b Y-pol
Phase
SMF
port 2
Lenses
Mirror
Intensity
Phase
Plates
Insertion loss
8.3 dB, 9.0 dB, 10.6 dB for LP01, LP11a, LP11b respectively, Crosstalk rejection > 28dB
One can selectively launch in and detect each fiber mode
From Ryf et.al., J. Lighwave Technol. pp. 521-531 (2013)
COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
Set-up of 6x6 MIMO Transmission Experiment
over 65 km
FEW-MODE FIBER SPAN WITH 6 SPATIAL MODES
…
DFB
O
InterMZM
leaver
E
50 GHz
25 GHz
12.5
GHz
Q
2ch – DAC
30 GS/s
Q
0..5x49 ns
I
PBS
1
2
3
4
5
6
Load
Switch
I
DN-MZM
59 km
FMF
1
2
3
4
5
6
6 x Blocker
DFB
O
Interleaver
E
DN-MZM
3DW-SMUX
…
DFB
ECL
Blocker
DFB
3DW-SMUX
6 x Loop Switch
400 ns
6 x Blocker
100 GHz
PD-CRX 1
PD-CRX 2
PD-CRX 3
PD-CRX 4
PD-CRX 5
PD-CRX 6
ECL
LO
LeCroy 24 ch,
20 GHz, 40 GS/s
DSO
Test signal: 12 x 20Gbd 16QAM
on 32 WDM wavelength
(25 GHz spacing)
See Ryf et al., Proc. of OFC, Post-deadline paper PDP5A.1 (2013)
COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
Historical Capacity Evolution by Multiplexing Types
System capacity (Tb/s)
1000
100
TDM Research
WDM Research
SDM Research
Nonlinear Shannon
capacity limit of
single-mode fibers
10
1
0.1
0.01
0.001
1980 1985
1990
1995
2000
2005
2010
Year
2015
2020
TDM: Time-division multiplexing
WDM: Wavelength-division multiplexing
SDM: Space-division multiplexing
Space-division multiplexing has already exceeded the
nonlinear Shannon capacity limit of single-mode fibers
from Essiambre et al., Photon. J., Vol. 5, No. 2, paper 0701307 (2013)
COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
Summary and Outlook
Summary and Outlook
Single-Mode Fiber Capacity Limit
• 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 3 and commercial systems are
about a factor of 10 from such a limit
• Advanced single-mode fibers produce limited increase in capacity
See Essiambre et al. “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol., pp. 662-701(2010)
Space-Division Multiplexing in Multimode and Multicore Fibers
• Multimode and multicore fibers can be used for space-division multiplexing
• These fibers may provide a dramatic increase in capacity per fiber strand
• Unclear which fiber type maximizes capacity and/or is most suitable for
implementation
• Nonlinear effects in these fibers open new forms of nonlinear interactions
See Essiambre and Tkach, “Capacity Trends and Limits of Optical Communication Networks,” Proc. IEEE, pp. 1035-1055 (2012)
35
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