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

COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED.


René-Jean EssiambreBell 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 FoschiniGerhard Kramer

Roland RyfSebastian Randel

Peter WinzerNick Fontaine

Bob TkachAndy Chraplyvy

and many others …

Jim GordonXiang Liu

S. ChandrasekharBert Basch

Antonia TulinoMaurizio MagariniHerwig Kogelnik

4


Outline1. Basic Information Theory2. The “Fiber Channel”3. Capacity of Standard Single-Mode Fiber4. Capacity of Advanced Single-Mode Fibers5. Polarization-Division Multiplexing in Fibers6. Space-Division Multiplexing in Fibers7. Nonlinear Propagation Modeling in

Multimode/Multicore Fibers8. 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

Syst

em c

apac

ity

Gbi

ts/s

Tbit

s/s

1986 1990 1994 1998 2002 2006 2010

0.01

0.1

1

10Sp

ectr

al e

ffic

ienc

y(b

its/

s/H

z)

WD

M c

hann

els

0.5 dB/year(12%/year)

2.5 dB/year(78%/year)

from Essiambre et al., J. Lightwave Technol., pp. 662-701 (2010)

Basic Information Theory

7


The Birth of Information TheoryOne 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 ChannelsC: 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)

Spe

ctra

l effi

cien

cy

(bits

/s/H

z)

-5 0 5 10 15 20 25 300123456789

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

-0.20

0.2

0.4

0.60.8

1

Time (symbol period)

Am

plitu

de (n

.u.) One pulse Adjacent

pulse

Sampling instant

1) Modulation:Nyquist pulses sin(t)/tDarker 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 dataInformation 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 bitsRedundant

bitsRedundant

bits

Detection of bit sequences can correct errors

The “Fiber Channel”

11


Dependence of Fiber Loss Coefficient on Wavelength for Silica Fibers

Wavelength (nm)

Fibe

r los

s co

effic

ient

(dB

/km

)

1200 1250 1300 1350 1400 1450 1500 1550 1600 1650 17000.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

EDFA

AllwaveSSMF

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

FrequencyRS

WDM channel of interest

NoisePow

er

WDM frequency bandNeighboring 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 35 400

1

2

3

4

5

6

7

8

9

10

SNR (dB)

Spec

tral

eff

icie

ncy

(bit

s/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 35 400

1

2

3

4

5

6

7

8

9

10

SNR (dB)

Spe

ctra

l effi

cien

cy(b

its/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-noiseinteractions

Nonlinear signal-signalinteractions

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

Standard single-mode fiber

100

101

102

103

104

4

6

8

10

12

14

16

Distance (km)

Spec

tral e

ffici

ency

(bits

/s/H

z)

Linear fitCapacity estimate data

FTTH Access Metro LHULH

SM

FTTH: Fiber-to-the-homeLH: Long-haulULH: Ultra-long-haulSM: 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

100

101

4

6

8

10

12

14

Loss coefficient, dB(dB/km)

Spe

ctra

l effi

cien

cy (b

its/s

/Hz)

Conjectured fibers with ultra-low loss coefficient

SSMFLowest achieved

fiber loss coefficient

Linear extrapolationCapacity estimate data


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 10-1 100 1016

8

10

12

14

16

Nonlinear coefficient, (W - km)-1

Spec

tral e

ffici

ency

(bits

/s/H

z)


Projected forhollow-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

100 101 1026

7

8

9

10

11

12

Dispersion, D (ps/(nm - km))

Spec

tral e

ffici

ency

(bits

/s/H

z)


SSMF fiber parameters except loss (distance = 500 km)


Polarization-Division Multiplexing in Fibers

24


Propagation Equations for Dual Polarization in Single-Mode FibersEquations 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-polarizationmodulation (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

Standard single-mode fiber(SSMF)

0 5 10 15 20 25 30 35 400

2

4

6

8

10

12

14

16

18

20

SNR (dB)

Spe

ctra

l effi

cien

cy (b

its/s

/Hz)

NL Shannon PDMNL 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

AirHoles

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

SDE

MU

X

SMU

Xh11 h12 h13 h1N

h21 h22 h23 h2N

h31 h32 h33 h3N

hN1 hN2 hN3 hNN

SDM fiber

Ch3

Ch1

Ch2

ChN

MIMO DSP

Out

1

Out

2

Out

3

Out

N

SDM fiber

SDMamplifier

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)from Essiambre and Tkach, “Capacity Trends and Limits of Optical Communication Networks,” Proc. IEEE, pp. 1035-1055 (2012)

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 loss8.3 dB, 9.0 dB, 10.6 dB for LP01, LP11a, LP11b respectively

Crosstalk rejection > 28dB

SMFport 2

SMFport 1

SMFport 0

PhasePlates

BeamSplitters

f1 f2

LensesMirror

MMUX

FMF

LP01 X-pol LP11a X-pol LP11b X-pol

Inte

nsit

yPh

ase

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 kmFEW-MODE FIBER SPAN WITH 6 SPATIAL MODES

Test signal: 12 x 20Gbd 16QAMon 32 WDM wavelength (25 GHz spacing)

59 kmFMF

400 ns

Q

0..5x49 ns

3DW

-SM

UX

3DW

-SM

UX 1

3

5I

Q I2ch – DAC

30 GS/sInter-leaver

O

EDFB

DFB

DFB ECL DN-MZM

DN-MZM

DFB 2

4

6

PD-CRX 5

PD-CRX 3

LOECL

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

6 x

Blo

cker

……

LoadSwitch

Bloc

ker

6 x Blocker

MZM

12.5GHz

Inter-leaver

O

E50 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 2020Year

Sys

tem

cap

acity

(Tb/

s)

0.001

0.01

0.1

10

100

1000

1

TDM ResearchWDM ResearchSDM 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 FibersFor 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 velocityGroup 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 ModesEquation of propagation for mode 1 polarization x:


Nonlinear m

ode coupling

NoisePhase 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 FibersFor 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 scatteringNRZ: Non-return-to-zeroECL: External-cavity laserMZM: Mach-Zehnder modulatorPPG: Pulse-pattern generatorMMUX: Spatial mode multiplexer MDMUX: Spatial mode demultiplexerOSA: Optical spectrum analyzer

π0

MDEMUX

LP11

LP01

SBS suppressor NRZ modulator

70MHz 245MHz

+

MMUX

π0 LP11

LP01

(c)LP01

LP01

(a)

GI-FMF

4.7 km

OSAECLs

PM MZM PPG PS

LP11

LP11

(b)

π0

π0

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 fiberSupports 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

400R

elat

ive

inve

rse

grou

p ve

loci

ty (p

s/km

)

1525 1530 1535 1540 1545 1550 1555 1560 156516

17

18

19

20

21

22

Chr

omat

ic d

ispe

rsio

n [p

s/(k

m-n

m)]

Wavelength (nm)

LP11 dispersionLP01 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

Pow

er 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

Pow

er (d

Bm

)

Wavelength (nm)

probe= 1546 nm

probe= 1547 nm

probe= 1548 nm

1530 1535 1540 1545 1550 1555Wavelength (nm)

probe= 1552 nm

probe= 1553 nm

probe= 1554 nm

1,530 1,535 1,540 1,545 1,550Wavelength (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)

LP01Probe (B)

LP11 Idler (I)

LP11 Idler (I)

(PROC2)LP11 Idler (I)

(PROC1)

LP11Pump (P1)

LP01Pump (P2)

LP11 Idler (I)

LP01Pump (P2)

LP01Pump (P2)

LP01Probe (B)

LP01Probe (B)

LP11Pump (P1)

LP11Pump(P1)

1 2 31 2 3 1 2 3

1 2 3

1231231 2 3

1530 15501535 1540 1545

One can experimentally observe that depending on the position of the probe


Summary and Outlook

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 capacityper 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

implementationSee 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)



Technology

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