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COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS RESERVED.


René-Jean EssiambreCrawford Hill Laboratory, Bell Laboratories, Alcatel-Lucent, Holmdel, NJ, USA

The Capacity Limit of Single-Mode Fibers: opportunity for multimode and multicore fibers?

Presentation at the IEEE NJ Coast, Women in Engineering Meeting on April 9, 2014

3


Acknowledgment

Jerry FoschiniGerhard Kramer

Roland RyfSebastian Randel

Bob TkachPeter WinzerNick Fontaine

Andy Chraplyvy

and many others …

Jim GordonXiang Liu

S. ChandrasekharGreg RaybonBert Basch

Antonia TulinoMaurizio MagariniHerwig Kogelnik

4


Outline

1. Basic Information Theory2. The “Fiber Channel”3. Capacity of Single-Mode Fiber4. Space-Division Multiplexing in Few-Mode,

Multimode and Multicore Fibers5. Summary and Outlook

5


Historical Evolution of Fiber-Optic Systems Capacity

What is the ultimate capacity that an optical

fiber can carry?0.01

0.1

1

10Sp

ectr

al e

ffic

ienc

y(b

its/

s/H

z)

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

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 Theory

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

One paper by C. E. Shannon in two separate issues of the Bell System Technical Journal (1948)

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

Darker area larger density of symbols

2) Constellation: bi-dim. Gaussian

3) Coding (a simple example here for illustrative puposes)

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 1 0 1 0 0 1 0 0 1

Coded data

Information bits Information bitsRedundant

bitsRedundant

bits

Detection of bit sequences can correct errors

-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

1) Modulation:Nyquist pulses sin(t)/t


-5 -4 -3 -2 -1 0 1 2 3 4 5

Time (symbol period)

Ampl

itud

e (n

.u.)

Sinc pulse

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Modulation and Constellations for Spectral Packing

• Spectrally compact modulation (Nyquist signaling “sin(x)/x” shaped pulses)• Arbitrary constellations can be generated (example above: 2 rings)

-1 -0.5 0 0.5 1Frequency (units of symbol rate)

-40

-30

-20

-10

0

10

Opt

ical

spe

ctru

m(d

Bm/s

ymbo

l rat

e)

RS = 1/TS

Real part of field ( mW1/2 )

Imag

par

t of

fie

ld (

mW

1/2

)

-1.5 -1 -0.5 0 0.5 1 1.5

-1.5

-1

-0.5

0

0.5

1

1.5

00.20.40.60.8

11.21.41.61.8

2

Symbol number

Fiel

d am

plit

ude

( m

W1/

2)

5 10 15 20 25 300

Nyquist pulsee.g. Sinc sin(x)/x

An arbitrary waveform generator is necessary to generate a spectrally compact input signal

TS

Sampling instant

The “Fiber Channel”

12


Fiber Loss Coefficient for Silica Fibers

EDFA

Silica-based optical fibers have a large wavelength band of ~400 nm (~55 THz) 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)

OH absorption

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

0.5C-band L-bandS-band U-bandE-bandO-band

SSMFAllwave

13


Wavelength

……

WDM channelsOptically-Routed Networks

In optically-routed networks, neighboring WDM channels waveforms are generally not known to a user but can be

transported over the same optical fiber!

Mesh Networks

Reconfigurable optical add-drop multiplexer (ROADM)

~ 50GHz

Rx

Tx

Tx

RxRx

14


The “Fiber Channel”

• 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

Optical path Electricaldomain

Electricaldomain

DSP E/OData Data’DSPO/E

Tx Rx

…

fiber type 1 fiber type 2 ROADM

The “fiber channel” is defined as a point-to-point connection in an optically-routed network

No other optical elements than optical fibers and optical filters (ROADMs) are present in the optical path

15


Nonlinear Equation of Propagation (Distributed Amplification)

Generalized Nonlinear Schroedinger 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

where,

The GNSE is very accurate in describing propagation in optical fibers but has no solution with arbitrary input field

16


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

Capacity of Single-Mode Fiber

18


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) Polarization-mode dispersion (PMD) Polarization-dependent loss (PDL) or gain (PDG)

• What is not considered

Fiber loss coefficient Fiber nonlinear coefficient Chromatic dispersion

• What fiber properties are studied

19


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)


20


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)

21


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


22


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)


23


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)


24


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-polarizationmodulation (XpolM)

XpolM is an additional term that nonlinearly couples the signals in both polarization

25


Nonlinear Shannon Limit (PDM) and Record Experiments

We are closely 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)

26


Capacity per Amplification Bandwidth

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)


~ 5 THzC band EDFA C+L band EDFA Full optical window

10 THz 50 THzBandwidth~ 85 Tb/s 170 Tb/s 0.85 Pb/sCapacity

OH absorption

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

0.5C-band L-bandS-band U-bandE-bandO-band

SSMFAllwave

Space-Division Multiplexing in in Few-Mode, Multimode and Multicore Fibers

28


Various Types of Optical Fibers

Optical fibers can support from two to hundreds of modes

‘‘Single-mode’’ fibers• One spatial mode but supports

two modes (two polarization states)• Only fiber used for distances > 1km

Few-mode fiber Multimode fiber

Multimode fibers• Can support a few or many spatial modes• Traditionally for short reach (~ 100 meters)

7-core 19 -core3-core

Multicore fibers• Can exhibit coupling or not between cores• Coupled-core fibers support ‘‘supermodes’’

Hollow-core fibers• Core made of air• Only short lengths (a few hundred meters)

with high loss have been fabricated

AirHoles

29


Examples of Spatial Modes Profiles

Spatial overlap of modes leads to nonlinear interactions between modes

Few-mode fiber

3 spatial modes x 2 polarizations= 6 modes

Single-mode fiber

1 spatial mode x 2 pol. = 2 modes

Three-core fibers

3 spatial modes x 2 polarizations = 6 modes

0°

0°

0° 0°

240° 120°

0°

120° 240°

Fiber cross-sections:

30


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)


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)

One can selectively launch in and detect each fiber mode


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)


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

from Essiambre et al., Photon. J., Vol. 5, No. 2, paper 0701307 (2013)

Nonlinear Shannon capacity limit of

single-mode fibers

Summary and Outlook

35


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 3 and commercial systems are about a factor of 10 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 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)

See Essiambre et al. “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol., pp. 662-701(2010)

Documents

COPYRIGHT © 2013 ALCATEL-LUCENT. ALL RIGHTS …sites.ieee.org/njcoast/files/2014/04/IEEE_Chapter_NJ_Coast_Women... · Crawford Hill Laboratory, Bell Laboratories, Alcatel-Lucent,