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Exabit optical communication explored using 3M scheme

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2014 Jpn. J. Appl. Phys. 53 08MA01

(http://iopscience.iop.org/1347-4065/53/8S2/08MA01)

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Exabit optical communication explored using 3M scheme

Masataka Nakazawa

Research Institute of Electrical Communication, Tohoku University, Sendai 980-8577, Japan

Received February 12, 2014; accepted March 24, 2014; published online July 3, 2014

The capacity of the optical communication infrastructure in backbone networks has increased 1000-fold over the last 20 years. Despite this rapidprogress, internet trafc is continuing to grow at an annual rate of 40%. This means that in 20 years, we will need petabit/s or even exabit/s opticalcommunication. In this paper, we present recent challenges and efforts toward achieving a hardware paradigm shift to overcome the capacitylimitation imposed by the current optical communication infrastructure. We will overview the latest advances on the three multi technologies, i.e.,multi-level transmission with ultrahigh spectral efciency, space division multiplexing in multi-core bers, and mode division multiplexing withmultiple-input multiple-output (MIMO). 2014 The Japan Society of Applied Physics

1. Introduction

The capacity of the optical communication infrastructure inbackbone networks has increased 1000-fold over the last 20years, and this has been made possible by the development ofthe erbium-doped ber amplier (EDFA) and wavelengthdivision multiplexing (WDM).1) Despite such rapid progress,information capacity is still growing at an annual rate of 40%,which means that in 20 years we will need petabit/s oreven exabit/s optical communication. However, it is widelyrecognized that the maximum transmission capacity of asingle strand of ber is rapidly approaching its limit at100Tbit/s owing to optical power limitations imposed bythe ber fuse phenomenon2) and the nite transmissionbandwidth determined by EDFAs. This situation is depictedin Fig. 1.To explore breakthrough technologies that will enable us

to exceed these limits and achieve a giant leap, we launcheda collaborative study group called EXtremely AdvancedTransmission (EXAT) in Japan in 2008, and advocated thepromotion of the three M technologies as shown inFig. 2.3) The rst M technology is a multi-level modulationformat, which enables us to achieve a high spectral efciencycomparable to that of wireless communication. The secondM technology is multi-core ber (MCF), which employsspace division multiplexing (SDM). The third M technol-ogy is mode division multiplexing in which multi-input andmulti-output (MIMO) technology, which originated fromwireless communication, will be useful for handling multi-modes in multi-core/multi-mode bers. These multitechnologies have attracted considerable interest fromresearchers worldwide, and intensive efforts have been madeto pursue these goals. As a result, a number of studies on thethree M technologies have been reported simultaneously atrecent conferences, and rapid and substantial progress hasbeen made in these elds.433)

In this paper, we describe recent challenges and the effortswe have made towards a hardware paradigm shift in theoptical communication infrastructure by employing themulti technologies. This includes ultra multilevel coherenttransmission including 1024 quadrature amplitude modula-tion (QAM) and an ultrahigh-speed and spectrally efcienttransmission using optical Nyquist pulses, ultralow-crosstalkMCF and its application to SDM transmission, and modedivision multiplexing with MIMO technology.

2. First M: Multi-level coherent transmission withan ultrahigh spectral efciency

Achieving an ultrahigh spectral efciency (SE) toward theShannon limit is one of the targets of our three-Mbreakthrough technologies, which allows us to expand thetotal WDM capacity within a nite optical amplicationbandwidth. Of the various available formats, M-ary QAM iscapable of approaching the Shannon limit most closely byincreasing the multiplicity M. QAM is a modulation formatthat combines two carriers whose amplitudes are modulated

100M

Link

Cap

acity

/ fib

er(s)

[bps

]

1.6G2.4G

1980 1990 2000

400M

10GTDM

Moores Law

2010 2020

100T

1G

1P

1E

1T

1G

1P

1E

1T

40G

WDM

10Gx80

EDFA

Increase in Internet Traffic in Japan

1st InnovationEDFA, WDM

2nd InnovationMulti-level coherent transmission

Multi-core fiberMulti-mode control

1 Tbit/s@200940% increase per year

100G

Optical power limitationBandwidth limitation of

optical amplifiers

Fiscal Year

120

100

80

60

40

20

0

Inte

rnet

traf

fic[G

bit/s]

Year1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

Fig. 1. (Color online) Technological overview of optical bertransmission.

Fig. 2. (Color online) 3M technologies for achieving >1000 capacityand throughput.

Japanese Journal of Applied Physics 53, 08MA01 (2014)

http://dx.doi.org/10.7567/JJAP.53.08MA01

REVIEW PAPER

08MA01-1 2014 The Japan Society of Applied Physics

independently with the same optical frequency and whosephases are 90 degrees apart. A 2N QAM signal represents Nbits, so it has N times the spectral efciency compared withOOK.The challenge with respect to a higher QAM multiplicity is

to meet higher SNR and phase noise tolerance requirements.Figure 3 shows the relationship between Eb/N0 and thetheoretical bit error rate (BER) forM-ary QAM. For a BER of2 103, the required Eb/N0 values are 21 and 24 dB for 512and 1024 QAM, which corresponds to SNRs of 30.5 and34 dB, respectively. To realize a better BER performance witha lower Eb/N0, the forward error correction (FEC) techniquehas been developed. Figure 4 shows the BER after applyingFEC vs the input Q value without FEC, Qin.34) Qin is the SNRgiven by

Qin I1 I01 0 1

where I1 and I0 are the mean values and 1 and 0 are thestandard deviations of the bits corresponding to 1 and 0,

respectively. Here, the Shannon limit describes the lowest Qinvalue needed to achieve an innitely low BER by employingFEC under a certain code rate R:

R 1 BERin log2 BERin 1 BERin log21 BERin

BERin 12erfc

Qin2

p

2

which is known as Shannons second theorem or the noisy-channel coding theorem.35,36) This provides the ultimate limitfor the minimum Q value needed to achieve an innitely lowBER. Recently, third generation FEC, namely a turbo blockcode with a soft decision, has been developed that enables usto realize BER performance very close to the Shannon limit.This indicates the possibility of realizing ultrahigh spectralefciency by combining QAM and FEC.Here we describe our recent demonstration of a 1024

QAM transmission, in which a polarization-multiplexed60Gbit/s signal was transmitted over 150 km.4) Figure 5shows the experimental setup. As a coherent light source, weused a 1.5 m acetylene frequency-stabilized ber ring laser

10-6

10-5

10-4

10-3

10-2

10-1

100

0 5 10 15 20 25 30Eb/N0 [dB]

BER

16 QAM

1024 QAM

64 QAM256QAM

512QAM

Fig. 3. (Color online) BER of 161024 QAM as a function of Eb/N0.

Qin (dB)

BER

ou

t

Uncoded

Shannon limit

(R=0.8, Hard decision)

10-2

10-3

10-4

10-5

10-6

10-7

10-8

10-9

10-10

10-114 5 6 7 8 9 10 11 12 13 14 15 16

FEC (3rd gen)

Fig. 4. (Color online) Relationship between BER after FEC and Q valuewithout FEC.34)

PCEDFA

IQ Mod.

(fOFS=2.03 GHz)OFS

Optical Filter (3.5 nm)

12 Gsample/s

PC AttAmplifier

PC

IQ Mod.

3 Gsymbol/s 1024 QAM signalw/ Nyquist raised cosine filter (roll off = 0.35)w/ FDE

PBC

XY

PC

PD

Synthesizer

FeedbackCircuit

LocalOscillator

DBMPC

PC fsyn=2.03 GHz

90Optical Hybrid75 km SLA

Digital Signal Processor

Etalon

Optical Filter ( 2.5 nm) (Tunable Fiber Laser)

Att PrecA/DB-PD

X

Y

Optical filter (0.7 nm)A/DB-PD A/DB-PD A/DB-PD

90

90PCRaman Pump-1 dBm

PC: Polarization ControllerOFS: Optical Frequency ShifterPBC: Polarization Beam CombinerSSMF: Standard Single-mode FiberDBM: Double Balanced MixerB-PD: Balanced Photo-Detector

Att

75 km SLA

Raman Pump -1 dBm

fQAM signal

2.03 GHz

Inte

nsity

Pilot signal

C2H2 FrequencyStabilized Fiber Laser

Arbitrary WaveformGenerator

Fig. 5. Experimental setup for 1024 QAM (60Gbit/s) coherent transmission over 150 km.

Jpn. J. Appl. Phys. 53, 08MA01 (2014) REVIEW PAPER


with a linewidth of 4 kHz.37) The output of the laser wasmodulated at an IQ modulator with a 3Gsymbol/s 1024QAM baseband signal produced by an arbitrary waveformgenerator (AWG) operating at 12Gsample/s. We employeda raised-cosine Nyquist lter at the AWG using a softwareprogram to reduce the bandwidth of the QAM signal. It iswell known in the microwave communication eld that aNyquist lter is very useful for reducing the bandwidth ofa data signal without introducing intersymbol interference.38)

Figure 6 shows the transfer function and impulse responseof the raised-cosine Nyquist lter. The transfer function isgiven by

Hf 12

1 sin f0:5

0:5 2 jfj < 0:5

2

1 jfj < 0:5 2

0 jfj 0:5 2

8>: ; 3

where is called a roll-off factor. As shown in Fig. 6(b), theimpulse response becomes zero at the location of neighboringsymbols. This indicates that the bandwidth can be reducedwith the Nyquist lter while avoiding intersymbol interfer-ence (ISI). We employed a root raised-cosine Nyquist lterwith a roll-off factor = 0.35 at the AWG as well as in thedigital signal processor (DSP) at the receiver using software,so that the bandwidth of the QAM signal was reduced to4.05GHz. In addition, a pre-equalization process basedon frequency domain equalization (FDE)39) was adopted toprovide high-resolution compensation for the distortions

caused by individual components such as the AWG and theIQ modulator.The optical QAM signal was then orthogonally polar-

ization-multiplexed and launched into a 150 km ber link. Atthe receiver, the QAM signal was homodyne-detected at a90 optical hybrid. As a local oscillator (LO), we used afrequency-tunable ber laser whose phase was locked to thepilot tone transmitted with the data signal via the opticalphase-locked loop (OPLL), which enables low phase-noisecoherent detection. After detection with balanced photo-diodes, the QAM data were A/D converted and processedwith a DSP in an off-line condition. In the DSP, a digitalback-propagation method was adopted to compensate forber nonlinearities and dispersion simultaneously.40) Here,we employed a split-step Fourier analysis of the Manakovequation, which describes the pulse propagation in a berwith dispersion, SPM, and XPM between the two orthogonalpolarizations under a randomly varying birefringence.41)

Finally, the compensated QAM signal was demodulated intobinary data, and the bit error rate was evaluated.The experimental results are shown in Fig. 7. In this

experiment, 60Gbit/s data were transmitted within an opticalbandwidth of only 4.05GHz. This indicates a net spectralefciency as high as 13.6 bit/s/Hz in a multi-channel trans-mission, even when accounting for the 7% FEC overhead.Along with the aim of higher multiplicity, it is very

important to explore ways of increasing the symbol rate,

= 0

= 1 = 0.5

(a)

= 0

= 1 = 0.5

(b)

Fig. 6. (Color online) Transfer function (a) and impulse response (b) of a raised-cosine Nyquist lter for = 0, 0.5, and 1.

-30 -25 -20 -15 -10

Back-to-back (X)Back-to-back (Y)After 150km transmission (X)After 150km transmission (Y)

10-5

10-4

10-3

10-2

10-1

BER

Received Power [dBm](a)

FEC threshold

Back-to-back After 150 km transmission

(b)

Fig. 7. (Color online) Experimental results for 60Gbit/s 1024 QAM transmission. (a) BER characteristics. (b) Constellations before and after transmission.



which are currently limited by the speed and bandwidth ofanalog-to-digital (A/D) and digital-to-analog (D/A) con-verters. To overcome these limitations, coherent optical timedivision multiplexing (OTDM) has been demonstrated thatemploys multi-level QAM modulation for ultrashort opticalpulses.57) However, typical pulse waveforms such asGaussian or sech proles generally occupy a large bandwidthin the frequency domain and thus may not be an appropriatewaveform in terms of SE. We recently proposed a new typeof optical pulse, which we call an optical Nyquist pulse,whose shape is given by the sinc-function-like impulseresponse of the Nyquist lter shown in Fig. 6(b).8) Thefundamental conguration of the ultrahigh-speed NyquistTDM transmission is shown in Fig. 8. The optical Nyquistpulse trains are bit interleaved to a higher symbol rate byOTDM. Here, in spite of a strong overlap, no ISI occurs dueto the zero crossing property of the Nyquist pulse at everysymbol interval. The OTDM demultiplexing from thiscontinuous data sequence can be realized with ultrafastoptical sampling, so that only data at the ISI-free point couldbe extracted. In this way, it is possible to reduce the signal

bandwidth without ISI during transmission, and therefore, theSE can be signicantly improved.Here we present the 1.28 Tbit/s (640Gbaud) polarization-

multiplexed transmission of Nyquist OTDM signals over525 km.9) Figure 9 shows the experimental setup. In thetransmitter, we rst generated an optical Nyquist pulse trainfrom a mode-locked ber laser (MLFL) that emits Gaussianpulses. The Gaussian pulses were transformed into a Nyquistprole by using a spectrum manipulation technique basedon the spatial intensity and phase modulation of spectralcomponents with a liquid crystal spatial modulator.42) Thegenerated waveform is shown in Fig. 10(a), where theperiodic zero crossing in the tail can be clearly seen. Theoptical Nyquist pulses were then DPSK modulated at 40Gbit/s and multiplexed to 640Gbit/s using a delay-line bitinterleaver. An eye diagram of the obtained Nyquist OTDMsignal is shown in Fig. 10(b). The OTDM signal becomesan analog-like continuous data stream, and the eye diagramappears greatly distorted due to the interference. However, asindicated by the blue line, no ISI occurs and a constant levelis maintained at every symbol interval. The 640Gbit/s

6.25 ps

DemultiplexerMultiplexer

Optical Fiber

MultiplexedOTDM signal

Time

25 ps40G 160G 40G

40G

40G

40G

40G

40G

40G

Optical Nyquist pulse train

Ultrafast optical sampling

Fig. 8. (Color online) Basic conguration for ultrahigh-speed OTDM transmission using optical Nyquist pulses.

1540 nm1.6 ps

MUX

PC EDFA Demod.EDFA

PDATT

DI

Prec40 GHzMLFL

PLL EDFA

OpticalDelay PC 15 nm

CLK

1563 nm800 fs

CLK

EDFA

HNL-DFF2 km

40 GHz

1 nm

EDFA

2 nm

40 GHzMLFL

ErrorDetector

40 GHz PPG40 Gbit/s215-1 PRBS

Q

Q

40 G640 Gbaud

10 nm

HNLF 100m

PC

PC

PC

EDFA

SMF50 km

PC

x7

DPSK Modulator

IDF25 km

640 Gbit/s DPSK transmitter525 km transmission link

40 Gbit/s DPSKrecieverDFF

500 m640 G 40 Gbit/sDEMUX

EDFA 15 nm

Pulseshaper

PC PBS //

Pulseshaper

EDFA

OpticalDelay

Optical Nyquist pulse generator

10 nm

640 G 1.28 Tbit/s polarization-multiplexed

NOLM

MLFL: Mode-Locked Fiber LaserHNL-DFF: Highly NonLinear-Dispersion Flattened FiberCLK: Clock RecoveryPPG: Pulse Pattern GeneratorIDF: Inverse Dispersion Fiber

DI: Delay InterferometerATT: Optical attenuatorPD: Balanced Photo DetectorNOLM: Nonlinear Optical Loop Mirror

Fig. 9. (Color online) Experimental setup for 1.28Tbit/s/channel525 km polarization-multiplexed DPSK transmission with 640Gbaud optical Nyquistpulse.



Nyquist pulses were polarization multiplexed to 1.28 Tbit/sand transmitted over a 525 km dispersion-managed trans-mission link. In the receiver, the transmitted Nyquist pulsewas rst demultiplexed to 40Gbit/s. Here, unlike conven-tional OTDM demultiplexing, we adopted an opticalsampling technique so that only data at the ISI-free pointcould be extracted from the continuous data stream. As anultrashort optical sampler, we employed a nonlinear opticalloop mirror (NOLM) switch with a gate width of 830 fs.Figures 11(a) and 11(b) show the BER characteristics for

1.28 Tbit/s-525 km Gaussian and Nyquist pulse transmission.As shown in Fig. 11(a), with a Gaussian pulse, the BER fora 1.28 Tbit/s polarization-multiplexed transmission wasgreatly degraded compared with the single-polarizationresult as a result of the depolarization-induced crosstalk43)

as shown in the inset of Fig. 11(a). On the other hand, theBER degradation associated with polarization multiplexingwas much smaller with a Nyquist pulse as shown inFig. 11(b), and a BER of 107 was achieved after a525 km transmission with a much lower power penalty and areduced error oor. These results indicate that the use ofNyquist pulses is very promising for ultrahigh-speed trans-mission. This scheme is scalable to a higher symbol rate perchannel of for example 1 Tbaud,10) and simultaneouslyenables ultrahigh SE by employing coherent QAM.11)

3. Second M: Multi-core optical ber for SDM

One of the strongest motivations for developing new bertechnologies is the huge increase in optical power. As theoptical power reaches a certain level, serious damage called aber fuse occurs. A ber fuse is a phenomenon whereby aber core is partially melted as a result of high optical power,and holes propagate through the core until the optical source

is shut down.19) The ber fuse propagation threshold isaround 1W, and it is especially disadvantageous for single-mode bers with small MFDs. The optical power for WDMsignals and the pump power for Raman amplication hasnow reached of the order of a few Watts, which is very closeto the threshold power for ber fuse propagation. This meansthat the allowable optical power input into an optical ber isapproaching its limit.The basic parameters for optical bers have remained

almost unchanged for more than 20 years, but if we are toovercome the power limitation, a paradigm shift from singlecore to multiple cores is indispensable. One of the mostimportant factors in multi-core design is to minimize thecrosstalk between any pair of cores. It has been found that thecrosstalk in MCF is described by coupled-power theory moreaccurately than coupled-mode theory.12,13) This indicates thatthe dominant factor as regards the crosstalk is stochastic

(a)

0

5

10

15

20

25

Pow

er [m

W]

1.56 ps/div(b)

Fig. 10. (Color online) The intensity prole of a 40GHz optical Nyquistpulse (a) and its OTDM to 640Gbaud (b).

-32 -30 -28 -26 -24 -22 -20 -18

Bit

Erro

r Rat

e

Received Optical Power [dBm]

10-4

10-5

10-6

10-7

10-8

10-9

10-10

10-3

Back to

back Single-pol

Pol-MUX

1530 1540 1550 1560

10dB

/div

Wavelength [nm]

Gauss (600 fs) signalcrosstalk

(a)

(b)

-32 -30 -28 -26 -24 -22 -20 -18

Bit

Erro

r Rat

e

Received Optical Power [dBm]10-10

10-3

10-4

10-5

10-6

10-7

10-8

10-9 Single-pol

Pol-MUX

Back to

back

1525 1535 1545 1555

10dB

/div

Wavelength [nm]

Nyquist (640 Gabud)

crosstalksignal

Fig. 11. (Color online) BER characteristics for 640Gbit/s single-channeland 1.28Tbit/s polarization-multiplexed transmissions over 525 km withGaussian (a) and Nyquist pulses (b). The inset shows optical spectra of signal(red) and crosstalk components (blue) after 525 km propagation.



mode coupling along the MCF caused by longitudinalperturbations. The crosstalk is also signicantly affected byber bending.14) From this perspective, heterogeneous MCFhas been proposed, which is composed of cores with differentpropagation constants.15) It has also been found that even avery small uctuation of the structural parameters results incrosstalk reduction. Trench-assisted MCF, which is com-posed of cores with depressed cladding, has been proposed asanother way of suppressing crosstalk without adverselyaffecting core density. Several groups have reported MCFwith ultra-low crosstalk,1618) including a 17.4 km MCF withcrosstalk as low as 77.6 dB.16) The details of these MCFsare shown in Table I. Recently, by using a low-crosstalk 12-core MCF, a record 1.01 Pbit/s capacity has been demon-

strated with the SDM of 222 WDM channels of 456Gbit/sPDM-32QAM signals.18)

If we can obtain the mode-coupling coefcient in thepropagation direction, we can analyze the optical powerdistribution along each core, which will give us usefulknowledge about SDM transmission using MCF. Recently,we proposed a novel technique for measuring the modecoupling along an MCF using synchronous multi-channeloptical time domain reectometry (OTDR).19) This techniqueclaries the nonuniformity of the mode-coupling coefcientalong the ber caused by the structural irregularity of theber. A schematic diagram of the MCF mode-couplingmeasurement and the experimental results are shown inFig. 12. As shown in Fig. 12(a), an optical pulse is coupled

Table I. MCFs for SDM transmission.

Number of cores 19 7 12

Core pitch (m) 35 45 37

Cladding diameter (m) 200 150 225

Loss (dB/km) 0.23 0.18 0.199

Aeff (m2) 72 80 88

Crosstalk (dB/km) 42 90 55 to 49

Reference 16 17 18

(c)

0.20 dB/km

(Input: Center core)

(d)

12

34

56

7

Time

Optical pulse

Pulse width:

Input power: P0

Pbs1Pbsm

MCF

Fiber length

Bac

ksca

ttere

d po

wer

Pbs1

Pbs2Pbs3

(a) (b)

Fig. 12. (Color online) Measurement of mode coupling along MCF using synchronous multi-channel OTDR. (a) Measurement principle, (b) backscatteredOTDR signals, (c) mode coupling ratio from center to outer cores, and (d) change in mode coupling coefcient as a function of position.



to the core 1, and the backscattered light in the core n, Pbsn,is detected by multi-channel synchronous OTDR. Examplebackscattered OTDR measurements from each core areshown in Fig. 12(b), when a 1 s optical pulse was coupledinto core 1 (center core) of a 2.9 km-long 7-core MCF with acore pitch of 46 m and a cladding diameter of 217 m. Themode coupling between core 1 and n along the ber under acondition of small mode coupling can be then obtained fromthe power ratio between Pbs1 and Pbsn:

n;1L PbsnPbs1

2hn;1L K for hn;1L 1; 4

where hn,1 is the mode coupling coefcient between core 1and n, L is the ber length, and K is a constant determinedby the Fourier transformation of the autocorrelation functionof the mode-coupling coefcient.44,45) This indicates that n,1is proportional to the ber length, with the slope given bytwice the mode-coupling coefcient. Figure 12(c) shows thepower ratio n,1 (n = 27) obtained from Fig. 12(b). We cantherefore obtain the mode-coupling coefcient by using thederivative of the power ratio, which is shown in Fig. 12(d).These results indicate that the mode-coupling coefcientvaries with position, and there is a structural irregularity thatmust be eliminated.For long-haul SDM transmission, it is essential to develop

optical ampliers for multi-cores2022) as well as other activeor passive components and splicing technologies. Figure 13shows the basic conguration of a multi-core opticalamplier. As in conventional EDF, multiple erbium-dopedcores are used as a gain medium. The EDF is pumped eitherwith an individual core pumping scheme using a multi-corecoupler as shown in (a),20,21) or with uniform clad pumpingas shown in (b),22) which has been adopted in high powerber lasers, namely the double clad pumping scheme. InRef. 20 a net gain of about 30 dB was obtained for sevencores with a crosstalk of less than 30 dB with individualcore pumping. With a cladding-pumped seven-core EDFA, again of >15 dB, a noise gure of

receiver without any manual adjustment of the polarizationaxis.47) Recently, a number of studies have reported theapplication of MIMO to mode-division-multiplexed trans-mission. MIMO-based multi-mode transmission is shownschematically in Fig. 15. For a single input signal x(t), thereceived signal y(t) is represented by

yt XQk1

hkxt nt 5

where n(t) is noise and Q is the number of modes. The rstterm has Q contributions representing the distortion in acertain mode k. The distortion includes the loss, group delay,and coupling ratio with mode k. By extending this repre-sentation to multiple inputs and outputs, the received signal atthe ith receiver is given by

yit XMj1

XQk1

hijkxjt nit XMj1

Hijxjt nit;

i 1; . . . ; N 6where hijk is the distortion when the signal is transmitted fromthe jth transmitter to the ith receiver via mode k, which isestimated from the input and received training symbols.Equation (6) can be represented in a matrix form:

yt Hxt nt: 7By estimating the channel matrix H from x(t) and y(t) usingsignal processing, and multiplying the inverse matrix of H,we can recover the input signal x(t). In general, to avoidincreasing the noise term through the multiplication of H1

by n(t), we diagonalize H in the form D = VHU usingunitary matrices U and V. Then, x(t) can be obtained byreceiving y(t) by multiplying U and V by x and yrespectively as follows:

Vyyt VyHUxt Vyn Dx Vyn: 8Each component of x(t) can be extracted by dividing theright-hand side of Eq. (8) with diagonal components of D. Itshould be noted here that the noise increase does not occur inthe term Vn, as the magnitude of this term is Vn = n dueto the property of a unitary matrix.Several groups have demonstrated MIMO-based multi-

mode transmission over a few-mode ber using fundamentaland higher-order LP modes. Figure 16 shows examples ofmode multiplexers and demultiplexers. Higher-order modesare excited and separated using free-space optics with phaseplates for phase inversion [Fig. 16(a)],26) long-period berBragg gratings for fundamental to higher-order mode con-version [Fig. 16(b)],27) or a liquid crystal on silicon (LCOS)-type spatial intensity and phase modulator for beam proling[Fig. 16(c)].28) Recent demonstrations of mode-division-

multiplexed transmission are summarized in Table II.2933)

For example, the 5-mode transmission of 100Gbit/s PDM-QPSK signals has been realized using the LP01, LP11a, LP11b,LP21a, and LP21b modes by using 4 4 MIMO (used toseparate degenerate modes, e.g., LP11a,x, LP11a,y, LP11b,x , andLP11b,y).31) A 6-mode transmission including the LP02 modehas also been achieved with 12 12 MIMO.33) These reportspotentially demonstrate the capability of spatial and polar-ization mode discrimination with MIMO.

5. Conclusions

We reviewed recent progress on the 3M scheme, whichconsists of multi-level modulation, multi-core bers, andmulti-mode technologies. These innovative technologies areexpected to overcome the power and capacity limitations oftodays optical communication, and ultimately lead to athousand-fold giant leap toward the Exabit optical commu-nication infrastructure in the coming 20 to 30 years.

Tx 1

Tx 2

Tx M

Rx 1

Rx 2

Rx N

Mode 1

Mode 2 Mode k

Fig. 15. (Color online) Mode-division-multiplexed transmission usingMIMO.

(a)

(b)

(c)

Fig. 16. (Color online) Mode multiplexers and demultiplexers for mode-division-multiplexed transmission.



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Table II. Recent mode-division-multiplexed transmission experiments.

Modes Modulation Distance Mux/Demux MIMO Ref.

LP01, LP11a, LP11b, Pol-Mux 20Gbaud QPSK 1200 km FMF (DGD comp.) Phase plates 6 6 MIMO 29

LP01, LP11a, LP11b, Pol-Mux 28Gbaud QPSK 88 WDM 50km FMF + FM-EDFA Phase plates 6 6 MIMO 30

LP01, LP11a, LP11b, LP21a, LP21b 28Gbaud QPSK 40 km FMF (Low mode coupling) Phase plates 4 4 MIMO 31

LP01, LP11a, LP11b, Pol-Mux 32Gbaud 16 QAM 96 WDM 119 km FMF Phase plates 6 6 MIMO 32

LP01, LP11, LP21, LP02, Pol-Mux 20Gbaud 16 QAM 32 WDM 177 km FMF Waveguide 12 12 MIMO 33



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