Transmission Performance Analysis of Fiber Optical ...downloads.hindawi.com/journals/aoe/2009/924340.pdf · the optimal span length to achieve the best transmission performance. Furthermore,

Hindawi Publishing CorporationAdvances in OptoElectronicsVolume 2009, Article ID 924340, 9 pagesdoi:10.1155/2009/924340

Research Article

Transmission Performance Analysis of Fiber OpticalParametric Amplifiers for WDM System

Xiaohong Jiang and Chun Jiang

State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University,Shanghai 200240, China

Correspondence should be addressed to Chun Jiang, [email protected]

Received 12 January 2009; Accepted 2 March 2009

Recommended by Samir K. Mondal

A numerical analysis is presented on the long-haul wavelength-division multiplexing (WDM) transmission system employingfiber-optic parametric amplifier (FOPA) cascades based on one-pump FOPA model with Raman Effect taken into account.The end-to-end equalization scheme is applied to optimize the system features in terms of proper output powers and signal-to-noise ratios (SNRs) in all the channels. The numerical results show that—through adjusting the fiber spans along withthe number of FOPAs as well as the channel powers at the terminals in a prescribed way—the transmission distance andsystem performance can be optimized. By comparing the results generated by different lengths of fiber span, we come tothe optimal span length to achieve the best transmission performance. Furthermore, we make a comparison among thelong-haul WDM transmission systems employing different inline amplifiers, namely, FOPA, erbium-doped fiber amplifier(EDFA), and Fiber Raman Amplifier (FRA). FOPA demonstrates its advantage over the other two in terms of systemfeatures.

Copyright © 2009 X. Jiang and C. Jiang. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

1. Introduction

In recent years, Fiber-optical parametric amplifiers (FOPAs)are attracting widespread interest among researchers in fiber-optic field because of efficient broadband amplification [1]and wavelength conversion [2]. They are also candidates forperforming all-optical networking functions [3, 4]. FOPAsare being studied as online amplifiers to compensate forthe fiber loss and to increase the transmission distancewithout O/E/O regeneration. Researchers have demonstratedthe ultra long-haul WDM links with hundreds of channels inthe range of thousands of kilometers without regeneration[5], and also presented a quantum theory of nondegeneratephase-insensitive FOPA, including the noninstantaneousresponse time of the fiber medium, which causes Ramanloss and gain [6]. A low noise figure is the most importantconcern in such amplifiers because noise accumulation alongthe amplifier links has to be minimized. It was reportedthat the noise figure of a phase-insensitive parametric

amplifier exceeds that of an ideal phase-insensitive amplifierby 3 dB [7].

Another major problem in implementing amplifiedWDM transmission systems is “gain equalization.” As thegain spectrum of FOPA is nonuniform and wavelength-dependent, each channel in a WDM system will experiencedifferent optical gain, which leads to unacceptable BERperformance in certain channels of the long-haul trans-mission system. Therefore, considerable effort has beenmade in inventing components that equalize the outputpowers at each amplifier repeater in all channels. Var-ious equalizer proposals have been presented, including“smoothing filters” such as Fabry-Perot or tunable Mach-Zehnder interferometers [8]. To ensure the performanceof long-haul transmission system, a practical and cost-effective equalization technique should be applied in thesystem.

In this paper, we numerically analyze the one-pumpFOPA model with Raman Effect. And then, a FOPA-based

2 Advances in OptoElectronics

−5

0

5

10

15

20G

ain

e(d

B)

−3 −2 −1 0 1 2 3×1012

Δ f (Hz)

Noi

sefa

ctor

(dB

)

Figure 1: Gain (Solid curve) and NF (dotted curve) spectraof the FOPA made with 1 km DSF and pumped at 1537.6 nmwith 1.5 W power. The zero-dispersion wavelength is 1537 nm,and the dispersion slope is 0.034 ps nm−2km−1. The nonlinearcoupling coefficient is 1.8 W−1km−1. Maximum value of Raman-gain coefficient for DSF is 0.8 W−1km−1, at the temperature of300 K.

WDM transmission system using end-to-end equalization isdesigned, analyzed, and optimized.

2. Analysis

The mathematical model of one-pump FOPA with RamanEffect is developed in Section 2.1, while Section 2.2 designsand numerically calculates a long-haul WDM transmis-sion system employing cascaded FOPAs, using end-to-endequalization, and based on different lengths of fiber span.Section 2.3 compares and presents an analysis on theseresults.

2.1. Mathematical Model of FOPA. The one-pump case ofFOPA is also called the degenerate case, whereas the two-pump case the nondegenerate case, which are both describedand developed in [5]. The parametric gain of one-pumpFOPA can be expressed as

Gs = 1 +

[γP0

gsinh(gz)

]2

. (1)

When FOPA is operated phase-insensitively, a coherent-state input signal is injected at the Stokes (anti-Stokes) fre-quency while the input at the anti-Stokes (Stokes) frequencyremains in the vacuum state. The NF is then defined asNFPIA ≡ SNRin, j /SNRout, j [9], where j = s(a), if the signalfrequency is on the Stokes (anti-Stokes) side and SNR is thesignal-to-noise ratio.

The quantum-limited NF of a FOPA exceeds the standard3 dB limit at high gains due to the Raman Effect [7].When the input-signal photon number is much greater than

the amplifier gain, we can calculate NF in the followingexpression [7]:

NF j,PIA = 1 +

∣∣∣ν j

∣∣∣2+ (1 + 2nth)

∣∣∣∣−1 +∣∣∣μj

∣∣∣2 −∣∣∣ν j

∣∣∣2∣∣∣∣∣∣∣μj

∣∣∣2 ,

(2)

where nth = [exp(�Ω/kT)− 1]−1 is the mean number ofoptical phonons at detuning Ω and temperature T ; here� is Planck’s constant over 2π; k is Boltzmann’s constant;Ω = ωa − ωp = ωp − ωs and ωj for j = p, s, ais the angular frequency of the pump, Stokes, and anti-Stokes fields, respectively. And μj , ν j are defined in [10].The assumption H(Ω) = H(−Ω)∗ (i.e., its time-domainresponse is a real function) is usually valid for Ω up to severalterahertzes in standard fibers [10]. This implies that the realpart of the nonlinear response in the frequency domain issymmetric about the pump frequency, and the imaginarypart in the frequency domain is antisymmetric about thepump frequency [11], μj , ν j may be simplified to [7]

μa = exp(− i(Δk − [2H(Ω)]IP)L

2

)

∗(iκ

2gsinh

(gL)

+ cos h(gL))

,

μs = exp(− i(Δk − [2H(Ω)]IP)L

2

)

∗(iκ∗

2g∗sinh

(g∗L

)+ cos h

(g∗L

)),

νa = exp(− i(Δk − [2H(Ω)]IP)L

2

)∗ iH(Ω)Ip

gsinh

(gL),

νs = exp(− i(Δk − [2H(Ω)]IP)L

2

)∗ iH(−Ω)Ip

g∗sinh

(g∗L

),

κ = Δk + 2H(Ω)IP ,

g =√−(κ/2)2 + {H(Ω)}2I2

P.(3)

Here Ip = |Ap(0)|2 is the pump power in watts; the complexgain coefficient g is defined as

g =√−(κ/2)2 + H(Ω)H(−Ω)∗I2

P , (4)

where

κ = Δk +[H(Ω) + H(−Ω)∗

]IP , (5)

Δk = β2Ω2 is the phase mismatch to second order causedby dispersion, where β2 is the group-velocity dispersioncoefficient. H(Ω) is the frequency-domain Raman responsefunction.

We build a mathematical model for the one pump FOPAwith Raman Effect, which will later be applied in the WDMtransmission system. Figure 1 shows its gain and NF spectra.

Advances in OptoElectronics 3

Tx

Tx

TxM

ux

Dem

ux

Rx

Rx

RxFOPA

Fiber span

Figure 2: The schematic configuration of long-haul WDM trans-mission system employing cascaded FOPAs. Eight channels aremultiplexed (total power is −3 dBm before Mux) to transmitthrough spans of conventional fiber. Loss is compensated by FOPAs.A preamplifier is applied before the demultiplexer.

2.2. Design of a FOPA-Cascaded Long-Haul WDM

Transmission System

2.2.1. System Configuration. Our major task is to design andnumerically analyze a long-haul WDM optical transmissionsystem employing FOPA cascades. The schematic configura-tion of the system is shown in Figure 2.

The system consists of eight 2.5 Gb/s externally mod-ulated channels with 0.4 THz channel spacing (193.8–196.6 THz). Each transmitter consists of a Pseudo-RandomBit Sequence Generator, a NRZ Pulse Generator, a CWLaser, and a Mach-Zehnder Modulator. Total signal poweris −3 dBm before multiplexing, that is, −12 dBm in eachchannel. The eight channels are then multiplexed, and thesignals are transmitted over spans of conventional opticalfiber with an attenuation factor of 0.2 dB/km. The fiberloss and excess losses in the system are compensated byFOPAs. The FOPAs are pumped by 1.5 W of 1537.6 nm pumplight. The demultiplexer is preceded by a fiber preamplifier.The bit-error-rate (BER) calculations take into accountintersymbol interference, signal-spontaneous beat noise, andpostdetection Gaussian noise [12]. Photodetector PIN, LowPass Bessel Filter, and 3R Generator are applied at eachchannel before BER Analyzer.

2.2.2. Features of the FOPA in the WDM Transmission System.We tested the performance of FOPA module operating insimulation transmission system. Equal input signal powersof −12 dBm are used in all eight channels. Figure 3 showsthe signal powers emerging after 1-km long FOPA. Data inlist are obtained in the WDM Analyzer connecting to theoutput of FOPA, displaying the output features. Note that thegraph agrees perfectly to the corresponding spectrum in themathematic model of FOPA (see Figure 1). Judging from thefollowing features, we find the performance of a single FOPAquite ideal.

2.2.3. End-to-End Equalization. In [13], an end-to-endequalization scheme was described to equalize either theoutput powers or the SNR in WDM channels of EDFA-amplified systems. Neither new optical components norupgrades or adjustments were required at inline amplifierareas. Equalization could be accomplished by adjusting

transmitter powers with variable attenuators at the terminalsbased on information obtained at the output terminal.

To have the output powers equalized, we only need toadjust individual input signal powers with attenuators whilekeeping the total input power constant. The power in eachchannel is scaled by a factor inversely proportional to thegain in that channel. The new input signal power of the ithchannel is adjusted to [13]

Pinew = PTotal

[1/Gi∑8i=11/Gi

], (6)

where PTotal is the total signal power before multiplexing(−3 dBm), Gi is the optical gain in the ith channel.

A similar adjustment algorithm is needed to equalizeSNR. The transmitter power for the ith channel should beadjusted to [13]

Pinew = PTotal

[Pi

in/SNRi∑8i=1P

iin/SNRi

]. (7)

An analysis has been presented to predict the perfor-mance of WDM lightwave transmission systems using powerand SNR end-to-end equalization [13]. It was said thatcompared to power equalization, the relative performanceof SNR equalization tends to improve with the increase ofchannel numbers, bit rate and receiver dynamic range anddeteriorate with the increase of amplifier gain imbalance.

In the long-haul transmission system we designed fornumerical analysis, although the output powers can beeasily equalized by power equalization, this might leadto unacceptable BER in some channels due to low SNR.Therefore, we apply both equalization techniques in thesimulation and choose the one that leads to better systemperformance in every individual case.

2.2.4. Long-Haul Transmission. We use Optical SpectrumAnalyzer (OSA) to display the modulated optical signalin the frequency domain and WDM Analyzer to monitorthe numerical results of signal and the noise power ateach optical signal channel. In amplified WDM systems,SNR and BER are routinely monitored as a measure ofsystem performance. In most cases, BER below 1 × 10−12

is considered acceptable, and the range of output powersshould not exceed that allowed by receiver dynamic range(−30 dBm to 10 dBm in this case). Therefore, we adjust thelength of fiber span and gradually increase the number ofFOPAs to enhance transmission distance. Power or SNR end-to-end equalization is applied for better system performance.For each set of fiber length (from 30 km to 65 km withan increment of 5 km), we look for the largest number ofamplifiers that can be employed in the transmission systemwithin the performance constraints we mentioned above.By comparing the results with different spans, we finallycome to the optimal span length to achieve the maximumtransmission distance with ideal performance in the above-mentioned system.

30-km Fiber Span. The fiber span is firstly set to be 30-kmlong. We gradually increase the amplifiers to look for the


−110

−80

−50

−20

10

Pow

er(d

Bm

)

191 193 195 197 199

Frequency (THz)

Frequency(THz)

Signal power(dBm)

SNR(dB)

BER

193.8 17.20 117.20 0.00E + 00

194.2 11.61 111.61 0.00E + 00

194.6 6.23 106.23 0.00E + 00

195 3.29 103.29 0.00E + 00

195.4 4.16 104.16 0.00E + 00

195.8 8.67 108.67 0.00E + 00

196.2 14.56 114.56 0.00E + 00

196.6 18.79 118.79 0.00E + 00

Figure 3: Output features of FOPA (described in Figure 1 caption) in the transmission system (described in Figure 2 caption). Equal inputsignal powers of −12 dBm. The list beside shows signal frequency, output signal powers, SNR and BER.

−110

0

Pow

er(d

Bm

)

191 193 195 197 199

Frequency (THz)

193.8

194.2

194.6

195

195.4

195.8

196.2

196.6

46.17 138.39

29.55 127.71

13.11 113.11

4.29 104.29

7.21 107.21

20.73 120.73

38.38 132.12

51.40 141.31

Frequency(THz)

Signal power(dBm)

SNR(dB)

BER

0.00E + 00

0.00E + 00

0.00E + 00

0.00E + 00

0.00E + 00

0.00E + 00

0.00E + 00

0.00E + 00

Figure 4: Output signal (red) and noise (green) powers after 90 km transmission using 30-km fiber span and equal input signal powers of−12 dBm. No equalization is applied. The list beside shows signal frequency, output signal powers, SNR and BER.

largest number in the system while the BER and outputpower features are within acceptable levels. Figure 4 showsthe output signal (red) and noise (green) powers emergingafter 3 loops of FOPA and 30-km fiber span with noequalization, the detailed features are denoted beside.

We find though BER features are good in all channelsbut some signal powers are overly high with an imbalance of47 dB. We choose to apply power end-to-end equalization.Figure 5 shows the output powers when the input powersare adjusted according to (6). The output powers are nicelyequalized. In this case, SNR equalization is not superiorto power equalization, for SNR in all eight channels arequite decent already. After applying three iterations of SNRequalization algorithm, the output features are quite closeto the result obtained by one-time power equalization,for in this case, noise in most channels has not beenaccumulated to a measurable level, equalizing SNR finallybecomes equivalent to equalizing signal power.

When fiber span is set to 30-km long, the largest numberof amplifiers we have found is 3. When we continue toincrease to 4, though the SNR and BER are still good in allchannels, but the signal powers remain 18 dBm after severaliterations of end-to-end equalization algorithm.

We set fiber span from 30-km to 65-km long with anincrement of 5 km, and repeat the simulation as above. Theresults of certain typical lengths are selected with graphs anddata displayed as follows.

40-km Fiber Span. When fiber span is set to be 40-kmlong, the largest amplifiers number we have found is 6.After applying power end-to-end equalization, the systemis optimized with equalized output powers and good BERin all channels; see Figure 6. When we continue to increaseamplifier number to 7, power equalization is no longerapplicable because it makes transmission power too low. But


−110

−80

−50

−20

10

Pow

er(d

Bm

)

191 193 195 197 199

Frequency (THz)

193.8

194.2

194.6

195

195.4

195.8

196.2

196.6

11.10 110.92

11.10 111.10

111.10

111.10

111.10

111.10

111.10

111.10

11.10

11.10

11.10

11.10

11.10

11.10

Frequency(THz)

Signal power(dBm)

SNR(dB)

BER

0.00E + 00

0.00E + 00

0.00E + 00

0.00E + 00

0.00E + 00

0.00E + 00

0.00E + 00

0.00E + 00

Figure 5: Same as Figure 4, except that the input power is adjusted according to power end-to-end equalization.

−110

−90

−70

−50

−30

−10

10

Pow

er(d

Bm

)

191 193 195 197 199

Frequency (THz)

193.8

194.2

194.6

195

195.4

195.8

196.2

196.6

7.79 63.50

7.79 66.04

7.79 71.29

7.79 84.81

7.79 77.29

7.79 68.05

7.79 62.96

7.79 60.57

Frequency(THz)

Signal power(dBm)

SNR(dB)

BER

0.00E + 00

0.00E + 00

0.00E + 00

0.00E + 00

0.00E + 00

0.00E + 00

0.00E + 00

0.00E + 00

Figure 6: Output signal (red) and noise (green) powers after 240 km transmission using 40-km fiber span and employing power end-to-endequalization. The list beside shows signal frequency, output signal powers, SNR and BER.

even with several iterations of SNR equalization till SNR inall channels are equalized to 70 dB, signal powers in certainchannels are not acceptable.

L = 50 Km. When fiber span is 50-km long, we graduallyincrease the amplifiers number to 6. In this case, BER inchannel 4 is found no longer good (only 1.62×10−2) becausethe amplifier gain at that wavelength is not high enoughto cover the larger attenuation experienced in longer fiberspan. We then apply power end-to-end equalization. Figure 7shows the optimized system with acceptable BER in allchannels. When we continue to increase amplifier numberto 7, power equalization is again no longer applicable forunacceptable low transmission power. Four iterations of SNRequalization leads to good BER features but signal powers inlast 2 channels are a little above the constraint; see Figure 8.

L = 55 km. We can increase the amplifiers number to 7with 55-km long fiber spans, which is the largest number

that we achieved with a group of fiber spans of differentlengths. When the fiber length becomes longer, signalsclose to the pump frequency experience larger power losswhich generates unacceptable BER. Figure 9 shows outputfeatures after three iterations of SNR equalization. Increasingamplifier number to 8, neither power equalization nor SNRequalization is able to optimize the system to a good level.Even with good SNR, BER features in the channels close topump frequency are bad because of low signal power.

2.3. Comparison of the Results. In this section, we sum upthe results and make a comparison based on the graphsbelow. Figure 10 shows the maximum transmission distancethat can be achieved in the long-haul WDM transmissionsystem employing cascaded FOPAs as we described before.The maximum transmission distance is determined by thefiber length and the number of amplifiers that could besupported in the system. End-to-end equalization is appliedto optimize the system so as to afford more amplifiers but atthe same time ensuring BER in all eight channels that are


−90

−70

−50

−30

Pow

er(d

Bm

)

191 193 195 197 199

Frequency (THz)

−16.21 39.50 3.13E − 43

−16.21 42.04 6.39E − 48

−16.21 47.29 6.60E − 39

−16.21 60.81 5.65E − 42

−16.21 53.29 3.65E − 47

−16.21 44.05 3.29E − 51

−16.21 38.96 8.33E − 40

−16.21 36.57 1.98E − 48

193.8

194.2

194.6

195

195.4

195.8

196.2

196.6

Frequency(THz)

Signal power(dBm)

SNR(dB)

BER

Figure 7: Output signal (red) and noise (green) powers after 300 km transmission using 50-km fiber span and employing power end-to-endequalization. The list beside shows signal frequency, output signal powers, SNR and BER.

−110

−80

−50

−20

10

Pow

er(d

Bm

)

191 193 195 197 199

Frequency (THz)

6.03E − 14

2.14E − 94

13.28 43.17

7.05 42.96

−8.26 42.76

−18.85 42.97

−14.52 42.70

−0.27 42.98

15.80 42.50

19.60 42.55

0.00E + 00

0.00E + 00

0.00E + 00

0.00E + 00

0.00E + 00

0.00E + 00

193.8

194.2

194.6

195

195.4

195.8

196.2

196.6

Frequency(THz)

Signal power(dBm)

SNR(dB)

BER

Figure 8: Output signal (red) and noise (green) powers after 350 km transmission using 50-km fiber span and employing 4 iterations ofSNR equalization. The list beside shows signal frequency, output signal powers, SNR and BER.

−110

−80

−50

−20

10

Pow

er(d

Bm

)

191 193 195 197 199

Frequency (THz)

5.1 21.72 3.42E − 133

0.84 21.93 4.02E − 116

21.72 1.97E − 111

21.76 5.48E − 82

21.73 1.31E − 89

21.85 4.07E − 116

5.92 21.54 4.88E − 98

10.15 21.63 3.19E − 127

−7.94

−12.91

−3.85

−11.55

193.8

194.2

194.6

195

195.4

195.8

196.2

196.6

Frequency(THz)

Signal power(dBm)

SNR(dB)

BER

Figure 9: Output signal (red) and noise (green) powers after 385 km transmission using 55-km fiber span and employing 3 iterations ofSNR equalization. The list beside shows signal frequency, output signal powers, SNR and BER.


100

200

300

400

Max

imu

mtr

ansm

issi

ondi

stan

ce(k

m)

30 35 40 45 50 55 60 65

Length of fiber span (km)

(a)

2

4

6

8

10

Max

imu

mn

um

ber

ofam

plifi

ers

30 35 40 45 50 55 60 65


(b)

Figure 10: (a) Maximum transmission distance achieved in thelong-haul WDM transmission system employing cascaded FOPAsand end-to-end equalization versus length of fiber span. (b)Constraints on number of amplifiers (with end-to-end equaliza-tion) ensuring BER below 1 × 10−12 and signal powers between−30 dBm and 10 dBm versus length of fiber span. The results arecomputed for Rb = 2.5 Gb/s, eight externally modulated channelswith 0.4 THz spacing (193.8–196.6 THz). Total signal power is−3 dBm before multiplexing. Optical fiber has the attenuationfactor 0.2 dB/km. The FOPAs are pumped by 1.5 W of 1537.6 nmpump light. FOPAs are made with 1 km DSF and pumped at1537.6 nm with 1.5 W power. The zero-dispersion wavelength is1537 nm, and the dispersion slope is 0.034 ps nm−2 km−1. Thenonlinear coupling coefficient is 1.8 W−1km−1. Maximum value ofRaman-gain coefficient for DSF is 0.8 W−1km−1, at the temperatureof 300 K.

below 1 × 10−12 and signal power is constrained between−30 dBm and 10 dBm. We find that in this system, boththe largest number amplifiers and the longest transmissiondistance are achieved when the fiber span is set to be 55-kmlong, that is, 385 km transmission distance.

Figure 11 shows the average BER and SNR achievedin eight channels when employing the largest number ofcascaded FOPAs in every individual case. We find averageSNR decreases monotonously with fiber span length. Thiscan be understood by realizing that the signal powersexperience larger attenuation in longer fiber span whilenoise keeps growing in proportion to the product of gainand noise figure From Figures 5 to 9, we can see with theincrease of fiber length, the noise powers after experiencingthe maximum transmission distance begin to overwhelm thesignals, reduce SNR, and deteriorate BER. For fiber spans of30-to 45-km long, BER in all channels are zero due to highSNR and signal power.

We further display in Figure 12 the SNR and BER featuresin individual channels after experiencing the achievablemaximum transmission distance corresponding to different

10−100

10−50

100

log

(ave

rage

BE

R)

30 35 40 45 50 55 60 65


(a)

0

20

40

60

80

100

200

Ave

rage

SNR

(dB

)

30 35 40 45 50 55 60 65


(b)

Figure 11: (a) Average BER (logarithmic scale) achieved in eightchannels of the long-haul WDM transmission system employingthe largest number of cascaded FOPAs versus length of fiber span.Note that for fiber span from 30 to 45 km, the logarithmic scaleof BER is -inf. (b) Average SNR achieved in eight channels of thesystem versus length of fiber span. System and FOPA descriptionare the same with Figure 10 caption.

lengths of fiber span. We find that SNR in each channeldecreases monotonously with fiber span length. It is inter-esting to notice the distribution of SNR in eight channelscorresponding to different lengths of fiber span. For fiberlength from 30 km to 50 km, power equalization is chosento optimize system performance because in these cases SNRand BER features are in good levels even before equalization.Therefore, for 35-to 50-km fiber span, SNR is distributedin a similar shape that is approximately symmetrical aboutthe center frequency. SNR is higher in the center becausethe gain in this frequency domain is small which leads tosmaller accumulated noise while signal powers are equalizedto the same. For fiber length from 55 km to 60 km, SNRequalization is chosen for optimization because in these casesSNR is acceptable but BER is bad because of small signalpowers. Despite the signal powers could be equalized higherafter power equalization, BER in some channels remainsunacceptable. However, with SNR equalization, BER in allchannels become decent and signal powers stay within theconstraints. Therefore, for 55-to 65-km fiber span, SNRis approximately in uniform distribution. But we shouldpoint out that when SNR are equalized, there remain powerdifferences in adjacent channels. However, such problemscan be avoided if the channel spacing is reduced or thechannels are not set in a domain of large gain variance.Moreover, the FOPA model employed in this paper ispowered by one-pump, whose gain spectrum is not flatover the amplifier bandwidth—obviously depressed whenclose to pump frequency. This large gain dip gets more


0

20

40

60

80

100

120

140

SNR

(dB

)

193.5 194 194.5 195 195.5 196 196.5 197

Frequency (THz)

30 km fiber span35 km fiber span40 km fiber span45 km fiber span

50 km fiber span55 km fiber span60 km fiber span65 km fiber span

Figure 12: SNR features in eight channels (from 193.8 to 196.6 THzwith 0.4 THz spacing) after experiencing the achievable maximumtransmission distance described in Figure 10 caption. Resultsachieved with different lengths of fiber span are identified withcorresponding groups of signs denoted in the graph text.

severe after going through several amplifiers, where the signalpower at pump frequency is far smaller than that at largedetuning area. Two-pump FOPA configuration could be usedin later research, which provides more freedom to allowoptimization of gain flatness. Last, for 30-km long fiber span,SNR is also uniformly distributed, for in this case, noises inmost channels have not been accumulated to a measurablelevel, equalizing powers is equivalent to equalizing SNR.

Finally, we compare the optimal transmission systememploying cascaded FOPAs with that employing cascadedEDFAs or FRAs. The transmission system configurationis ensured to remain the same other than using differentinline amplifiers. Transmission distance is set to be 385 kmby using seven spans of 55-km-long fibers. We graduallyadjust the transmission powers in eight channels to obtainthe corresponding BER features. To optimize the gain andSNR imbalance, end-to-end equalization is also appliedin three long-haul systems employing FOPA, EDFA, orFRA so that BER in all channels are almost on the samelevel. Figure 14 shows the average BER in eight channelscorresponding to the different signal transmission powersafter experiencing 385-km transmission distance with seven55-km-long fiber spans. FOPAs are made with 1 km DSFand pumped at 1537.6 nm with 1.5 W power, the zero-dispersion wavelength is 1537 nm and the dispersion slopeis 0.034 ps nm−2 km−1, the nonlinear coupling coefficient is1.8 W−1km−1. Maximum value of Raman-gain coefficientfor DSF is 0.8 W−1km−1, EDFA parameters are: core radius2.2 μm, erbium doping radius 2.2 μm, erbium metastablelifetime 10 milliseconds, numerical aperture 0.24, erbiumion density 1025 m−3, 0.1 dB/m loss at 1550 nm, 0.15 dB/m

10−140

10−120

10−100

10−80

10−60

10−40

10−20

100

log

(BE

R)

193.5 194 194.5 195 195.5 196 196.5 197

Frequency (THz)

50 km fiber span55 km fiber span

60 km fiber span65 km fiber span

Figure 13: BER features (logarithmic scale) in eight channels (from193.8 to 196.6 THz with 0.4 THz spacing) after experiencing theachievable maximum transmission distance described in Figure 10caption. Results achieved with different lengths of fiber span areidentified with corresponding groups of signs denoted in the graphtext. Note that for fiber span from 30 to 45 km, the logarithmic scaleof BER is -inf.

10−160

10−140

10−120

10−100

10−80

10−60

10−40

10−20

100

log

(ave

rage

BE

R)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Transmission power (mW)

BER = 1e − 12 EDFAFOPA FRA

Figure 14: Average BER (logarithmic scale) in eight channels (from193.8 to 196.6 THz with 0.4 THz spacing) versus signal transmissionpowers.

loss at 980 nm, length 5 m, 100 mW forward pump power at980 nm. FRA Parameters are: Polarization factor 2, Rayleighback scattering 2.349 × 10−25 /km, pumped with 1500 mWpower at 1450 nm, length 25 km. Results achieved withdifferent inline amplifiers are identified with correspondingsigns denoted in the graph text.


We come to find and to achieve the same level of BERthat is acceptable (less than 1 × 10−12); FOPA requires theleast signal transmission power comparing with the othertwo types of amplifiers.

3. Conclusion

In this paper, we present a numerical analysis on the long-haul WDM transmission system employing FOPA cascades.FOPA is modeled as one-pump and with Raman Effect.End-to-end equalization scheme is applied to optimize thesystem features. The numerical results show that—throughadjusting the fiber spans along with the number of FOPA,and the channel powers at the terminals in a prescribedway—the transmission distance and system performancecan be optimized. In our project, the WDM system isoperated at Rb = 2.5 Gb/s with eight externally modulatedchannels (193.8–196.6 THz, 0.4 THz spacing), total signalpower −3 dBm before multiplexing, employing cascadedFOPAs pumped by 1.5 W of 1537.6 nm pump light. Theoptimal fiber span length we find is 55 km to achievemaximum transmission distance of 385 km by employingseven amplifiers. The system has an average SNR 21.735 dBand an average BER 6.85× 10−83.

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (Grant nos. 60377023 and 60672017)and New Century Excellent Talents Universities (NCET)Shanghai Optical Science and Technology project.

References

[1] J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers andtheir applications,” IEEE Journal on Selected Topics in QuantumElectronics, vol. 8, no. 3, pp. 506–520, 2002.

[2] K. K. Y. Wong, K. Shimizu, M. E. Marhic, K. Uesaka, G.Kalogerakis, and L. G. Kazovsky, “Continuous-wave fiber opti-cal parametric wavelength converter with +40-dB conversionefficiency and a 3.8-dB noise figure,” Optics Letters, vol. 28, no.9, pp. 692–694, 2003.

[3] Y. Su, L. Wang, A. Agarwal, and P. Kumar, “Wavelength-tunable all-optical clock recovery using a fiber-optic paramet-ric oscillator,” Optics Communications, vol. 184, no. 1, pp. 151–156, 2000.

[4] L. Wang, Y. Su, A. Agarwal, and P. Kumar, “Synchronouslymode-locked fiber laser based on parametric gain modulationand soliton shaping,” Optics Communications, vol. 194, no. 4–6, pp. 313–317, 2001.

[5] R. H. Stolen and J. E. Bjorkholm, “Parametric amplificationand frequency conversion in optical fibers,” IEEE Journal ofQuantum Electronics, vol. 18, no. 7, pp. 1062–1072, 1982.

[6] P. L. Voss and P. Kumar, “Raman-noise-induced noise-figurelimit for χ(3) parametric amplifiers,” Optics Letters, vol. 29, no.5, pp. 445–447, 2004.

[7] P. L. Voss and P. Kumar, “Raman-effect induced noise limits onχ(3) parametric amplifiers and wavelength converters,” Journalof Optics B, vol. 6, no. 8, pp. S762–S770, 2004.

[8] K. Inoue, T. Kominato, and H. Toba, “Tunable gain equaliza-tion using a Mach-Zehnder optical filter in multistage fiberamplifiers,” IEEE Photonics Technology Letters, vol. 3, no. 8, pp.718–720, 1991.

[9] R. Tang, P. L. Voss, J. Lasri, P. Devgan, and P. Kumar,“Noise-figure limit of fiber-optical parametric amplifiers andwavelength converters: experimental investigation,” OpticsLetters, vol. 29, no. 20, pp. 2372–2374, 2004.

[10] N. R. Newbury, “Raman gain: pump-wavelength dependencein single-mode fiber,” Optics Letters, vol. 27, no. 14, pp. 1232–1234, 2002.

[11] R. H. Stolen, J. P. Gordon, W. T. Tomlinson, and H. A. Haus,“Raman response function of silica-core fibers,” Journal of theOptical Society of America B, vol. 6, no. 6, pp. 1159–1166, 1989.

[12] D. Marcuse, “Calculation of bit-error probability for alightwave system with optical amplifiers and post-detectionGaussian noise,” Journal of Lightwave Technology, vol. 9, no.4, pp. 505–513, 1991.

[13] O. K. Tonguz and F. A. Flood, “EDFA-based DWDM lightwavetransmission systems with end-to-end power and SNR equal-ization,” IEEE Transactions on Communications, vol. 50, no. 8,pp. 1282–1292, 2002.

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Transmission Performance Analysis of Fiber Optical ...downloads.hindawi.com/journals/aoe/2009/924340.pdf · the optimal span length to achieve the best transmission performance. Furthermore,