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Optik 122 (2011) 1376– 1380

Contents lists available at ScienceDirect

Optik

j o ur nal homepage: www.elsev ier .de / i j leo

mpact of ASE noise in WDM systems

ing Huang ∗

hysics Department, South China University of Technology, Room 803, Building 8, Beiqu, Guangzhou 510640, China

r t i c l e i n f o

rticle history:eceived 1 April 2010

a b s t r a c t

The small signal analysis method is presented for the discussion of amplified spontaneous emission (ASE)noise in dispersion and nonlinear transmission fibers in wavelength division multiplex (WDM) systems.

ccepted 6 September 2010

eywords:mplified spontaneous emission noise

Based on it, the complete ASE noise spectra (include the ASE noise, the ASE noise enhanced by parametricgain and the crosstalk caused by ASE noise and parametric gain) are described and the factors impactingon them are discussed. The crosstalk caused by ASE noise and parametric gain in single mode fibers,non-zero dispersion shift fibers and dispersion compensation fibers are analyzed. Taking into accountthe dispersion effect in the transmission fibers, the three types of ASE noise may decrease.

rbium-doped fiber amplifieravelength division multiplexing

. Introduction

In a long-haul WDM system, erbium-doped fiber amplifierEDFAs) are used to provide a wide and flat gain spectrum in ordero accommodate and amplify as many WDM channels as possible1]. ASE noise emitted from the erbium-doped fiber (EDF) adds toignal and grows rapidly along a cascade [2,3]. In the last amplifierf a cascaded link, the accumulated ASE noise may limit the effec-ive signal amplification due to saturation effect and influence theeceiver’s bit error ratio (BER) [4–6].

ASE noise may be modified by fiber nonlinear phenomena suchs Parametric Gain (PG) [6–8]. The interaction between Kerr non-inearity and quadratic dispersion causes the optical carriers to acts a set of pumps and to generate spectral regions where the ASEoise may experience gain. These alterations in the ASE noise spec-ral shape may potentially degrade the system performance. Annalytical method which considers spectral and statistic featuresf the optical noise and the shapes of the optical and electrical fil-ers at the receiver was presented in Ref. [7]. Based on the nonlinearchrödinger propagation equation and, under the assumption of ann-depleted pump, a PG transfer matrix that allows the easy ana-

ytical evaluation of ASE noise enhancement spectra over chains ofmplified fiber spans was introduced in Ref. [9].

Applying a Karhunen–Lobve Series Expansion (KLSE) on theffects of the noise altered by PG, the impact of PG on a 10 Gb/ser channel long-haul multi-wavelength system was evaluated and

he impact of the quadrature noise on system performance hadeen pointed out. The maximum length L was plotted versus theransmitted power [10].

∗ Corresponding author. Tel.: +86 13268039147.E-mail address: huanggesheng@tom.com

030-4026/$ – see front matter © 2010 Elsevier GmbH. All rights reserved.oi:10.1016/j.ijleo.2010.09.013

© 2010 Elsevier GmbH. All rights reserved.

Most of the researches focus on the strongest ASE noise whichis related to parametric gain and less refer to the whole scenery ofASE noise spectra.

In this paper, we will apply the small signal analysis methodto describe the whole ASE noises (includes the ASE noise, the ASEnoise enhanced by PG and the crosstalk induced by ASE noise andPG) in transmission fibers. The ASE noise spectra impacted by thesystem’s parameters are discussed. Furthermore, by my deduction,in the nonlinear and dispersion transmission fibers, the impactson ASE noise include not only the PG enhancement but also thesolo effect of second order dispersion which may reduce ASE noise.The crosstalk caused by ASE noise and PG in single mode fibers(SMFs), non-zero dispersion shift fibers (NZDSFs) and dispersioncompensation fibers (DCFs) are also analyzed.

2. Theory

In the transmission fiber, when the carried waves are continuewave (CW) or not-return-zero (NRZ) formats, applying the smallsignal analysis method and repeating the process from Eq. (16) toEq. (23) in Ref. [11], we obtain the noise or modulation �P(z + dz, t)[11–13]:

�P(z + dz, ω)

= e−adz/2−iˇ1dzω[

cos(

12

ˇ2dzω2)

�P(z, ω)

+ sin(

12

ˇ2dzω2)

2P(z)�(z + dz, ω)]

(1)

In the nonlinear fibers, there is

�(z + dz, ω) = �

∫ z+dz

0

[P(z, ω) + 2P ′(z, ω)]dz (2)

J. Huang / Optik 122 (2011) 1376– 1380 1377

),( ωΔ zP ),( ωΔ dzzP +

Ft

ˇcωi

ts(m

g

T

U

b

�

T

P

I

in

�

D

Tdnmot(t

3

cia(tLmb

Fig. 2. The ASE spectra. The solid line is ASE power over transmission fibers. Thedash line is ASE power enhanced by PG. The black solid line is ASE power generatingin EDFAs. �1, �2 is the channel wavelengths.

Table 1Fiber parameters.

a (dB/km) � (km/W) D (ps/nm/km) Ds (ps/nm2/km) �1 (nm)

SMF 0.21 1.3 17 0.085 1550

modulation instability. It is determined by ωc = 4�P(z)/|ˇ2|.For all kinds of fibers, their parameters are constants. Thus, thecrosstalk is determined by the input power and channel space. The

Fig. 3. Power versus wavelength. Mark “x” is signal power Pin exp( − aL), “+” is theaccumulated ASE noise without nonlinear and dispersion effects MPASE(ωk), “·” is the∑M m

ig. 1. Schematic illustration of optical fibers. �P(z, ω) and �P(z + dz, ω) correspondo the power fluctuations at z, z + dz.

1 and ˇ2 are the dispersion, a is the loss of fibers, and � is nonlinearoefficient. P(z, ω) and P′(z, ω) describe the signal powers. �P(z,) and �P(z + dz, ω) are the noise or modulation terms as Fig. 1

llustrates. P(z) is the average signal intensity P(z) = P0 exp( − az).In the right side of Eq. (1), the second term represents that

he dispersion among dz translates the phase in z + dz into inten-ity fluctuation, and the corresponding gain in the sidebands of ωkthe frequency of signal) is gPG(z, ω) which is called as cross-phase

odulation instability (MI) gain or parametric gain [13]:

PG(z, ω) =

∣∣�P(z + dz, ω) − �P(z, ω)∣∣

P(z)dz

= 2e−adz/2 sin

(12

ˇ2dzω2

){�

{∫ z+dz

z

[P(z, ω) + 2P ′(z, ω)]dz

dz

}}

(3)

he first order sideband’s range is ω < ωc =√

4�P(z)/∣∣ˇ2

∣∣ [13].

sually, only the first sideband is considered [6–10].In the frequency region of [ωk, ωk ± ωc] (k is the channel num-

er), ASE noise is enhanced by the gPG:

P(z, ω) = exp[gPG(ω)z]PASE(ω) (4)

he ASE power generating in EDFAs in a bandwidth �ω is equal to

ASE(ω) = 2nsp(G − 1)hω�ω

4/�2(5)

n the complete inversion case nsp = 1. G (or g) is the gain of EDFAs.Regard ASE noise as an intensity modulation �P(0, ω) = PASE(ω),

n the transmission fibers, the intensity modulation caused by ASEoise is

P(z, ω) = cos(

12

ˇ2zω2)

PASE(ω) = D(z, ω)PASE(ω) (6)

(z, ω) = cos(

12

ˇ2zω2)

(7)

he transfer function cos((1/2)ˇ2dzω2) cannot be compensated byispersion and it makes the ASE noise reduce. Therefore, the ASEoise experience two effects in the dispersion and nonlinear trans-ission fibers. It is amplified by the gPG in the frequency range

f [ωk, ωk ± ωc] (k is the channel number), �P = PASEGPG. Simul-aneously, it is impacted by the ˇ2 which is described with Eq.6). Fig. 2 presents the ASE spectra in the dispersion and nonlinearransmission fibers.

. Results

The effects of nonlinear and dispersion on ASE noise arealculated in this section. We assume cos((1/2)ˇ2zω2) = 1n Eq. (6) and thus estimate the maximum ASE noise. Thisssumption is reasonable because for the typical values,1/2)ˇ2zω2 = (1/2)ˇ2z(2�c/�)2 = m2� (m is a integer). Parame-

ers are list in Table 1. Fig. 3 plots the ASE spectra for three cases.abel “o” is the crosstalk power caused by ASE noise and gPG. Forost cases, it is zero. From Figs. 4–9, we summarize the relations

etween the ASE powers and channel spacing, channel number,

DCF 0.59 5.5 −87 −0.135 1550NZDSF 0.21 2.2 4.4 0.045 1550

input signal power, amplifier space, EDFA number and gain. Thebroadening of channel space makes all the ASE power increase.Note that, in this case, the match filter’s bandwidth has increase.Channel number’s adding has no effect on ASE power except theenhanced ASE noise’s proportional increase. With the increasing ofinput signal power, the ASE power enhanced by PG quickly rises.The filtered of this sideband power will cause SNR improvement,but this sideband is too close to the signal channel. When theamplifier space turns longer, the enhanced ASE noises rise, thesignal powers drop and the ASE noise values approach signalpowers. Thus, signal’s powers are distorted by two types of ASEnoise. EDFA number increase causes the ASE power accumulationand the signals may be disguised by the enhanced ASE noises.

All the ASE crosstalk powers are zero in the above figures. Notethat, we only consider the first sidebands induced by the above√

maximum of enhanced ASE noisem=1

exp[gPG,k(ωk ± ωmax)L] PASE(ωk ± ωmax).

“o” is crosstalk power caused by ASE noise and PG∑M

m=1exp[gPG,k+1(ωk)Lm]∑M

m=1exp[gPG,k−1(ωk)Lm] PASE(ωk). �� = 0.1 nm, N (channel number) = 4, M (ampli-

fied span) = 10, L (amplifier space) = 80 km. g = 16.8 dB.

1378 J. Huang / Optik 122 (2011) 1376– 1380

Fig. 4. Power versus wavelength. (a) �� = 0.2 nm and (b) �� = 0.4 nm. Labels andother parameters are the same as Fig. 3.

Fig. 5. Power versus wavelength. �� = 0.2 nm. (a) N = 8 and (b) N = 16. Labels andother parameters are the same as Fig. 3.

Fig. 6. Power versus wavelength. N = 4. Pin = 0.5 mW, Pin = 4 mW. Labels and otherparameters are the same as Fig. 5.

Fig. 7. Power versus wavelength. N = 4. (a) L = 40 km and (b) L = 120 km. Labels andother parameters are the same as Fig. 5.

J. Huang / Optik 122 (2011) 1376– 1380 1379

Fig. 8. Power versus wavelength. N = 4. (a) a = 0.22 dB, g = 17.6 dB and (b) a = 0.2 dB,g = 16 dB. Labels and other parameters are the same as Fig. 5.

Fig. 9. Power versus wavelength. N = 4. (a) M = 5 and (b) M = 15. Labels and otherparameters are the same as Fig. 5.

Fig. 10. Crosstalk power versus wavelength. N = 4. Parameters are the same as Fig. 5.

input power’s increase will cause crosstalk. Once the crosstalk isgenerated, the ASE noise in this case increases fast with the signalpower (Fig. 10). Fig. 11 gives the threshold input powers gener-ating crosstalk for different channel space. A smaller input power

Fig. 11. Threshold input power generating crosstalk versus channel space. N = 4.Parameters are the same as Fig. 5.

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nd wide channel space can avoid crosstalk. For SMFs, DCFs andZDSFs, it is easier to produce crosstalk in NZDSFs but in SMFs andCFs the results are similar. This attributes to the value �/|ˇ2|.

The dispersion effect in Eq. (6) can reduce ASE noise whenos((1/2)ˇ2zωk

2) /= 1. For these cases, the amplified space can turnonger. But this is never reported by literatures, the reason may lien the accurate degree of z which should reach 0.0001 m.

. Conclusion

In WDM systems with nonlinear and dispersion transmissionbers, the impacts of dispersion and nonlinear effects on ASE noise

nclude not only the PG enhancement but also the second order dis-ersion’s solo effect which may reduce ASE noise. The whole ASEoise spectra (include the ASE noise, the ASE noise enhanced by PGnd the crosstalk induced by ASE noise and PG) are related to chan-el space, channel number, input launched power, amplifier space,DFA number and gain. Channel space’s broadening makes the ASEower increase. Channel number’s adding will causes the propor-ional increase of the enhanced ASE noise. With the increase ofnput launched power, the enhanced ASE power increases quickly.

hen the amplifier space turns longer, the amplified ASE noisesise, the signal powers drop and the ASE noise values approach sig-al powers. Thus, signal’s powers are distorted by two types of ASEoises. EDFA number increase causes the ASE power accumulationnd the signals may be disguised by the enhanced ASE noise. Theltered of the sideband enhanced ASE noise will improve SNR, buthis sideband is too close to the signal channel.

The ASE noise enhanced by PG can cause crosstalk. It is deter-ined by the input power and channel space. A smaller input power

nd wide channel space can avoid crosstalk. It is easier to producerosstalk in NZDSFs than that in SMFs and DCFs. A suitable choice of

[

[

011) 1376– 1380

channel’s wavelength or transmission distance can reduce all typesof the ASE noises.

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