The 23rd National Radio Science Conference (NRSC 2006)The. 23 NationalMarch 14-16,2006 LIC22 1i

z Y Faculty of Electronic Engineering, Menoufiya University, Egypt.

Four-Wave Mixing Crosstalk in DWDM Optical Fiber Systems

Farag Z. El-Halafawy2 (faragehalafawy@yahoo.com),Moustafa H. Aly (mosalyaaast.edu) andMaha A. Abd El-Baryl(mahy@aast.edu)

1 College of Engineering and Technology, Arab Academy for Science & Technology &Maritime Transport, Alexandria, Egypt.

* Member of the Optical Society of America (OSA).2 Faculty of Electronic Engineering, University of Menoufia, Menouf, Egypt.

AbstractIn this study, we introduce the third nonlinear optical effect known as four-wave mixing(FWM), its implications in optical fiber systems and finally a proposed technique for channelallocation to reduce its effect. Then, we investigate the channel crosstalk due to the FWM forvarious values of fiber length, core effective area, dispersion, channel spacing and channelpower as a function of the number of multiplexed channels in a multi-channel system.Results show that, the ultimate factor, which degrades the system performance, is the FWMpower.

I, IntroductionFour wave mixing (FWM) is one of the major limiting factors in wavelength division multiplexing (WDM)optical fiber communication systems that use low dispersion fibers III or narrow channel spacing. As a result,estimating the FWM efficiency is beconming very important for both the design and evaluation of densewavelength division multiplexed (DWDM).

The generation of a new frequency of radiation due to FWM lhas applications in the development of tunablesources and wavelength conversion in all-optical routing systems 121. However, generation of light throughfour-wave mixing has serious implications for the rapidly expanding telecommunications field of wavelengthdivision multiplexing (WDM). If two or more channels interact with each other through four-wave mixing,optical power will be generated with new frequencies at the cost of a reduction of power in the originalchannels. This power loss makes it more difficult to correctly detect the digital data in these channels at the farend of the fiber, making errors more likely. A more damaging consequence is that the FWM between two orthree channels generates light at a frequency that coincides with one ofthe other allocated channels. TheFWMgenerated light then acts as noise on this channel and leads to even greater degradation of the overall systemperformance. It is therefore important to take steps to avoid four-wave mixing in multi-clannel opticalcommunication systems. Four-wave mixing in WDM systems can be minimized by ensurinig that phasematching does not occur. This can be achieved by using a number of methods including spacing channelsunequally and operating at wavelengths where channels propagate at diferent speeds f2J.

In multi-channel systems, a signal channel suffers from FWM, which generates various combinations ofdifferent channel frequencies and causes cross talk degradation. For any thlree co-propagating optical Sigaswith frequencies fi, fJ, and fk, the new frequencies f ijk generated by FWM are represented by 11, 21

gkfi+kftf-fk fori j,kCf l,Njandk.{i,j}. (1)

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'~k~%" Faculty of Electronic Engineering, Menoufiya University, Egypt.

Considering all the possible pennutations, N co-propagating optical signals will give rise to M new opticalsignals as 11,31

M = N2(N-1)/2. (2)

Some of these new frequencies fall onto the N original channels, while others are found in other new frequencylocations. Those FWM signals, which overlap with the original ones, are considered as crosstalk and willinterfere with the normal operation ofthe WDM channels. This crosstalk between neighboring channels placesa lower limit on the wavelength separation between adjacent channels and an upper limit on the input power ineach channel.

In the present paper, the crosstalk in optical fiber systems has been studied and investigated and finally asuitable technique for channel allocation to reduce its effect is proposed.

II. Basic Model and analysisA well-known formula used for FWM estimation was originally derived by Hill et al. 131 and was laterreformulated to include the phase-matching dependent efficiency by Shibata et al. 14]. This formula has beenwidely used in recent years to evaluate the FWM induced crosstalk in WDM systems and can be written as_l,5,6]

1024li6 LPFWf(ff fk)( 422C2 )(d 3)( ) PiPjPk (3)

Aeffwhere P Fm is the power of the lightwave resulting from FWM at the frequency, fFWM (fFwm = fi+ fj- fk), Pi Pj,and Pi represent the input power of the frequencies: f, fj, and fk, n is the fiber refractive index, Aff is theeffective mode area of the fiber; a is the fiber loss coefficients, d is the degeneracy factor (d=3 for i=j, d=6 fori.j ), and X3 (z 6x 10 -14 m3 /J) 151 is the third-order nonlinear susceptibility.

The effective length is a parameter commonly used in the study of nonlinear effects in fibers and is defined asthe length of lossless fiber that would generate the same amount of nonlinearity as the lossy fiber underconsideration. It is defined as

Leff = (1 - e- aXLYa, (4)where a is the attenuation of the fiber in neper/knm.

The four-wave mixing efficiency parameter, q is a function of phase mismatch, AO and is the most usefulmeasurable quantity for describing four-wave mixing in optical fibers. The efficiency is normalized to 1 at zerophase mismatch and is given by 15, 61

a2 2 4exp(-aLL)sin 2 (fL/2) (a2 +/ ,2 L {1-exp(-aL)}2 J (5)

where A43 represents the phase mismatch and may be expressed in terms of signal frequency differences 11,5,61

lc fIfIf[D dD 2c l. (6)

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The 23rd National Radio Science Conference (NRSC 2006)Kd F %'>March 14-16, 2006 LLC22L3I

Faculty of Electronic Engineering, Menoufiya University, Egypt.

The amount of crosstalk, C r between channels is defined as, the ratio ofFWM power to signal power in theworst affected channel 151, i.e.

Cr = Pm/(Ps e CaL) (7)

Equation (5) indicates that FWM in an optical fiber can be suppressed either by increasing channel spacing orby increasing dispersion. Large dispersion can cause unacceptable power penalties especially in high bit ratesystems. However, careful design of the dispersion map (often called dispersion management which allowslarge local dispersion but limits the total average dispersion to be below a certain level) is found to be veryeffective to combat both dispersion and FWM induced degradations. However, the advantage of unequalchannel spacing is that it requires no modification of the transmission media; only the frequency selectivecomponents along the transmission link need to be matched with the channel allocation. In order to takeadvantage of this technique in WDM systems, array waveguide (AWG) multiplexers need to have unequalchannel spacing.

IH. Results and DiscussionIn this study, we investigate the channel crosstalk due to the FWM for various values of: fiber length, coreeffective area, dispersion, channel spacing and channel power as a function of channel number in a multi-channel system. Simulation is performed from 3 to 300 channels per fiber.

In undersea cables the input power should be large enough to permit the propagation of the signals for largedistance to reduce number of amplifiers. Hence, the present work tries to reduce the effect ofFWM crosstalkwith less concern on power parameter. As the number ofFWM signals depends on channel spacing, unequalchannel spacing scheme for adjacent channel inDWDM system was proposed 121 which guarantee that non ofthe FWM generating lights will coincide to channel wavelengths. The disadvantage of this technique is thelarge bandwidth required compared to system operating in equally channel allocation.

We propose a combination of unequal channel spacing. We take 5 different channel spacings in the range (0.25- 0.4 nm) that can be repeated for group of channels. This group ofunequal channel spacing can be repeated foranother new group until fully allocate the required number of channels. Firstly we investigate a channel schemefor a repeated unequal spacing. A base sclheme of unequal spacing is fixed for a number of channels, N, and aspacing between adjacent channels is A),, where n =1 to N-i. This base allocation scheme will be repeated asmany times as it requires to complete the allocation for all the channels in the DWDM system.

Secondly, we propose a random permutation for the scheme [AX,, AX2, AX3, AX4,.. AXN II for every new groupof channels until all the channels assignment in DWDM system is completed. This reduces the number ofpossible combinations ofFWM lights that are coincident with the channel wavelengths, and hence reduce theeffect of channel crosstalk.

The number of four wave mixing lights and the reduction in crosstalk factor is investigated at the worst casechannel. The worst channel is the channel that has the maximum number of four wave mixing lights. Weassume that all channels have the same input power with no depletion in signal power due to the generation ofFWML1-61.

Figure 1 shows the FWM efficiency as a function of channel separation for various values of dispersion. It isobvious that the FWM efficiency increases by decreasing the dispersion as the condition for phase matchingcondition is fullly satisfied.

The number of FWM: lights produced is displayed, in Fig.2, versus the number of multiplexed channels. Themost affected channel by FWM effect is the middle channel and the effect of FWM is symmetric for thechannels after and before the mddle channel. One can also note that as the number ofFWM signals increaseswith the number of multiplexed channels.

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Fig. I Four wave mixing efficiency versus channel Fig.2 Number of FWM. lights produced versus channelspacing at different dispersion. number in equal channel distribution schemne.

The number ofFWM lights produced versus channel number in a repeated unequal channel distribution schemeis shown in Fig.3. The number ofFWM signals at the middle channel and all other channels are reduced nearlyby a factor of 3 compared to equally channel allocation scheme.

Figure 4 shows the number ofFWM lights produced versus channel number in an unrepeated (random) unequalchannel distribution scheme. The nuimber ofFWM signals at the iniddle channel and all other channels arereduced nearly by a factor of6 compared to equally channel allocation scheme and by a factor of2 compared tothe repeated unequal channel spacing.

5M~~~~~~~~~~~'!,S~~~ ~ ~ ~~~2.0- lOp7mJ 3

2UO __ _, . ~~~~~~~Unequal channel102eanIsono

l J~~~~~- '3. lr. ,iko n ..P.nalio. 100~~~~~~~~~~~5.

0 _ . ~~~~~~~~ ~ ~ ~~ax={ 0.40 e x nr- sul10 20 30 40 S O0 b O 1 10 20 30 4 SsD 60 70 bO 90 IOD

Number ef uftipl.sed channel. rnub., of mviple.ed channels

Fig.3 Number of FWM lights produced versus channel Fig. 4 Nurmber of FWM. lights produced versus channelnumber in a repeated unequal channel distribution scheme number in unrepeated (random) unequal channel

distribution scheme

The crosstalk power factor, in dB, is displayed in Fig.5 for an equal cliannel distribution scheme due to FWMproduced at the most effected channel versus'channel number at different input power and different effectivearea. It is clear that channel crosstalk can be less than -IO dB if the channel input powver does not exceed - 20dBm. Channel crosstalk due to core effective area is reduced by 1.6 dB for larger core effective areas.

Figure 6 is similar to Fig.3 but the fiber length replaces the effective area. It is evident that channel crosstalkdue to fiber length is reduced by 2 dB for larger fiber lengths from 1o0-150 km.

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20 Mr50izn~~~~~~~~~~~~~~~~~~~~~~~~L=I50km

30 ~'=0 ,rn2 ..20 -- :Q.;._......... ,::: .-_

;-' om. .2h-1J ' , * - - - -OS a;-20~~~~~~~~~~~_ > > .>,;*., > .:; + -ZOdBm .e- ,,::

-SQ;0 Equal channel spacing 0.4nmo Equal cnannel spacing 0.4 nm- 1psdnm.km, L=100 km 0,0 D=1ps1nm.km

-7 50 0 0 1 150 200 250 -300Number of mulliptexed chann~s4Nse frititxdcanl

Fig. 5 Crosstalk due to FWM produced at the most Fig. 6 Crosstalk due to FWM produced at the mostaffected channel versus channel nunber at different input affected channel versus channel number at different inputpower and different effective area. power and different effective lengths.

Again, at the most affected channel, the crosstalk power factor is displayed in Fig.7 for repeated unequalchannel distribution scheme It is easily noted that channel crosstalk can be less than -20 dB ifthe channel inputpower does not exceed -10 dBm for a DWDM system not greater than 40 channel per fiber. Figure 8 is plottedfor an unrepeated unequal channel distribution. It is obviously noted that channel crosstalk can be less than -20dB if the channel input power does not exceed -10 dBm for a DWDM system up to 80 channels per fiber at hesame power constraints as in the other two schemes.

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.20~~~~~~~~~~~~2eB,; ~~~~~sd .m7 ._ _---eIvsTJ e _ . -.)

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repea tedequalchnelistributionshemepoepeated ubcun 5 sm.4Gfl ~~L= tJINb7. 0- pc-::m km doe.

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rw sgqlI f iDr 2GOL 2S(J 30e 0 so C., :> 2Qo 2se 3m

Fig. 7 Crosstalk due to FWM produced at the most affected Fig. 8 CrosstaLk due to FWM produced at the mostchannel versus channel number at different input power in affected channel versus channel number at different inputtrepeated unequal channel distribution schemne. power in repeated unequal channel distribution scheme.

Figure 9 shows the number ofFWM signals for a number ofchannels per fiber up to 100 channels under equal,repeated unequal and randomly repeated unequal channel spacing schemes.

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4000 - .-1''

. equal channel separation3500 repeated unequal channel separationunrepeated unequal channel separation3000

~2500-

2= -;2000

E~1s00z

100031 . *~~~~~~~~~~~~~~

a503 _ .

10 20 30 40 50 60 70 80 90 lOCNumber of multiplexed channels

Fig.9 Number ofFWM lights at different channel distribution at the most effected channel.

IV. ConclusionOne of the nonlinear processes that limit the infornation carrying capacity of a WDM system is four-wavemixing (FWM), which causes cross-talk between neighboring channels. This places a lower limit on thewavelength separation between adjacent channels and an upper limit on the input power in each channel. In thisstudy, the channel crosstalk due to theFWM is investigated in a multi-channel system. Simulation is performedfrom 3-300 channels per fiber.

Results show that, the ultimate factor which degrades the system performance, is the FWM power rather thanthe number of FWM signals on each channel. However, the number of FWM signals could be a usefiulmeasure. In the equally spaced channel allocation, FWM affects the middle channel most strongly. This isbecause the number ofFWM signals at the middle channel is maximum.

The change of the crosstalk factor with the channel separation, fiber length, and core effective area are notsignificant compared to the variation in channel power and unequal channel spacing. The channel crosstalk canbe easily kept below -20 dB if the channel power is kept below -20 dBm for equal channel spacing. However,for the first proposed technique of repeated unequal channel spacing, the channel crosstalk can be easily keptbelow - 20 dB if the channel power does not exceed -10 dBm for a DWDM system not greater than 40 channelper fiber. For the unrepeated unequal channel spacing allocation scheme, the number ofmultiplexed signals canbe up to 80 channels per fiber for the same power constraints

References[1] Shuxian Song, Christopher T. Allen, Kenneth R. Demarest and Rongqing Hui, "Intensity-Dependent

Phase-Matching Effects on Four-Wave Mixing in Optical Fibers," J. Lightwave Technol., Vol. 17, No. 11,pp. 2285-2290, 1999.

[2] Jeff Hecht, Light Nonlinear Effects: Understanding Fiber Optics, Prentice Hall, 2004.[3] K. 0. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, "CW Three-Wave Mixing in Single-Mode

Fibers." J. Appl. Phys., Vol. 49, No. 10, pp. 5098-5106, 1978.[4] Shibata N. ";Phase-Mismatch Dependence of Efficiency of Wave Generation through Four-Wavte Mixing in

a Single-Mode Optical Fiber," IEEE J. Quantum Electron., QE-23, pp. 1205-1210, 1987.[5] Kyong Hon KIM, Hak K;yu Lee, Seo Y. Park and El-hang Lee, "Calculation of Dispersion and Nonlinear

Effect Limited Maximum TD)M and FDM Bit Rates of Transform-Limited Pulses in Single-Mode OpticalFibers," J. Lightwave Technol., Vol. 13, No. 8, pp. 1597-1605, 1995.

[6] Liren Zhang and Junhua Tang, "The Effect of IP Traffic on WDM-Based Networks," IEEE Commni. Lett..Vol. 4. No. 9, pp. 295-297, 2000.

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