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42 1 CLEO96 1 MONDAY MORNING

cMc4 11:15 amNonlinear polarization-mode dispersionin optical fibers with randomlyvarying birefringencel? K. A. Wai, W. L. Kath: C. R. Menyuk,D. Marmse, Department of Compu ter Scienceand Electtical Engineering, University ofMa yland-Baltimore County ,Baltimore,Maryland 21228-5398Random fluctuations in birefringencealong an optical fiber result in polariza-tion-mode dispersion, which degradesthe transmission rate in both NRZ andsoliton systems. Recently, we proposedtwo physical models to study the polar-ization-mode dispersion (PMD) when theaxes of birefringence rotate randomly.I2In the first model, we allow the birefrin-gence orientation to vary randomly butkeep the strength fixed; in the secondmodel, we assume that the birefringenceorientation and strength have a two-di-mensional Gaussian distribution. Weshow that the coupled nonlinear Schrcl-dinger equation, which describes waveevolution over long lengths along a com-munication fiber, can be reduced to theManakov equation with corrections dueto linear and nonlinear PMD, i.e.,

wheret (U, V) is the electric field, bis the strength of randomly varying bi-refringence,

and N = (Nl, NJ hereNI = S$(Zlq - q Z ) U- S&(ZlUr - 1q)V

- &S6UZV* SpVW, (3a)NZ S,@lW- I q ) V + s3s6(zlq - W)U

+ s&vZu* s:uv*, (3b)The notation (U) epresents the ensembleaverage of U and (N)epresents replacingthe coefficients S,S, in N by their ensem-ble averages. The Coefficients (SI, S2, S3)and (S,, S5 , s6) are Stokes parameterswith different initial conditions.When the right-hand side equals zero,Eq. (1) is known as the Manakov equa-tion. The first term on the right-hand sideof Eq. (1)corresponds to the usual linearPMD that has been considered exten-sively by Poole and co-workers, by Curtiand coworkers, and others3while the sec-ond term will lead to a nonlinear PMD,which to ou r knowledge, has not beenpreviously discussed. The coefficients onthe right-hand side of Eq. (1)have zeromean when averaged over the Poincadsphere and they change sign on a lengthscale given by the filer autocorrelationlength h- , which is much shorter thanthe dispersion length scale. Physically,the pulse envelope only responds to the

l o alinear coefficient

nonlinear coefficients10-2 10-1 I00 IO Id

hRber 3CMG4 Fig. 1 The variances of theaveraged random Coefficients of thelinear and nonlinear polarization-modedispersion to the Manakov equationversus &-LE at large distance. Thesolid curve gives var[(l/z) $0 d z ( S 1-(SI))], the long-dashed curve givesvar[(l/z) $0 dz(S: - 1/3)], and thedotted curve gives var[(l/z)fl dzRe(S3S6)]. he variances arenormalized by the distance Z and thebeat length L B .cumulative effects of these rapidly vary-ing coeffiaents. The relative strength ofthe linear and nonlinear PMD dependson the strength of the birefringence band the variances of the averaged ran-dom coefficients that appear in Eq. (2) (Sland Sf) . In Fig. 1, we plot the varianceof the averaged random coefficients ver-sus & h r / L B at large distance. The solidcurve gives varI(l/z) $0 dz(S1 - (SJ)l,the long-dashed curve gives var[(l/z)f i d z ( S : - 1/3)], and the dotted curvegives var[(l/z) fi dzRe(S,S6)]. The vari-ance of ( l / z ) $0 dzS4(z) is also given bythe solid line in Fig. 1, while the vari-ances of the averaged nonlinear coeffi-cients closely resemble those shown inFig. 1.In a new type of communication fiber,linear polarization-mode dispersion is re-duced by twisting the fibers during thedrawing process. The twisting of the fi-bers decreases hnb, and hence linear PMDdecreases. However, when h , e< L E , hecontribution of nonlinear PMD, which isproportional to the nonlinear coefficientsin Fig. 1 become more important. Thereis an optimal twist length at which thecombined effect of linear and nonlinearpolarization-mode dispersion is minimal.

This work was supported by NSF andDOE. Numerical work was carried out atN E W and SDSC.EngineeringScience and AppliedMathe matics, McCormick School ofEngineering and Applied Science,Northwestern University, Evanston,Illinois 60208

and S,) and in Eq. (3) (Si, Sass, S&, Si ,

1.2.3.

C. R. Menyuk, P. K. A. Wai, J. Opt.Soc. Am. B.11,1288 (1994).P. K. A. Wai, C. R. Menyuk, Opt.Lett. 119,1517 (1994).See C. D. Poole, J.H. Winters, J. A.Nagel, Opt. Lett. 16,372 (1991);F.Curti, B. Daino, G. De Marchis, EMatera, J. Lightwave Technol. 8,1.162(1990), nd the referencestherein.

CMC5 11 30 amElimination of four-wave mixing indispersion-shifted optical fibers by usingmidway optical phase conjugation in asemiconductor optical amplifierb u n , Kikuchi, Department of ElectronicEngineering, University of Tokyo,7-3-1 Hongo, BunkyeKu, Tokyo 113, JapanIn the long-distance wavelength-divisionmultiplexed (WDM) optical communica-tion system, the cruss talkgenerated fromfour-wavemixing (PWM) in optical fiberslimits the performance of the system,when channel wavelengths are set nearthe zero-dispersion wavelength of opticalfibers. To cope with this problem, it waspointed out that midway optical phaseconjugation could cancel such cross talkinduced by FWM.n the proposed sys-tem,the FWM sidebands grown by Kerrnonlinearity of the first half of the fiberlinkbring back their power to the origi-nal signal through Kerr nonlinearity ofthe latter half of the fiber link. This pro-cess ispossible owing to the time reversalnature of optical phase conjugation.In this paper, we experimentally dem-onstrate that a midway optical phaseconjugator using a semiconductor opticalamplifier actually eliminates FWM side-bands from a dual-channel signal trans-mitted thmugh dispersion-shifted opticalfibers.The experimental setup is shown inFig. 1.Two cw signal lights, whose wave-lengths are A1 = 1555.1nm and Az= 1554.9nm, are amplified by an erbium-doped i-ber amplifier (EDFA), and are launchedinto the first half of the fiber link. We usea 20-km-long dispersion-shifted (DS) op-tical fiber, whose zero-dispersion wave-length is 1555 nm. The total transmittedpower is 10 dBm. The FWM process sig-nificantly occurs in the 20-km DS fiber,because the phase-matching condition forFW M is satisfied near the zero-dispersionwavelength?The signal lights are then led to theoptical phase conjugator (OPC). A semi-conductor optical amplifier is used asthird-order nonlinear (x) medium. Thepump wavelength A, is 1552.8 nm andthe pump power injected to the amplifieris 3 dBm. The saturated amplifier gain is7 dB in this case. The phase-conjugatedreplica is filtered out by a bandpass filterwith a bandwidth of AA = 0.7nm, and isamplified by adjustable EDFA gain G.The amplified signal travels the latterhalf of the fiber link which is a IO-km-long DS iber having he zero-dispersionwavelength of 1553 nm.Figure 2 shows the optical spectrumjust after optical phase conjugation. Wefind that the signal transmitted throughthe first half of the fiber link has twosidebands caused by PWM, nd that thephase-conjugated replica is efficiently gen-erated from the original signal.Figures 3(a) and (b)show optical spec-tra of the output from the latter half ofthe fiber link.Figure 3(a) is measuredwhen the EDFA gain G is small enough.The phase-conjugated replica passesthrough the latter half without changing

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DS Fiber DS Fiber20 km .......................................... , 1okmf OPC ..hl+> .+- I / ' -EDFA ?v:.......................................CMC5 Fig. 1for eliminathg four-wave mixing sidebands.Experimental setup of the midway optical phase conjugation scheme

Wavelength [nm]CMG5 Fig. 2 Optical spectrum justafter optical phase conjugation.

Wavelength [nm]

1550 1551Wavelength [nm]CMCS Fig. 3 Optical spectra of theoutput signal measured when the EDFAgain G is smal l enough (a), and G isoptimized (b).Note that the FWMsidebands almost perfectly disappear in(b).

its spectrum, and the FWM sidebandsstill remain. This is because the Kerr ef-fect in the 10-km fiber is negligible.On the other hand, when the EDFAgain G is adjusted a t an optimum value,we can observe the spectrum shown inFig. 3@), where the FWM sidebands dis-appear almost perfectly. The Kerr nonlin-

earity in the latter half of the fiber linkcancels the FWM sidebands in coopera-tion with the effect of the OX.In conclusion, we have experimentallyshown that FWM sidebands can be elim-inated by midway OPC. This schemeseems very attractive for the future denseWDM system, because it has potential forcanceling the cross talk due to the cross-phase modulation and the stimulated Ra-man scattering in addition to the FWMcross talk desaibed here.C. Lorattamsane, K. Kikuchi, inConference on Lasers and Electro-Optics, Vol. 15,1995 OSA TechnicalDigest Series (Optical Society ofAmerica, Washington,DC, 995),paper CTuN3.K. Kikuchi, C. Lorattanasane, IEEEPhoton. Technol. Lett. 6, 992-994(1994).

CMC6 11:45 amReduction of Raman penalty inmultiwavelength transmission usingmidspan spectral inversionG. J. Pendock, J. R R Lacey, PhotonicsResearch Laboratory, Australian PhotonicsCooperative Research Center, Department ofElectrical and Electronic Engineering,The University of Melbourne, Parkville,VlC.3052, AustraliaMidspan spectral inversion (MSSI) hasbeen used to compensate for first-orderchromatic dispersion in optical fiiertransmission systems.' MSSI, unlike otherdispersion compensation schemes suchas compensating fiber or Bragg gratings,can also reduce the effects of fiber nonli-nearities.2 This is significant because non-linearities may ultimately limit transmis-sion capacity. MSSI has been shownexperimentally to reduce self-phase mod-ulation in single-wavelength transmis-sion: and to reduce four-wave mixing inmultiwavelength (WDM) transmission.'MSSI has also been shown numerically toreduce the effects of stimulated Ramanscattering (SE) in single-wavelengthsoliton transmission: and has been pro-posed for reducing SRS in multiwave-length transmission systems! A reduc-tion in Raman penalty would enable thepotential transmission capacity of WDMsystems to be increased by allowinghigher powers to be transmitted! Herewe numerically simulate Raman penal-ties in a WDM transmission system andconfirm that MSSI can reduce these pen-alties.We consider an optically amplified

MONDAY MORNING / CLEO'96 / 43

WDM transmission system with four 2.5Gbit/s channels spaced 2 nm apart. Theamplifiers are spaced at 50-km intervalsand compensate exactly for the fiber at-tenuation (0.25 dB/km) between them.SRSinduced power transfer betweenchannels is numerically calculated usingrate equations,' assuming typical S Wgains in fiber! Our simulation includesthe walk-off in the data timing betweenchannels caused by first-order dispersion(16 ps/nm/km). Nonlinear effects otherthan SRS are neglected. Data consistingof NRZ 2' - 1 psuedorandom sequences(delayed between channels) are propa-gated through the system, and the Ra-man penalty is determined from the clo-sure of the received eye-pattem for themost severely affected channel. MSSI isimplemented in the simulation by simply

0

1 ...............................

0Elldb)0lDI(cl

CMG6 Fig. 1 Eye-patterns (a) at theinput to the transmission link, nd after2OOO-km transmission in links b)without MSSI and (c) with MSSI.

Dlstancap"CMG6 Fig.2 Ramanpenaltyasafunction of transmission distance fortransmission systems with and withoutMSSI.