998 OPTICS LETTERS / Vol. 29, No. 9 / May 1, 2004

Cascaded Raman generation in optical fibers: inf luence ofchromatic dispersion and Rayleigh backscattering

Frédérique Vanholsbeeck, Stéphane Coen, and Philippe Emplit

Service d’Optique et Acoustique, Université Libre de Bruxelles, 50 Av. F. D. Roosevelt, CP 194/5, B-1050 Brussels, Belgium

Catherine Martinelli

Alcatel Research & Innovation, Route de Nozay, F-91461 Marcoussis Cedex, France

Thibaut Sylvestre

Laboratoire d’Optique P. M. Duffieux, Université de Franche-Comté, Unité Mixte de Recherche du Centre National de la RechercheScientifique 6603, 16 Route de Gray, F-25000 Besançon, France

Received January 5, 2004

We study experimentally the inf luence of chromatic dispersion and Rayleigh backscattering on cascaded Ra-man generation in silica optical fibers. Effects ranging from enhanced spectral broadening of the Stokesorders to generation of higher Stokes order at unexpected wavelengths are observed. Additionally, we showthat four-wave-mixing processes can quench the noisy Rayleigh lasing lines generated in power Raman ampli-fiers. Our observations are confirmed by numerical simulations. © 2004 Optical Society of America

OCIS codes: 190.5650, 190.4380, 290.5870, 060.2320.

Cascaded Raman generation is a nonlinear process bywhich a series of Stokes waves of decreasing frequen-cies are successively generated through the excitationof a vibrational wave of the propagating medium bya powerful optical pump beam. It can be understoodas an iteration of fundamental stimulated Raman scat-tering (SRS) processes in which each generated Stokeswave acts as a pump to produce the next one. Sil-ica optical f ibers were recognized early on as an idealmedium to take advantage of this process with the aimsof generating new laser wavelengths and of developingwideband optical amplif iers.1 Today, it is admittedthat cascaded Raman fiber lasers and Raman ampli-fiers will play a leading role in the multiterabit-per-second telecommunication networks of the future.

Early theoretical and experimental studies re-vealed, however, that Raman-active media typicallyexhibit various competing nonlinearities that canstrongly affect cascaded Raman generation. Amongthese, parametric four-wave mixing (FWM) wasfound to have a critical inf luence.2 In particular,when chromatic dispersion is suff iciently weak, evennon-phase-matched parametric processes can play animportant role by seeding waves that are subsequentlyamplified through SRS, bypassing in this way thenormal cascade.3,4 FWM effects can also lead to can-cellation or enhancement of the Raman gain, depend-ing on the dispersion of the propagating medium.2,5

Apart from a few specif ic studies,4 – 6 these processeshave been widely investigated only in gases andunder pulsed pumping conditions,3,7 i.e., in experi-mental conditions different from those of moderncontinuous-wave (cw) fiber devices. Given the strongpotential of cascaded Raman fiber lasers and ampli-fiers, a complete understanding of these competingmechanisms in optical f ibers is, however, of primaryimportance. The goal of the present work is to ex-amine these aspects more deeply. Here, in additionto FWM, we also consider the inf luence of Rayleigh

0146-9592/04/090998-03$15.00/0

scattering on cw cascaded Raman generation. Thisprocess is indeed known to strongly affect the noiseproperties of fiber Raman amplifiers.8

To perform our investigations we have observedthe Raman spectra generated in various silica f iberspresenting different chromatic dispersion properties.As a pump laser, we use a cw Raman fiber laseremitting at lp � 1455 nm. With this laser, thefirst two Stokes orders, S1 and S2, should appearat lS1 � 1555 nm and lS2 � 1669 nm, respectively.The pump power is injected into the f iber througha dichroic coupler. An optical spectrum analyzer(2-nm resolution) is then placed either at the outputend of the f iber or at the second port of the dichroiccoupler to record the forward and backward amplifiedspontaneous emission (ASE) spectra, respectively.The fibers under study are four nonzero dispersion-shifted f ibers (NZDSF 1, 2, 3, and 4) of lengthL � 15 km that differ only in their zero-dispersionwavelengths (ZDWs), l0 � 1550, 1554, 1565, and1567 nm, respectively. Note that the ZDW of allthese f ibers lies in the vicinity of the f irst Stokesorder, S1. These f ibers present a Raman gain coeffi-cient CR � 0.74 W21 km21. For comparison, we alsoperform our experiments in f ibers with their ZDW farfrom S1, namely, a 20-km-long standard single-modefiber (SMF), l0 � 1310 nm, CR � 0.46 W21 km21, anda 12-km-long reverse-dispersion fiber (RDF) for whichCR � 1.2 W21 km21. The RDF has no ZDW and ex-hibits normal dispersion at 1.5 mm with a dispersionslope of opposite sign with respect to a SMF.

The forward Raman ASE spectra observed experi-mentally in our six fibers are shown in Fig. 1. Theyare recorded for the maximum pump power Pp thatcould be coupled into each fiber, as shown in the f ig-ure. Comparison of these measures reveals strikingdifferences. First, the four NZDSFs exhibit strongspectral broadening of S1 in comparison with the twoother f ibers. This broadening can be attributed to

© 2004 Optical Society of America

May 1, 2004 / Vol. 29, No. 9 / OPTICS LETTERS 999

Fig. 1. Experimental forward Raman ASE spectra ob-served in each of the f ibers under investigation.

the high eff iciency of FWM effects occurring withinS1 in the NZDSFs as a result of the close proximity ofthe ZDW.6 Note that a slight difference in dispersionamong the four NZDSFs leads to a significant changein the spectral shape of S1. More importantly, S2 isnot generated in the SMF, whereas this band is clearlypresent in the output of three of the NZDSFs. Thisobservation cannot be explained solely in terms of SRSsince these f ibers all exhibit an equivalent integratedRaman gain, CRPpL � 33.1 Moreover, notice that S2,when present, appears at different wavelengths. Thisremarkable fact is not accounted for by the standardRaman cascade theory, which predicts a constantRaman shift between successive orders.1,2

These observations actually result from Raman-assisted FWM processes.3,4 Here, S2 is generatedparametrically through mixing of two photons fromthe frequency components of S1 with a pump photonand through subsequent Raman amplification. S2appears for a lower pump power than in a normalcascade because of the additional gain resulting fromFWM. With this scheme, the wavelength of S2 isno longer fixed by the peak of the Raman gain butdepends on the most efficient FWM process. Theproblem is complex because the net FWM efficiencyis not simply determined by the phase mismatch1

but is also inf luenced by the power available in thefirst Stokes order frequency components involvedin the parametric interaction and by the relativepositions of the generated S2 photons with respectto the peak of the spontaneous Raman line.9 Boththe dispersion profile of the f iber and the particularshape of S1 therefore plays a critical role in fixing theposition of S2, which is in practice diff icult to predictab initio. S2 is not generated in the SMF or in theRDF because of their large dispersion about S1. Thephase mismatch is too large for efficient seeding ofS2 (the case of NZDSF 1 will be discussed below).NZDSF 3 illustrates our discussion particularly well.

In this case S2 exhibits a double-peak structure thatis due to a competition between two different FWMprocesses. From the measured dispersion of thefiber, we can deduce that the 1685-nm peak resultsfrom a phase-matched interaction between 1547- and1576-nm photons with the 1455-nm pump. Addition-ally, the mixing of two photons from the powerful1566-nm component of S1 with a pump photon leadsto the generation of 1690-nm radiation. Despite thefact that this latter interaction is not perfectly phasematched, it is slightly more efficient than the f irstone because of the large power available at 1566 nm.Note that the 1566-nm peak does not match thetheoretical f irst Stokes wavelength of our pump laser,lS1 � 1555 nm, because of Raman-induced energytransfer within S1 that tends to redshift all thespectral lines.6 This phenomenon can actually beobserved in all our fibers.

We have been able to reproduce these observationsnumerically with a generalized nonlinear Schrödingerequation (GNLSE) model.1 The simulations take intoaccount spontaneous and stimulated Raman scatter-ing, FWM, the measured dispersion profile D�l� of thefibers, and the spectral width of the pump wave. Theresults for the NZDSFs are plotted in Fig. 2. As onecan see, the spectral broadening of S1 and the posi-tion of S2 are satisfactorily reproduced by our model.We must stress that none of these phenomena wouldappear if FWM was neglected. NZDSF 1 is a specialcase in that S2 is not detected in the experiment butis present in the simulation. A reduced experimen-tal FWM efficiency explains this difference and agreeswith our observation of comparatively large longitudi-nal variations of dispersion in this f iber. Our GNLSEmodel does not, however, account for all the obser-vations. Observing the pump to S1 power ratio, wenotice that the strong depletion of the pump wave isnot reproduced correctly. Also, measurements revealthat, above a certain pump power threshold, the powerof S1 grows faster than an exponential. This behavioris not explained by the standard Raman cascade modelor by the inf luence of FWM. As we show below, theinclusion of backward-traveling waves eliminates these

Fig. 2. Experimental forward ASE spectra (thin curve)compared with GNLSE simulations (thick curve) for thefour NZDSFs.

1000 OPTICS LETTERS / Vol. 29, No. 9 / May 1, 2004

Fig. 3. (a) Output power characteristics of the pumpand the forward and backward f irst Stokes orders inNZDSF 4. Experiment (dotted curve) versus simulationswith (solid curve) and without (dashed curve, aR � 0)Rayleigh scattering. (b) Experimental forward RamanASE spectra from the SMF at 3-W pump power (SMF andRDF spectra are averaged).

discrepancies, which are due to a laserlike behavior in-duced in the f iber by double distributed Rayleigh re-f lections.8

We have performed a second set of simulations witha model that neglects FWM but includes forward andbackward SRS as well as Rayleigh scattering8:

Pp0 � �2ap 2 CR �g1P1 1 g2P2��Pp , (1)

P60 � 6��g6CRPp 2 as 2 aR�P6 1 aRP7 1 rspPp� .

(2)

Here the primes denote derivatives with respect tothe longitudinal fiber coordinate z, and P6 representsthe S1 power co- �1� and counterpropagating �2� withthe pump. The forward–backward Raman thresholdasymmetry is described by g1 � 1, g2 � 16�20.1 apand as are the absorption coefficients for the pump andS1, respectively, aR � 1027 m21 is the Rayleigh scat-tering coefficient, and rsp accounts for spontaneousRaman scattering.2 The output powers obtainedwith this model for various pump power levels aresuperimposed with the experimental measurements(integrated over 12 nm) in Fig. 3(a). As seen fromthe figure, the agreement is excellent. The Rayleigh“lasing” threshold observed for S1 at Pp � 1.5 Wis correctly reproduced, as is the subsequent strongpump depletion.8 Additional simulations performedin the absence of Rayleigh scattering [dashed curvein Fig. 3(a)] make even clearer the importance of thisphenomenon in our experiments. Here, no threshold-type behavior is observed, depletion of the pump waveis postponed, and the backward Stokes power P2

appears weaker by several orders of magnitude.Rayleigh scattering also manifests itself quite

remarkably through the appearance of many sharpf luctuating spectral lines on the experimental outputspectra, as illustrated in Fig. 3(b) for the SMF. Theselines are not seen in the measurement presented inFig. 1 because they mostly vanish at higher pumppower. As Rayleigh scattering is not sensitive to chro-matic dispersion, we should expect similar behavior inall the f ibers that we study. Remarkably, NZDSFsbehave differently. Only a few lasing lines can be

seen for pump powers within 10% of the Rayleighthreshold, but otherwise the spectra generated in theNZDSFs do not present any sharp spectral features.We can understand this difference by considering thatthe high FWM efficiency of the NZDSFs essentiallyfunnels all the available gain into the growth of S2.Our experiments therefore demonstrate that the noisyRayleigh lines that are generated in Raman poweramplifiers can be eff iciently quenched through FWMin low-dispersion fibers.

In conclusion, we have studied the inf luence ofchromatic dispersion and Rayleigh backscattering oncw cascaded Raman generation in silica optical fibers.Our work extends early experiments performed ingases3 and reveals that the generated spectra resultfrom a subtle interplay among these three processes.We have shown that even non-phase-matched FWMprocesses can strongly affect cascaded SRS in low-dispersion fibers. Typically, strong spectral broad-ening of the low-dispersion Stokes order is observed,and the wavelength of the next Stokes order becomesdetermined by the most eff icient FWM process andno longer by the Raman gain maximum. FWM isalso responsible for quenching of the noisy lasing linesgenerated through Rayleigh scattering. Numericalsimulations confirm our observations. Our analysiscan be applied to cascaded Raman fiber lasers, forwhich including chromatic dispersion as a new degreeof freedom could potentially lead to powerful multi-order lasers or to second-order pumping units.10

This research was supported by the Inter-University Attraction Pole program, the Fondspour la Formation à la Recherche dans l’Industrieet dans l’Agriculture, and the Fonds National de laRecherche Scientifique (Belgium). F. Vanholsbeeck’se-mail address is fdv@phy.auckland.ac.nz.

References

1. G. P. Agrawal, Nonlinear Fiber Optics (Academic,San Diego, Calif., 2001).

2. Y. R. Shen and N. Bloembergen, Phys. Rev. 137, A1787(1965).

3. V. S. Butylkin, G. V. Venkin, L. L. Kulyuk, D. I.Maleev, Yu. G. Khronopulo, and M. F. Shalyaev, Sov.J. Quantum Electron. 7, 867 (1977).

4. T. Sylvestre, H. Maillotte, E. Lantz, and P.Tchofo Dinda, Opt. Lett. 24, 1561 (1999).

5. F. Vanholsbeeck, Ph. Emplit, and S. Coen, Opt. Lett.28, 1960 (2003).

6. R. H. Stolen, C. Lee, and R. K. Jain, J. Opt. Soc. Am.B 1, 652 (1984).

7. M. D. Duncan, R. Mahon, L. L. Tankersley, andJ. Reintjes, Opt. Commun. 86, 538 (1991).

8. C.-J. Chen, H. Lee, and Y.-J. Cheng, in Optical FiberCommunication Conference, Vol. 86 of OSA Trends inOptics and Photonics Series (Optical Society of Amer-ica, Washington, D.C., 2003), paper TuC2.

9. F. R. Barbosa, Appl. Opt. 22, 3859 (1983).10. F. Vanholsbeeck, S. Coen, C. Martinelli, Ph. Emplit,

and T. Sylvestre, in Optical Amplif iers and Their Ap-plications, Vol. 93 of OSA Trends in Optics and Pho-tonics Series (Optical Society of America, Washington,D.C., 2003), paper MC4.