Bromage, J

Leng, L

Rottwitt, Karsten

Scaling rules for the Raman gain coefficient are provided with emphasis on the effective area and wavelength dependence. Translation from measurements made at one pump wavelength to other pump wavelengths is demonstrated

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Downloaded from orbit.dtu.dk on: Dec 17, 2017Scaling the Raman Gain Coefficient of Optical FibersRottwitt, Karsten; Bromage, J; Leng, LPublished in:28th European Conference on Optical Communication, 2002. ECOC 2002.Publication date:2002Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Rottwitt, K., Bromage, J., & Leng, L. (2002). Scaling the Raman Gain Coefficient of Optical Fibers. In 28thEuropean Conference on Optical Communication, 2002. ECOC 2002. (Vol. 3, pp. 1-2). IEEE.Symposium 3.3SCALING THE RAMAN GAIN COEFFICIENT OF OPTICAL FIBERSKarsten Rottwitt (1), Jake Bromage (2) and Lufeng Leng (2)1: OFS Fitel Denmark, present address Research Center COM, Technical Univ. of Denmark, Building. 345v,2800 Lyngby, Denmark, e-mail: kar@com.dtu.dk2: Systems Testing, OFS Laboratories, 791 Holmdel-Keyport Road, Holmdel, NJ, 07733, USAAbstract Scaling rules for the Raman gain coefficient are provided with emphasis on the effective area andwavelength dependence, Translation from meastrements made at one pump wavelength to other pumpwavtelengths is demonstrated,IntroductionThe Raman gain coefficient of an optical fiber is acritical parameter when designing Raman amplifiersas it determines the magnitude and spectral shape ofthe gain for a given pump wavelength and power. Itis convenient to be able to predict the Raman gainoefficient for arbitrary pump wavelengths for differenttypes of fibers or apply measurements made at onepump wavelength to other pump wavelengths. Oftenthe Raman gain coefficient is assumed to scaleinversely both with the pump wavelength and theeffective area of the fiber at the signal wavelength [1],In this work, we discuss these assumptions andpresent results that show the oorrect scaling, derivedfrom a classical model for Raman scattering. Wethen test these predictions using measurements ofRaman gain spectra for several pump wavelengths,Raman gain coefficientThe optical properties, such as the refractive indexand the Raman gain coefficient, of a light-guiding fiberdepend on the constituents of the fiber. Mostcommon fibers consist of a silica, SiO2, host to whichgermania, GeO2, is added in the core to increase therefractive index.The Raman effect originates from interactionsbetween optical phonons and the propagating eletricfield. The phonons can be imagined as oscillations ofthe oxygen atom in a Si-O-Si, Si-O-Ge, or Ge-O-Gebridge. The induced polarization of the molecule canbe expanded in terms of the displacement of theoscillator. In this expansion, the permanentpolarizability is responsible for Rayleigh scattering,whereas the differential polarizability is responsiblefor Raman scattering [2].The force that drives the oscillator originates from theelectric energy stored in the material. Thus byapplying a conventional model for a harmonicoscillator, the amplitude of the oscillations can beexpressed through the induced polarization and theelectric field [3],Combining the induced nonlinear polarization with theamplitude of the oscillations, one may derive thewave equation for light propagating in a dielectricmaterial starting from Maxwell's equations. Bysolving this wave equation, the gain coefficient due tostimulated Raman scattering is found to beJjR, I2IR~ l'imjI),~jd3e),A J ,(1)5 afi>;Et,trp JR1 tIA JR 12Awhere the subscripts s and p refer to the signal andpump, a) is the angular frequency, n, the effectiverefractive index, R,(r4, w;) the transverse part of theelectric field, X the velocity of light, and the integralsare over the cross-sectional area of the fiber, A. Dueto space limitations, the complete derivation will beshown elsewhere. Equation (1) shows th69reticallyhow the Raman gain coefficient scales with materialproperties, wavelength, and modal overlap betweenpump and signal.Dependence on fiber-compositionEquation (1) also shows how the radial dependenceof X'3) is taken into account when predicting theRaman gain coefficient. In Ref. [4] we treated this bydecomposing ytj3 into a sum of contributions fromSi-O-Si and Si-O-Ge. For realistic germaniaconcentrations, Ge-O-Ge bridges are rare. Therelative distribution of Si-O-Si and Si-O-Ge bridges is(1-20):2x, where x is the GeO2 cncentration, whichcan be obtained from the refractive index profile usingSellmeioer data. In Ref. [4] we showed that thisdecomposition can be used to predict the Raman gaincoefficients of germanosilicate fibers. We verified thisexperimentally for fibers with a broad range of peakRaman coefficients, ranging from 0.35 to 6.0(W km)-'.Dependence on wavelength and effective areaIn some cases the refractive index profile may not beavailable but the spectrum of the Raman gaincoefficient of a specific fiber type may be known froma single measurement at a specific pump wavelength.The task is then to scale the spectrum of the Ramangain coefficient to another pump-wavelength.If the third-order susceptibility, y{3 is assumed to beconstant over the entire fiber cross-section, Eq. (1)reduces toAuthorized licensed use limited to: Danmarks Tekniske Informationscenter. Downloaded on March 10,2010 at 10:15:41 EST from IEEE Xplore.  Restrictions apply. Symposium 3.31P,'?r .s-,I ' ~ (>3AfpI"Ip iZ,//0-,WpLJwhere AP' accounts for the radial overlap betweenpnffpump and signal light,(3)Aiw- t ^Ay (op ) _Ji s 1t dXAft2, 212 JA/SI 121Ri 'dA,A1 A .4The conventional effective area, A (6() is given byEq. (3) with ,0,R[1J. Using the scaling shownin Eq. (2), the gain coefficient for new pump andsignal frequencies (Op, Uis) Is:For relevant optical frequencies, £.sla&- f.po(p andthus, for convenience, the ratio of pump frequenciesis used rather than signal frequencies. To verify thisscaling, we performed the following experiment. First,we measured the Raman gain coefficient of a non-zero dispersion shifted fiber (with a 55_Am2 effectivearea at 1550 nm) for four pump wavelengths; 1423.6nm, 1443.8 nm, 1471.3 nm and 1496.0 nm. ThesemEeasurements are shown in Fig. (1).1.0- -- 4- -21 3.6.1471.31496.00.6.*.........m0.24~,0.2 ....0.0 .......1450 1500 1 550 1600 1650$ (nmJFig. 1: Measurements of Raman gain coefficientfor fourpump wavelengths.If we assume that the transvere part of the electricfield is Gaussian, the effective area representing theoverlap between pump and signal is as shown inRef. [5], as,We used this assumption of Gaussian spatial modesto re-scale each of the Reaman gain coefficientscurves from their original pump wavelengths to a newpump wavelength of 1454 nm. Aeff was calculatedfrom the refractive index profile. Figure 2 shows there-scaled coefficients versus the frequency differencebetween pump and signal, ((q, Q)Starting from the measurements made for pumpwavelengths that span 73 nm, we obtain a predictionof the Raman gain coefficient for the new pumpwavelength that differ by only 4%, confirming thevalidity of this approach.1.00.8-dI.._oixcn0.60.40.20 5 10 15 20 25Fig. 2: Re-scaled Raman gain coefficientsversus frequency difference between pump andsignal for a 1454-nm pump.This example also denonstrates that the reduction inRaman efficiency with increasing pump wavelength isdue in part by the reduced spatial overlap betweenthe pump and signal modes, The difference betweenthe peak Raman gain coefficients for 1423.6 nm and1496 nm pumps is approximately 15%, which canonly be partially accounted for by the 5% reduction inao. Hence, to fully explain the reduced Ramanefficiency one must take into account the reducedoverlap of pump and signal with increasing pumpwavelength.ConclusionIn this work we have demonstrated how the Ramangain coefficient scales with fiber design and pumpwavelength, with emphasis on the scaling witheffective area and pump wavelength. In one example,the Raman gain coefficient decreases 10%, when thepump wavelength increases 73 nm. It is demonstra-ted that a Raman gain coefficient measurement maybe accurately scaled to other pump wavelengths if therefractive index profile of the fiber or the effective areaversus wavelength is known.Referencos[1] G. Agrawal 'Nonlinear Fiber Optics", AcadernicPress, 1995[2] P. N. Butcher and D. Cotter: "The Elements ofNonlinear Opics" Cambridge Studies in Modern OpticVol. 9, Cambridge University Press 1990.(3] A. Yariv 'Quantum Electronics"', John Wiley andSons, Third edition,1989.[4] J. Bromage, K. Rottwitt, and M.E. Lines, IEEEPTL, vol. 14, p. 24 (2002)[5] W.P. Urquhart and P.J. Laybourn, IEE Proc., vol.132, p. 201 (1985)- fror 1423.6- - from 1443?8from 1471.3. . frmr 1496.0I I i I3wS imle " I2 (S..^^.)Authorized licensed use limited to: Danmarks Tekniske Informationscenter. Downloaded on March 10,2010 at 10:15:41 EST from IEEE Xplore.  Restrictions apply. 

Scaling the Raman Gain Coefficient of Optical Fibers

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Scaling the Raman Gain Coefficient of Optical Fibers

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