Aalysis of Low Noise ad Gai Flatteed Distributed Rama Amplifiers Usig Differet Fibers FARZIN EMAMI, AMIR H. JAFARI Opto-electroic Research Ceter, Electroic Departmet Shiraz Uiversity of Techology Airport Boulevard, Shiraz Uiversity of Techology, Shiraz IRAN emami@sutech.ac.ir http://www.sutech.ac.ir a.h.afari@sutech.ac.ir Abstract: - I this paper we preset the performaces ad characteristics of Rama amplifiers by utilizig a set of differetial equatios ad umerical simulatios. For this purpose, we use two types of fibers with differet gai characteristics such as germaium-doped ad silica fibers. I this simulatio, the optimum iitial values of the pump powers for a system with 0 pumps are recalculated ad optimized agai, so that a flat gai ad low oise characteristics ca be obtaied. I additio, the effects of the effective area o the et gai of the Rama amplifiers ad o the oise figure are discussed for this optimized 0 pumps bidirectioal amplifier. Key-Words: - Rama amplifiers, fibers, amplified spotaeous emissio, oise figure. Itroductio Rama amplificatio is a widely used cocept for high capacity log distace wavelegth divisio multiplexig (WDM) trasmissio systems. It supports high bit rate data trasmissio over log fiber spas, due to its beefits such as proper gai ad optical sigal to-oise ratio (OSNR) []. I additio, it ca be used for icreasig the badwidth of Erbium-doped fiber amplifiers (EDFAs) i hybrid systems [2]. Aother importat feature of Rama amplifiers (RAs) is its gai badwidth, which is determied by pump wavelegth. Multi-wavelegth pumpig scheme is usually used to icrease the gai flatteig ad badwidth for high capacity WDM trasmissio systems. I backward-pumped fiber Rama amplifiers, other oise sources, such as the relative-itesity oise (RIN) trasfer are miimized [3]. These amplifiers also have the uique characteristic of beig tuable at ay wavelegth, simply by chagig the pump frequecy, sice gai depeds oly o the sigal-pump frequecy shift [4]. The saturatio power of fiber Rama amplifiers is by far larger tha that of the equivalet EDFAs, thus, limitig the effects of cross-gai modulatio i recofigurable dese WDM (DWDM) systems. Due to these reasos, Rama amplifiers are widely used i the fiber optical commuicatio systems. Ideed, attetio has bee focused o RAs because of the availability of high-power compact pump lasers [5], their superior performace, such as ultra-wide badwidth, low oise ad suppressed oliearity performaces i trasmissio systems, ad lower oise figure. I silica-optical fibers, Ramaamplificatio bad exteds over a few terahertzes, ad it ca be further broadeed by multiple pumpig schemes [3] ad [4]. There are may methods to desig a multistage gai flatteed fiber RAs usig multi-wavelegth pumpig scheme (for example i [6]). Usig equally spaced pumps with a fixed cetral pump wavelegth we ca aalyze the amout of the gai flatess of multi-wavelegth pumped fiber RA [7]. The gai spectrum of such systems has a lower ripple ad good OSNR. I aother scheme, W-type fibers are used for gai flatteig with a simple system which has good oise performaces [8]. I this techique a fiber is used so its leakage loss spectral variatios are optimized similar to the variatios of Rama gai spectrum. Other methods for optimizig the oise ad havig a flatte gai spectrum use multi-pump techiques [9]-[], which used a few pumps to icrease the badwidth. I this article, we discuss two differet types of fibers such as germaium-doped ad silica fibers to have Rama gai ad the a desiged structure are simulated ad corrected whe a 0 pump Rama amplifier with optimum oise figure ad optimum gai spectrum is used. A brief summery is give i last Sectio. 2 Theoretical Backgroud Aalysis of fiber Rama amplifiers are based o a set of coupled differetial equatios which iclude the physical effects such as the spotaeous Rama emissio, its temperature depedece, Rayleigh scatterig, amplified spotaeous emissio (ASE), spotaeous Rama scatterig, higher-order Stokes geeratio, ad arbitrary iteractio betwee a arbitrary umber of pumps ad sigals. Pump sources of these amplifiers are usually ISSN: 790-57 9 ISBN: 978-960-474-053-6
semicoductor or Rama fiber lasers. I the steady state, the coupled differetial equatios i fiber Rama amplifiers ca be described as [2]-[4]: dp ± k dpase ± dpsrb s + p = k Pk + g k P Pk α (a) + s p = k PASE + g k P ( PASE + hvk ΔvF k α ) (b) + s p = k PSRB + g k P PSRB + KPk α (c) + s p dpdrb = k PDRB + g k PPDRB + KPSRB α (d) where s are the umber of pump waves ad s is the umber of sigal chaels. The values P l, ν l ad α l (l= or k) describe the power, the frequecy, ad the atteuatio coefficiet for the -th ad k-th wave respectively, where k=, 2,... p + s. The quatities P ASE ad P SRB, k are the powers correspodig to amplified spotaeous emissio (ASE) oise, sigle Rayleigh backscatterig (SRB), ad double Rayleigh backscatterig (DRB), respectively. The gai coefficiet g k describes the power trasferred by the stimulated Rama backscatterig betwee th ad kth waves ad is give by g / g v v for v > ad g k k = ( 2A eff ) ( k ) ( / A ) v g ( v ) = 2 eff v k v k v k for v <, where g i ( Δ v) is the Rama gai spectrum measured with respect to the pump frequecy v i, show i Fig. for silica fiber ad germaium-doped fiber, ad A eff is the fiber effective area. v k The temperature depedet term cotributig to ASE oise is give by F k = N phot +; for v > v k, ; for v <, where F k = N phot v k N = [ exp ( h v v k / k B T ) ] phot. Here, the parameters K, T B, ad h are the Rayleigh backscatterig coefficiet, the temperature of the system, the Boltzma s costat ad the Plak s costat, respectively. For a fiber with legth L, the boudary coditios (to solve the equatios) are defied at z=0 for a sigal waves P k (0)=P k0 (k=,2,, s ), ad at z=l for the backward-propagatig pump waves P k (L)=P k0 (k= s +, s +2,, s + p ). I equatios (), the ± deote the forward ad backward waves. 3 Numerical Results ad Discussio For solvig Rama amplifier equatios, the umerical method is used ad the the results are discussed for two types of fibers such as silica fibers ad germaium-doped fibers. We ca optimize the pump powers ad their wavelegths to have low oise ad flatted gai. Figures 2, 3 show the Rama gai coefficiets for these two types of fibers. It is clear from this figure that the peak gai coefficiet for germaium-doped fibers is grater tha that from the silica fibers, but silica fibers has a larger badwidth [5]. This system has two forward pumps ad eight backward-pumps. I this aalysis, the sigal-sigal, the pump-sigal ad the pumppump effects are cosidered ad the Rayleigh effect is eglected. The forward-pump wavelegths are calculated ad optimized to tue i 423 m ad 450 m with powers 55 mw ad 40 mw respectively (more steps respect to [6]). Fig. Gai spectrum of differet types of fiber versus wavelegth [5] Fig. 2 The o-off gai for silica fiber versus wavelegth ad A eff ISSN: 790-57 20 ISBN: 978-960-474-053-6
flatteed gai spectrum ad the proper NF amouts. The differet values of NF for germaium-doped fibers are also show i Fig. 5. From this figure, it is clear that the NF value i germaium-doped fibers is more tha that i silica fibers. The reaso is the more amplificatio of ASE i the germaium-doped fibers with respect to silica fibers. I coclusio, the values plotted i figures 2, 3, 4 ad 5 are desiged for miimum oise figure ad maximum gai flatteig. Fig. 3 The o-off gai for germaium-doped fiber versus wavelegth ad A eff The backward-pump wavelegths are also computed to tue i 434, 436, 450, 465, 483, 494 ad 52.2 m. From the data reported i [6] ad after more optimizatio cosiderig oise ad gai badwidth specificatios, the backward-pump powers are desiged i: 254, 28, 60, 2, 93, 67, 77, ad 36 mw. The legth of the silica fiber is 75 km ad for germaium-doped fiber is 00 km. The umber of chaels is equal to 00 with o.2 mw for each sigal from 86.33THz to 92.95THz ad the frequecy guard of 95THz from the each other. It is clear that by decreasig the value of effective area (A eff ), the o-off gai ad its variatio will icrease. O the other had, for loger values of wavelegths, the growth of gai is grater with respect to the shorter wavelegths. By icreasig A eff, the o-off gai decreases ad loger wavelegths are affected much more tha shorter wavelegths. For A eff equal to 85μm 2, the o-off gai will be flat with miimum ripples. The value of o-off gai is betwee 6.8-7.6 db ad it is flat with 80m badwidth. The variatios of gai versus differet values of A eff are show i the Fig. 2. I this figure the loger wavelegths have more variatios tha shorter wavelegths. I additio, for A eff =00μm 2, amplifier with germaium-doped fiber has a o-off gai betwee 20.2-22dB which is higher i compariso with silica fiber. The oise figure (NF) is calculated ad show i Fig. 4, for differet wavelegths ad differet effective areas, A eff i silica fiber. From the figure, the NF is betwee 0.3-.8dB ad its value icreases as the A eff decreases. To obtai a appropriate value for NF, we must cosider large A eff, but with large value of A eff the optimum gai ca t be obtaied. So the value of A eff is desiged so that we have both Fig. 4 The NF for silica fiber versus wavelegth ad A efff Fig. 5 The NF for germaium-doped fiber versus wavelegth ad A eff Fig. 6 shows et-gai for silica ad Fig. 7 shows this parameter for germaium-doped fibers. As show i the figures, whe A eff chages, the et gai variatio of silica fibers are more tha that the variatios of the germaium-doped fibers (ote that the maximum of gai icreases). Also, for optimum value of A eff (to have a flat O-off gai) the et gai curve is flat relatively. For example i this simulatio, for a silica fiber A eff is the typically 00μm 2 ad for a germaium-doped ISSN: 790-57 2 ISBN: 978-960-474-053-6
fiber A eff is 85μm 2. I additio, it ca be show that for shorter legth fibers the ASE oise is less tha that the systems with loger legth. The ASE parameter becomes importat especially for the low power sigals. Fig. 6 The et gai for Silica fiber versus to wavelegth ad A eff Fig. 7 The et gai for germaium-doped fiber versus wavelegth ad A eff 4 Coclusio I this paper we discussed the differet values of effective areas for a bidirectioal optimized Rama amplifier with 0 pumps by usig the umerical simulatio. I this amplifier, we used two types of fibers; germaium-doped ad silica fibers. It is show that the ASE oise ad NF vary with differet values of effective areas i silica ad germaium-doped fibers. I additio the sesitivity of two differet types of fibers with variatios of the effective area is show. Fially, the optimum value for effective area is obtaied to have a flat gai spectrum ad low oise figure. Refereces: [] D. N. Maywar, D. F. Grosz, A. Kug, L. Altma, M. Movassaghi, A. Agarwal, S. Baeree, ad T. H. Wood, Ultra-wide-bad trasmissio of.28 Tb/s (28 λ 0.7 Gb/s) over 2000 km usig 50% RZ data, Electro. Lett., vol. 38, o. 24, pp. 573 575, 2002. [2] M. Bolshtyasky, J. DeMarco, ad P. Wysocki, Flat, adustable hybrid optical amplifier for 60 m 640 m bad, i Tech. Dig. OFC 2002, Aaheim, CA, Paper ThJ5. [3] C. R.S. Fludger, V. Haderek, ad R. J. Mears, Pump to sigal RIN trasfer i Rama amplifiers, J. Lightwave Techol., vol. 9, o. 8, pp. 40 48, Aug. 200. [4] A. Galtarossa, L. Palmieri, M. Satagiustia, ad L. Ursii, Polarized backward Rama amplificatio i radomly birefriget fibers, J. Lightwave Techol., vol. 24, o., pp. 4055 4063, Nov. 2006. [5] D. Garbuzov, R. Mea, A. Komissarov, M. Maiorov, V. Khalfi, A. Tsekou, S. Todorov, ad I. Coolly, 400 480 m ridge-waveguide pump lasers with watt CW output power for EDFA ad Rama amplificatio, i Proc. Optical Fiber Commuicatios Cof., Aaheim, CA, pp. PD-8- PD-8-3, 200. [6] J. Che, X. Liu, C. Lu, Y. Wag, ad Z. Li, Desig of Multistage Gai-Flatteed Fiber Rama Amplifiers, J. Lightwave Techol., vol. 24, o. 2,pp. 935-944, 2006. [7] J. Hu, B. S. Marks, ad C. R. Meyuk, Flat-gai fiber Rama amplifiers usig equally spaced pumps, J. Lightwave Techol., vol. 22, o 6, pp. 59-522, 2004. [8] C. Kakkar, ad K. Thyagaraa, High gai Rama amplifier with iheret gai flatteig ad dispersio compesatio, sciece direct, Opt. Commu., 250, pp. 77 83, 2005. [9] X. M. Liu ad Y. H. Li, Optimizig the badwidth ad oise performace of distributed multi-pump Rama amplifiers, Opt. Commu. 230, pp. 425 43 2004. [0] V. E. Perli ad H. G.Wiful, Efficiet desig method for multi-pump flat-gai fiber Rama amplifiers, i OFC 02, pp. 57 59, 2002. [] X. Liu ad Y. Li, Efficiet algorithm ad optimizatio for broadbad Rama amplifiers, J. Opt. Soc. of Amer., pp. 564-573, 2004. [2] H. Kidorf, K. Rottwitt, M. Nissov et al, Pump iteractios i a 00-m badwidth Rama ISSN: 790-57 22 ISBN: 978-960-474-053-6
amplifier, IEEE Photo. Techol. Lett., vol., pp.530-532, 999. [3] J. Bromage, Rama amplificatio for fiber commuicatios systems, J. Lightw. Techol., vol. 22, o., pp. 79 93, 2004. [4] B. Mi, W. J. Lee, ad N. Park, Efficiet formulatio of Rama amplifier propagatio equatios with average power aalysis, IEEE Photo. Techol. Lett., vol. 2, pp. 486-488, 2000. [5] K. Rottwitt, J. Bromage, A. J. Stetz, L. Leg, M. E. Lies, ad H. Smith, Scalig of the Rama gai coefficiet: Applicatios to germaosilicate fibers, J. Lightwave Techol., vol. 2, o. 7,pp 652-662, 2003. [6] Z. Tog, H. Wei, ad S. Jia, Theoretical ivestigatio ad optimizatio of bidirectioally pumped broadbad fiber Rama amplifiers, Opt. Commu., vol. 27, pp. 40-43, 2003. ISSN: 790-57 23 ISBN: 978-960-474-053-6