Adaptive optical post distortion linearization

Transcription

1 Adative otial ost distortion linearization Jason Chou, Ozdal Boyraz, and Bahram Jalali Otoeletroni Ciruits and Systems Laboratory University of California, Los Angeles (UCLA) CA , U.S.A. Tel: , Fax: Abstrat: A tehnique to suress otial nonlinearities is demonstrated using adative otial domain ost distortion. The onet, rooted in eletrial domain linearization, mitigates otial nonlinearities by generating sidebands that are equal but oosite in hase from the unwanted omonents. We model and exerimentally demonstrate > db extintion in four wave mixing by an adative hase ontroller and omuter feedbak loo. 5 Otial Soiety of Ameria OCIS odes: (19.438) Nonlinear otis, four-wave mixing; (6.437) Nonlinear otis, fibers. Referenes and Links 1. M. Nazarathy, J. Berger, J. Ley, M. Levi, and Y. Kagan, Progress in externally modulated AM CATV transmission systems, J. Lightwave Tehnol. 11, 8-15, (1993).. R. Sadhwani, B. Jalali, Adative CMOS redistortion linearizer for fiber-oti links, J. Lightwave Tehnol. 1, , (3). 3. J. Basak, R. Sadhwani, B. Jalali, WDM ilot tone tehnique for analogue otial links, Eletron. Lett. 39, , (3). 4. R. H. Stolen and J. E. Bjorkholm, Parametri amlifiation and frequeny onversion in otial fibers, J. Quantum Eletron. 18, 16-17, (198). 5. H. Taga, Long distane transmission exeriments using WDM tehnology, J. Lightwave Tehnol. 14, , (1996). 6. Forghieri, F. Tkah, R.W., Chrayvy, A.R., WDM systems with unequally saed hannels, J. Lightwave Tehnol. 13, , (1995). 7. Forghieri, F., Tkah, R.W. Chralyvy, A.R., Maruse, D., Redution of four-wave mixing rosstalk in WDM systems using unequally saed hannels, Photon. Tehnol. Lett. 6, , (1994). 8. M. W. Maeda, W. B. Sessa, W. I. Way, A. Yi-Yan, L. Curtis, R. Sier, and R. I. Laming, The effet of four-wave mixing in fibers on otial frequeny-division multilexed systems, J. Lightwave Tehnol. 8, , (199). 9. G. P. Agrawal, Nonlinear Fiber Otis (Aademi, San Diego, Calif., 1989). 1. H. Takahashi and K. Inoue, Canellation of four-wave mixing by use of hase shift in disersive fiber inserted into a zero-disersion transmission line, Ot. Lett., 86-86, (1995). 11. M. E. Mahri, F. S. Yang, M.-C. Ho, and L. G. Kazovsky, High-nonlinearity fiber otial arametri amlifier with eriodi disersion omensation, J. Lightwave Tehnol. 17, 1-15, (1999). 1. J. Kim, O. Boyraz, J. H. Lim, M. N. Islam, Gain enhanement in asaded fiber arametri amlifier with quasi-hase mathing: theory and exeriment, J. Lightwave Tehnol. 19, 47-51, (1). 1. Introdution Eletroni re- and ost- distortion tehniques have roven to be a highly versatile tehnique for suressing intermodulation distortion in RF and otial ommuniation links [1-3]. These tehniques rely on intentional generation of intermodulation tones that are equal in amlitude and oosite in hase to those rodued by the nonlinear devie or the transmission medium. Both these funtions, i.e. generation and shaing of intermodulation tones, are erformed in # $15. US Reeived 16 May 5; revised 8 July 5; aeted 1 July 5 (C) 5 OSA 5 July 5 / Vol. 13, No. 15 / OPTICS EXPRESS 5711

2 the RF domain. Adative digital ontrol of the generated intermodulation tones is highly desired in order to ahieve large distortion suression and stable oeration. Although eletroni linearization tehniques have been advantageous for narrowband aliations, erforming linearization in the otial-domain would offer muh greater bandwidth. In this aer, we roose and demonstrate an otial-domain adative ost distortion linearization of an otial link. As a roof of onet, the system is used to adatively suress Four Wave Mixing (FWM) omonents rodued by the third order nonlinearity of otial fiber. The adative ontrol is the key in roduing a robust solution where a high level of FWM suression is ahieved for a wide range of otial owers and fiber lengths.. Aroah The onet of an adative otial ost distortion linearizer is illustrated in Fig. 1(a). Consider an n-hannel WDM transmission link imaired by FWM. An arbitrary air of hannels loated at λ 1 and λ generates nonlinear sidebands at λ f1 and λ f. These unwanted omonents will ause interferene and rosstalk between neighboring WDM hannels. FWM in fiber has been studied extensively and its effet on ommuniation systems is well known [4-8]. In order to redue the imairment, an adative otial ost distortion linearizer, desribed here, attenuates the sidebands in a nonlinear medium by reating FWM omonents that are similar, but oosite in hase, to the original. The tehnique an be desribed in two stages. First, a reise and adative hase shift is indued onto the FWM sidebands at λ f1 and λ f. Seond, a nonlinear fiber generates a new air of FWM omonents at λ f1 and λ f, 18 degrees out of hase from the old waves. The sidebands will exeriene destrutive interferene at the outut. As a result, the FWM omonents from the link are suressed, mitigating rosstalk in neighboring WDM hannels. By monitoring the residual FWM distortion, an adative hase ontroller (e.g. satial light modulator) is adjusted to maintain maximum suression. (a) λ1 λ λf λ1 λ λf λ1 λ λf λ1 λ Nonlinear Inut Linearized Outut (b) FWM Generation Adative Phase Shift Deonstrutive Interferene FWM Suression LD nm LD nm EDFA 3km DSF1 EDFA SLM Driver 3km DSF OSA PC Feedbak Loo Fig. 1. (a) Basi onet of the Otial-domain Post Distortion Linearizer. (b) Exerimental setu. LD: laser diode. SLM: satial light modulator. DSF: disersion shifted fiber. EDFA: erbium doed fiber amlifier. PC: ersonal omuter. # $15. US Reeived 16 May 5; revised 8 July 5; aeted 1 July 5 (C) 5 OSA 5 July 5 / Vol. 13, No. 15 / OPTICS EXPRESS 571

3 The roess of FWM indued rosstalk anellation and enhanement of arametri gain in a fiber has been reviously roosed and demonstrated [4], [9-1]. Here, we resent a detailed desrition and method of an adative otial domain ost-distortion linearization derived from fundamental equations governing FWM interations. Our model will rovide a hysial insight into the key arameters, e.g. hannel owers and nonlinear fiber lengths, whih will affet the erformane of the anellation. For generality, we will begin with a desrition of the four ouled wave equations governing the amlitude evolution in a nondegenerate FWM roess [9]: da s, iδkz = iγ A + s, Ak As, + A1 A A, se dz k s, (1a) da 1, iδkz = iγ A + 1, Ak A1, + A As Ae.,1 dz k 1, (1b) We will assume a degenerate four-wave mixing roess in a low-loss medium involving three wavelength omonents without um deletion. The amlitude evolution of all three waves redues to a set of ouled-wave equations [4]: da s, dz i φ o [( ks, + P ) As, + γp e A, ] = i γ (a) s da dz = i γ P A (b) where, k s, is the roagation onstants of signal and onjugate, γ is the nonlinear fator of the fiber, P is the eak um ower, and φ o is the initial hase of the um wave. From hereafter, we will denote the signal wave as the unwanted nonlinear omonent we aim to suress. Under a degenerate FWM ase, the signal, um, and onjugate waves are ouled through Eq. (). Alying this notation to Fig. 1, the signal at λ f1 is reated by a um at λ 1 and onjugate at λ, and similarly, the signal λ f is reated by a um at λ and onjugate at λ 1. The exat analytial solution to Eq. () an be exressed in matrix form [1]: A ( z) A e i φ + i ϕ s s e s = i φ i ϕ ( z) e b a A e a b A (3) where κ a = osh( gz) + i sinh( gz) g (4a) γp i φ b = i e sinh( gz) g (4b) κ = Δk + γp (4) ( P ) κ g = γ. (4d) φ is the aumulated nonlinear hase of the um wave and A,s, and φ,s, are the initial field amlitudes and hases of a um, signal, and onjugate, resetively. The matrix elements a and b are omlex numbers that determine the hanges in amlitude and hase of signal and onjugate waves. When λ < λ, k is always ositive and onsequently g is always urely imaginary. Therefore, the hyerboli funtions in (3) an be onverted to # $15. US Reeived 16 May 5; revised 8 July 5; aeted 1 July 5 (C) 5 OSA 5 July 5 / Vol. 13, No. 15 / OPTICS EXPRESS 5713

4 orresonding trigonometri funtions. On the other hand, if λ > λ, g will always be urely imaginary for P < k /4γ. In either ase, the resulting intensity of the nonlinear signal, as a funtion the interation length z and inut field arameters, is found to be [11,1]: ( ϕ + ϕ + φ φ ) = a As + b A + a b As A os s As ( z) a b (5a) κ φ ( ) a = tan 1 tan g z g (5b) π φ = ϕ +. b (5) As observed by the interferene Eq. (5a), maximum destrutive interferene of the signal field is ahieved when the magnitudes of the first two terms are equal and the argument of the osine is an odd multile of π. Written in terms of an otimal interation length, z ot = L, and the initial hase values, φ, φs, φ, two neessary and suffiient onditions for maximum suression are: L = 1/ 1 A γ A arsin κ + 1 (6) g g A g s ϕ + ϕ ϕ + ξ = (n + 1) π n,1, (7) s = where ξ is initial hase mismath. Eq. (6) determines the otimal nonlinear fiber length from the owers of all three waves. Eq. (7) seifies their required hase relationshi at the inut of the nonlinear fiber. When these arameters are simultaneously met, the third-order nonlinearity of the otial link will be omletely suressed. The magnitude of FWM suression deends on the degree to whih the above onditions are satisfied. If the distortion in the link is deterministi, inserting a fixed length of fiber will be adequate to reate a fixed hase shift and anel the FWM omonents. Unfortunately, due to nondeterministi nature of the inut hase, the aroah suffers from the inability to maintain a high degree of linearization. A revious exeriment using a fixed delay line ahieved only 6 db of suression [1]. In the resene of random hase variations of WDM hannels, from add/dro modules or environmental fators, Eq. (5) and (6) annot be simultaneously satisfied using a stati sheme. As a result, an adative aroah is highly desired for ahieving an aurate and dynami linearization of FWM. Our simulations demonstrate the need for an adative hase ontrol in a FWM imaired fiber transmission link. Equation (5a) was used to determine the FWM ower as a funtion of average WDM hannel ower P ave (equal to A, A ) and nonlinear fiber length L. Fig. (a) illustrates the onventional aroah where a fixed length of fiber with ertain disersion and nonlinearity harateristis is inserted in the link. The observed attenuation eak shows the oint of omlete destrutive interferene, i.e. when Eq. (5) and (6) are satisfied. Sine the onstant hase shift is unable to adat to variations of the inut hase values, large suression is only ahieved for a seifi inut hase, P ave, and L. A far more effetive aroah is the adative ase, shown in Fig. (b). Due to a feedbak loo, the FWM attenuation is insensitive to inut hase flutuations. Maximum linearization is ossible for arbitrary ower levels or fiber lengths. A dynami hase ontroller and roer hoie of nonlinear fiber length ensure Eq. (5) and (6) will be simultaneously satisfied. Our simulation demonstrates FWM suression > db whih agrees with the exerimental results (as shown in Fig. 3()). # $15. US Reeived 16 May 5; revised 8 July 5; aeted 1 July 5 (C) 5 OSA 5 July 5 / Vol. 13, No. 15 / OPTICS EXPRESS 5714

5 (a) FWM Suression [db] Ave. Channel Power Pave [mw] Nonlinear Fiber Length L [km] (b) FWM Suression [db] Ave. Channel Power Pave [mw] Nonlinear Fiber Length L [km] Fig.. Simulation of FWM suression for (a) stati and (b) adative hase ontrol tehniques. Red oloring indiates suression > db. An adative hase adjustment an rovide reision and agility to hase variations at many wavelengths. # $15. US Reeived 16 May 5; revised 8 July 5; aeted 1 July 5 (C) 5 OSA 5 July 5 / Vol. 13, No. 15 / OPTICS EXPRESS 5715

6 3. Exeriment We exerimentally quantify the suression of FWM omonents through otial ostdistortion linearization by using a satial light modulator (SLM). Figure 1 shows the exerimental setu. Two laser diodes at nm and nm, orresonding to λ 1 and λ resetively, are amlified by an L-Band EDFA. We emulate a FWM imaired transmission link by using a 3.6 km disersion shifted fiber (DSF1) with λ = nm, GVD sloe.5 s/km/nm, and nonlinear arameter γ =.1 W -1 /km. The length of this fiber is hosen without loss of generality. The indued nonlinear rosstalk omonents are loated at λ f1 ( nm) and λ f ( nm). These nonlinearities will be suressed by the following otial ost-distortion setion whih onsists of an SLM followed by a fixed length of DSF. In order to demultilex the wavelengths, we inororate a 4-f grating (1 lines/mm) and lens ( m foal length) onfiguration. The setral resolution is.65 nm. A liquid rystal amlitude/hase satial light modulator is laed at the foal lane. The SLM onsists of 18 ixels whih are indeendently ontrolled by a omuter oerated eletroni driver, to gray sale auray. The finite setral resolution used with our SLM resulted in residual attenuation dis between eah hannel. An L-band EDFA is laed before the 4-f onfiguration to omensate for the system insertion loss of 6. db. Next, a seond DSF fiber (DSF) is used to erform the interferene between the new and old FWM waves, made out-of-hase by the SLM. Without loss of generality, DSF is idential to DSF1. The average inut ower of λ1 and λ rior to the ost distortion linearizer is 3. mw. Finally, an otial setrum analyzer (OSA) measures FWM suression. This data is feedbak to a PC and used to erform a least squares routine that will determine the roer hase shifts used by the SLM to maximize suression. Figure 3(a) illustrates the inut setrum before the otial ost distortion linearizer. An initial 31 db ower differene between the hannels (λ 1, λ ) and the nonlinearities (λ f1, λ f ) is measured. Assuming degenerate FWM, we define λ f1 to be the signal omonent, while λ 1 and λ to be the um and onjugate waves, resetively. Likewise, λ and λ 1 are the um and onjugate, resetively, for λ f. Figure 3(b) demonstrates the exerimental result after FWM is linearized. The maximum attenuation for λ f1 and λ f is.74 db and db, resetively. In this figure, the hase values were hosen suh that otimal suression was seleted for λ f1. Figure 3() demonstrates a lose agreement between our alulations and exerimental data. The redited and measured FWM ower is lotted as a funtion of relative hase between the three waves (as defined by Eq. 5). The advantage of our adative sheme is learly observed near the extreme suression hase where the sensitivity is measured to be 1 db er.5 radians. 4. Disussion By monitoring the FWM degradation and ontrolling the hase for individual hannels, FWM suression an our over many wavelengths. Suh a sheme reresents a signifiant imrovement over a fixed delay line that rovides suression at a single hannel [1]. In the adative sheme, a omuter feedbak an monitor and ontrol the hase of individual hannels to reate a hase ma that will globally minimize rosstalk. Sine a hase solution for a single hannel involves a total of three hannels, as desribed by Eq. 7, a global suression an be reahed by fixing two hannels and varying the hase of the third. One ossible algorithm whih ould be imlemented suresses the FWM at hannel i by adjusting the hase at hannel i+. When erformed sequentially over n hannels, the hase ma for eah hannel is individually otimized until all hannels ahieve FWM suression. An imortant onsideration in WDM links is how to measure the FWM amlitude used by the feedbak algorithm. In a standard WDM system, FWM omonents fall at the loation of hannels, and thus annot be measured diretly. However, sine nonlinear omonents and hannels share the same wavelength, inline erformane measures (e.g. BER or otial Q # $15. US Reeived 16 May 5; revised 8 July 5; aeted 1 July 5 (C) 5 OSA 5 July 5 / Vol. 13, No. 15 / OPTICS EXPRESS 5716

7 1 Before PPDL After PPDL 1 (a) λ1 λ (b) λ1 λ Power [dbm] -1 - λf λf Wavelength [nm] Wavelength [nm] FWM Power [dbm] () Relative Phase [rad] Fig. 3. Otial setrum measured (a) before and (b) after the Otial-domain Post Distortion Linearizer shows > db suression. () FWM ower vs. relative inut hase illustrates the sensitivity of the nonlinear attenuation to variations in hase. value) may be used to reflet the magnitude of FWM omonents. This information an dynamially feed bak into a global linearization algorithm. When data is imressed onto the otial waves the effetiveness of this tehnique will deend on the modulation format. In ure on-off keying, the FWM imairment will be onstant over many bit eriods and may be mitigated by a feedbak loo. However, in ommuniation systems using random hase modulation, suh as DPSK, a fast feedbak loo on the order of a bit eriod would be required for dynami ost omensation. PMD will also affet the hase mathing ondition, and hene, the effiieny of FWM loally. Sine the FWM suression ours at the reeiver, the feedbak algorithm an adat to these hanges, rovided that the time eriod of the flutuations are relatively slow. By using the feedbak algorithm, any environmental variations an be omensated. The amlified sontaneous emission (ASE) introdued by # $15. US Reeived 16 May 5; revised 8 July 5; aeted 1 July 5 (C) 5 OSA 5 July 5 / Vol. 13, No. 15 / OPTICS EXPRESS 5717

8 EDFAs in a transmission system will affet the overall dynami range of this tehnique. The final omensation will be limited by an ASE noise floor, below whih this tehnique will not be able to suress FWM. A more detailed study is neessary to investigate the effetiveness of this aroah in a ratial transmission system. One hallenge with this tehnique is to mitigate all FWM roduts whih oexist at a single hannel. Sine eah FWM rodut has a unique hase ma, a global hase solution may not suress all the FWM roduts at a single hannel. One solution is to mitigate only the most dominant FWM ontributions. In a WDM system, this orresonds to FWM omonents generated by adjaent hannels (first-order). The nonlinear effiienies involving non-adjaent (higher-order) hannels redue as their wavelength searation inreases. Deending on the wavelength saing and hannel ower, an otimum hase solution will minimize FWM indued ross talk for all WDM wavelengths. 5. Conlusion In summary, we have introdued an adative otial domain ost distortion linearization tehnique. The onet has its root in eletrial domain linearization tehniques [1-3], but offers muh greater erformane in terms of bandwidth. As a roof of onet, we demonstrate the suression of four-wave mixing in the ontext of a WDM link. The method utilizes an adative hase ontroller and otial ost-distortion to destrutively interfere FWM omonents. Comared to reviously demonstrated FWM anellation shemes [1] the new aroah works for arbitrary fiber lengths or signal ower levels. We have theoretially shown and exerimentally verified > db extintion of FWM using an SLM, 3km of DSF fiber, and adative feedbak from an OSA. Aknowledgments This work is suorted by DARPA. The authors are grateful to Dr. Jagdee Shah for his suort of this work. # $15. US Reeived 16 May 5; revised 8 July 5; aeted 1 July 5 (C) 5 OSA 5 July 5 / Vol. 13, No. 15 / OPTICS EXPRESS 5718