Transients control in Raman fiber amplifiers

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1 Transients control in Raman fiber amplifiers Marcio Freitas a b, Sidney Givii Jr ab, Jackson Klein a, Luiz C. Calmon b, Ailson R. de Almeida b a Optiwave Corporation, 7 Capella Cour Ottawa, Ontario, K2E 71, Canada b Dep. of Electrical Enineerin, Univ. Federal do Espírito Santo, Caixa Postal , Vitória, ES, Brazil, CEP ABSTRACT Raman fiber amplifiers (RFA) are bein used in optical transmission communication systems in the recent years due to their advantaes in comparison to erbium-doped fiber amplifiers (EDFA). Recently the analysis of RFAs dynamic response and transients control has become important in order to predict the system response to add/drop of channels or cable cuts in optical systems, and avoid impairments caused by the power transients. Fast sinal power transients in the survivin channels are caused by the cross-ain saturation ect in RFA and the slope of the ain saturation characteristics determines the steady-state survivin channel power excursion. We are presentin the modelin and analysis of power transients and its control usin a pump control method for a sinle and multi-pump scheme. Keywords: Raman fiber amplifier, Power transients 1. INTRODUCTION For the past few years, research on Raman fiber amplifiers has been boosted due to the advantaes they have over erbium-doped fiber amplifiers, such as the existence of Raman ain in every fiber, the availability of ain over the entire transparency reion of the fiber, the fact that the ain spectrum of Raman amplifiers may be tailored by adjustin the pump wavelenth confiuration, improved noise fiure, and reduced nonlinear penalty [1]. One of the biest concerns in usin rare-earth fiber amplifiers for optical WDM networkin is that networks become vulnerable to transient interchannel cross-ain modulation while underoin dynamic confiurations [2, 3]. Since optical amplifiers in eneral, and RFAs in particular, saturate on a total-power basis, addition and/or removal of channels in a WDM network may disturb channels at other wavelenths that share the same path, causin power transients in the survivin channels that could result in serious service impairment [2]. For this reason, a control scheme that reduces power transients and protects survivin channels is necessary. Several papers are particularly focused on analyzin the dynamic behavior of RFAs and the power transients in survivin channels [4-6]. Simulations have demonstrated consistency with experimental results, and add/drop of channels or cable cuts have been studied for co-pumped and counter-pumped confiurations. The observed differences between the steady-state ain and the ain in the survivin channels after some of the channels are dropped can cause serious impairmen and therefore must be predicted in order to implement control systems that avoid such phenomena. The objective of this article is to develop a procedure to obtain and tune controllers independently of specific systems characteristics. Section 2 presents the numerical modelin for simulation of dynamic events in RFAs. Section 3 presents the structure of an auto-tunin scheme for PD controllers by usin enetic alorithms. Section 4 presents simulation results for cases wherein one and two counter-directionally pumps are used. 2. NUMERICAL MODEL The numerical model used to describe the dynamic behavior of a RFA is based on the one derived in [6]. The physical ects taken into account in this model are: - Pump-to-pump, sinal-to-sinal, and pump-to-sinal Raman interactions; 424 Photonics North 2004: Photonic Applications in Telecommunications, Sensors, Software, and Lasers, edited by J. Armitae, R. Lessard, G. Lampropoulos, Proc. of SPIE Vol. 557 (SPIE, Bellinham, WA, 2004) /04/$15 doi: /

2 - Spontaneous Raman emission and its temperature dependency; - Stimulated Raman scatterin; - Pump depletions due to Raman enery transfer; - Hih-order Stokes eneration; - Multiple Rayleih backscatterin; - Fiber loss dependent on the wavelenth. When all these ects are considered, the propaation equations describin the forward and backward power evolutions are written in the followin form: P ( z, ) z 1 V () P ( z, ) t = P h P 2h () P ( z, ) J () P ( z, ) D ( z, ) < ( z, ) P r( ) [ P ( z, ) + P ( z, )] ( ) r [ ( ) + ( )] + ( P z, ) P z, 1 exp h Q < > A K r K ( ) ( z, ) ZKHUH ζ are the wave frequencies [Hz], P + ( z,) ( z,) A A > r [ P ( z, ) + P ( z, )] ( ) h( ) A 1 + exp P LV WKH EDFNZDUG SRZHU RI VLJQDO SPS DW IUHTHQF\ >:@ () 1 kt 1 1 kt (1) LVWKHIRUZDUGSRZHURIVLJQDOSPSDWIUHTHQF\ >:@ V is the frequency-dependent roup velocity, α LVWKHILEHUDWWHQDWLRQ>1P@γ(ν) is the Rayleih backscatterin coicient [N/m], r (ν-ζ) is the Raman JDLQFRHIILFLHQWIRUIUHTHQF\GLIIHUHQFH -ζ) [m/w], A is ective area [m 2 ], K is polarization fafwru LVWKH frequency interval [Hz], h is the Plank s constan k is the Boltzman s constan and T the absolute temperature of the fiber [K]. For the solution of (1), the steady-state solution is found throuh the application of the fourth-order Rune-Kutta. This first result consolidates the lonitudinal distribution of all individual powers (pumps, sinals, ASE waves) alon the fiber. Then, this solution is directly interated, [7] and the time evolution of pumps, sinals, and ASE waves is determined. In order to uarantee that the solution in time domain does not present undesirable oscillations, the bin widths in spach ]DQGWLPH WPVWEHFKRVHQFDUHIOO\7KHVWDEOHVROWLRQKDVEHHQREWDLQHG>@ZKHQWKHWLPHELQ WLVHTDOWRRUVPDOOHUWKDQWKHSURSDJDWLRQWLPHWKURJKWKHVSDFHELQLH. The Raman ain coicients used in this work are calculated based on the normalized ain profile shown in Fi. 1. As shown in [10] and [11] the normalized profiles are very similar even for different fibers such as standard sinle-mode fibers (SMF), dispersion-shift fibers (DSF), and dispersion-compensation fiber (DCF). The sliht differences can be nelected without losin accuracy. Therefore, this normalized Raman ain profile is considered the same for all fibers used here and the Raman ain coicients are calculated in accordance with: r () v G () v r rnor v v pump = (2) ref Where Gr is the Raman ain peak for the reference pump frequency, ref coicien see Fi. 1, and v pump is pump frequency. t z V v. () v 1 rnor is the normalized Raman ain Proc. of SPIE Vol

3 Normalized Raman Gain Coeficient [m/w] Frequency Shift [THz] Fiure 1 - Normalized Raman Gain Coicient for silica fiber 3. CONTROLLER TUNING As described in the numerical model section, the numerical solvin of the equation (1) is carried out in two steps: the first for the steady-state and the second for the time interation. Once the first step is complete, the second one (where the control loop is performed) can be rewritten as: (3) p = Ap + Bu where p is the power for each sinal, A is related to the steady-state power distribution, B is the control matrix, and u is the new input on time for each channel bein propaated in the fiber. Assumin that a PID controller does not ive a satisfactory result [2], and since the only inputs that can be controlled are the pumps, the feedback-loop may be closed by usin: p = p K ( p p ) + K p ) (4) pump pump ( P sur 0 D sur where p pump is the pump channels, p sur is the power of the survivin channel chosen at the time t considered, p 0 is the power of the survivin channel at steady-state, and K D and K P are the ains of the proportional and differential errors used in the feedback control loop. If we restate the problem above, the requirement is to find the coicient matrices K D and K P in order to minimize the transient for the survivin channels in eneral and, specifically, for the survivin channel chosen to monitor the control stratey. Karásek and Menif [2], proposed a procedure based on the Zieler-Nichols method [8] to solve this problem. However, two other problems arise from the solution they proposed. Firstly, it is necessary to have a complete, in-depth knowlede of the characteristics of the system to be controlled. Secondly, it appears to work just for one pump. Since most current systems work with multiple pumps, this last problem becomes critical. To address these stated issues, we used enetic alorithms to obtain the ain matrices K D and K P. The followin two objectives are stated for desin []: - Minimize the maximum overshoot of the output: f1 max psur p 0 = (5) t 426 Proc. of SPIE Vol. 557

4 ( p p p sur 0 ) 2% - Minimize the settlin time of the output: ( 0 ): f 2 = t s (6) These two criteria are used to find the fitness of each individual in the population. Each one of the functions above were transformed and normalized, because we are lookin for a minimum, i.e., we want the values of f 1 and f 2 to o towards zero. The fitness function then becomes []: ( r w f () x ) 2 f ( x) = i i i (7) r i= 1 i Where r i is the maximum value allowed for each function and w i is a weiht function. Clearly, in our case, the maximum fitness for an individual will be 2. In the next section, usin some numerical simulations that utilize the described stratey, we will show that the ain matrices can be easily found without any a priori analysis of the problem (other than the limits of each coicien which are easily distinuishable). 4.1 Power Transients in RFAs 4. SIMULATION RESULTS AND CONCLUSIONS Here, the power transients are analyzed in Raman amplifiers considerin three pump confiurations and add/drop of channels in a 16 channels-wdm system usin optical fibers DSF and DCF as Raman ain media. The eneral schematic of the system simulated is shown in the fiure below. T1 Optical Fiber T14 M U T15 T16 Pump Pump Fiure 2 Raman amplifier system schematic The attenuation and roup delay of the fibers used in the simulation are showed at Fi. 3. The fiber lenth for the RFAs are 50 km for the DSF, and 10 km for the DCF. The pump in both RFAs was fixed at 1450nm and its total power was 800 mw for the DSF and 200mW for the DCF, for the counter, co-pumped and bi-directional pumped schemes. In the bi-directional pump scheme the power is split at half for each pump laser. Proc. of SPIE Vol

5 DCF DSF DCF DSF Attenuation [db/km] Group delay [1e6 ps/km] Wavelenth [nm] Wavelenth [nm] (a) (b) Fiure 3 (a) Attenuation and (b) roup delay for the fibers used in the simulations. The system simulated has 16 channels occupyin a bandwidth of 12nm ranin from 1544 nm to 1556 nm and channel spacin equals to nm, see Fi. 5(b). Each input sinal launches -3dBm optical power into the fiber, what leads the amplifier to operate in a saturation reime. The saturation characteristics of each RFA were analyzed varyin the input sinal power per channel from 30 dbm to 1 dbm and usin the CW RFA model to find the ain for each sinal input power. Fi. 4 shows the ain results found for DSF and DCF fibers for the sinal at 155 nm. It is possible to see that the different pump schemes do not cause any lare difference in the RFA ain for the DCF fiber and all pump schemes have practically the same ain compression. However, differences are quite considerable when the RFAs usin the DSF fiber reach the saturation. In this case the copumped has the larest ain compression and the bi-directional one has an intermediate compression. In eneral the DSF-RFA presents a stroner saturation than the DCF-RFA that could be explained by the hiher pump power of the DSF-RFA [13] Gain [db] DSF counter-pumped DSF copumped DSF bidirectional DCF counter-pumped DCF copumped DCF bidirectional Input Sinal Power / channel [dbm] Fiure 4 Gain as function of the input sinal power Some of the channels in the system are 100% square wave modulated to simulate add/drop of channels. Three different patterns were considered here. In the first one, we dropped and then added 2 sinals (1544nm and 1556 nm). In the second one, the procedure is repeated with 4 sinals (1544 nm, nm, nm and 1556 nm). Finally, in the 428 Proc. of SPIE Vol. 557

6 third one 8 sinals (1544 nm, nm, nm, nm, , , nm and 1556 nm) are added/dropped. The sinals are always dropped at 1.5 ms and added at 2.5 ms. Fi. 5(a) shows the input modulated sinal of the channel at 1544 nm Sinal input power [mw] Power [dbm] Wavelenth [nm] (a) (b) Fiure 5 (a) Modulated sinal at 1544 nm to represent the add-drop of channels. (b) Channels distribution. Before doin the simulations to study the power transients in the RFAs, the output power distribution of this WDM system without the add-drop of channels is found. Fi. 6 shows the output powers; from these values the power excursion is calculated to verify the power evolution of the sinals after the add-drop of channels. 8 Output Sinal Power [dbm] Counter-DSF 2 Co-DSF Bi-DSF 1 Counter-DCF Co-DCF Bi-DCF Wavelenth [nm] A. DCF-RFA Fiure 6 Output sinal power of the 16 channels for the RFAs before the add-drop of channels. Fiure 7 shows the power excursions on a survivin channel at 155 nm for the RFA counter-pumped when 2, 4 and 8 channels are added-dropped. Proc. of SPIE Vol

7 Power excursion [db] Fiure 7 Output-survivin sinal at 155 nm for a DCF counter-pumped. The leadin-ede (drop of channels) in the output sinal overshoots and then reaches a new steady-state condition with approximately 0. db hiher than the initial condition. In the trailin-ede, (add of channels) the output sinal undershoots and then the sinal reaches the steady-state condition aain. The transients in leadin-ede are caused by the lower saturated ain that the survivin channels experience when some channels are dropped. The stroner power in the front sinal leads to the depletion of the pump, and the remainin sinal does not experience the same ain as in the leadin ede due the lower pump power. In the case of the trailin-ede, after the addition of the channels the pump is more depleted, and because it propaates backward, the sinal et a lower ain than the steady-state saturated ain. Unlike the counter-pumped RFA, in the co-pumped confiuration the overshoot and undershoot were not noticed, as showed in Fi. 8. Even when the number of add/drop channels was increased, the presence of them was not clearly noticed. 1.2 Power excursion [db] Fiure 8 Output-survivin sinal at 155 nm for a DCF copumped. The transients occur faster in the co-pumped RFA due to the fact that the pump and survivin sinals are propaatin in the same direction with approximately the same roup-velocities. 430 Proc. of SPIE Vol. 557

8 Finally, the bi-directional pumpin scheme seems to have an intermediate response between the co and counter pumped ones (Fi. ). The overshoot and undershoot are lower than the counter-pumped, but larer than the copumped scheme. Reardin the speed of the transients, we noticed the same pattern: they are faster than the counter-pumped, but not as fast as the copumped RFA. Power excursion [db] Fiure Output-survivin sinal at 155 nm for a DCF bidirectional-pumped. B. DSF-RFA Fi. 10 shows the power excursions on survivin channels for the RFA counter-pumped. 1.2 Power excursion [db] Fiure 10 Output-survivin sinal at 155 nm for a DSF counter-pumped. The curves show the overshoot and undershoot like in the DCF counter-pumped, however, in the DSF case the transients are loner, which could be explained by larer lenth of fiber [6]. In the co-pumped RFA, Fi. 11, the transient ects present a behavior similar to the one found in the co-pumped DCF case; the transients are very fast and the steady-state condition is soon reached. The power excursion in the copumped RFA is larer than in the counterpumped case. This may be explained by the saturation curves, Fi. 4. The Proc. of SPIE Vol

9 copumped scheme has larer ain compression and when the channels are dropped it tends to have a larer increase in the ain Power excursion [db] Fiure 11 Output-survivin sinal at 155 nm for a DSF co-pumped. In the bi-directional pumped RFA, the responses Fi. 12, like in the DCF case, are located between the co and counter pumped cases. Power excursion [db] Fiure 12 Output-survivin sinal at 155 nm for a DSF bidirectional-pumped. 4.2 Transient Control in RFAs As demonstrated in the last section, one of the biest concerns in usin optical amplifiers for optical WDM networkin is that the networks become vulnerable to transient inter-channel cross-ain modulation while underoin dynamic confiurations. Since optical amplifiers in eneral, and RFAs in particular, saturate on a total-power basis, addition and/or removal of channels in a WDM network may disturb channels at other wavelenths that share the same path, causin power transients in the survivin channels that could result in serious service impairment. For this reason, a control scheme that reduces the power transients and protects the survivin channels is necessary. 432 Proc. of SPIE Vol. 557

10 The simulation cases presented here used 40 Km of a DSF fiber as ain medium, this fiber has characteristics similar to the used in last section. In [2], eiht sinals are propaated with one counter-directional pump. A controller PD with proportional ain, K P, equal to 10 and differential ain, K D, equal to 2.4x10-4 is defined. Usin the method based on enetic alorithm described in section 3, after just 15 enerations with 20 individuals, a PD controller with K P =17.74 and K D =4.83x10-4 is found within the limits: 0<K P <20 and 0<K D <10-3. Fi. 13 shows the results of this last controller when six sinals are dropped-added. It should be noticed that it has the same behavior observed in [2], but presents a much better peak and settlin time. Fiure 13 - Power fluctuation for the survivin channel and pump In the other simulation case, eleven sinals, ranin from 1520 nm to 1600 nm with power of 0 dbm/channel, are propaated with four counter directional pumps (141 nm, 1437nm, 1461, and 145 nm). In this case four controllers are used, one for each pump, and the parameters were found after 10 enerations with 20 individuals each. The power fluctuation for the survivin channel, compared to the case without the controller, is shown in Fi. 14. Fiure 14 - Power fluctuation for the survivin channel when four pumps are counter-propaated Proc. of SPIE Vol

11 In this case the results found are not so ood as the one presented at Fi. 13, but it could be improved by increasin the number of enerations and individuals in the optimization method. Nevertheless, in both simulations, it was observed better control results, usin this technique to find the control parameters, than the one used in [2]. For lare transients, this technique will help to minimize the impact of power transients in the system performance. REFERENCES [1] M. N. Islam, Raman Amplifiers for Telecommunications, J. of Selected Topics in Quantum Electronics, vol. 8, pp , [2] M. Karásek and M. Menif, Protection of survivin channels in pump-controlled ain-locked Raman fibre amplifier, Optics Communications, vol. 210, pp , [3]C. Dimopoulos, Study of dynamic phenomena in WDM optical fibre links and networks based on EDFAs, Doctoral thesis, Department of Electronic Systems Enineerin, University of Essex, [4] M. Menif, et. al., Cross-Gain Modulation in Raman Fiber Amplifier: Experimentation and Modelin, IEEE Photonics Technoloy Letters, vol. 13, no., pp , [5] M. Freitas, et. al., Dynamic Behavior in Raman Fiber Amplifiers, Simpósio Brasileiro de Telecomunicações, SBT 03, Rio de Janeiro, [6] M. Karásek and M. Menif, Channel Addition/Removal in Raman Fiber Amplifiers: Modelin and Experimentation, J. Lihtwave Technoloy, vol. 20, pp , 2002 [7] W. H. Press, et al., Numerical Recipes: The Art of Scientific Computin, 2 nd Edition, Cambride University Press, 12. [8] J. G. Zieler and N. B. Nichols, Trans. ASME, G, J. Dyn. Sys. Meas. Control 4 (142) 75. [] D. H. Kim, Tunin of PID controller of dead time process usin immune based on multiobjective, Proceedins of the 7 th IASTED International Conference ARTIFICIAL INTELLIGENCE AND SOFT COMPUTING, pp , [10] S. Namiki and Y. Emori. Ultrabroad-band Raman Amplifiers pumped and Gain equalized by Wavelenth-Division- Multiplexed hih-power lasers. J. of Selected Topics in Quantum Electronics, vol. 7, pp. 3-16, [11] Yuhon Kan. Calculations and Measurements of Raman Gain Coicients of Different Fiber Types. Master thesis presented at Faculty of the Virinia Polytechnic Institute and State University, [12] S. Givii, M. Freitas, J. Klein, A. R. de Almeida, and L. C. Calmon. Transient Control in RFAs for multi-pumpin environments by usin a multi-objective optimization approach. Proc. OFC [13] S. A. E. Lewis, S. V. Chernikov, and J. R. Taylor. Gain saturation in silica-fibre Raman amplifier. Electronics Letters, Vol. 35, pp , May Proc. of SPIE Vol. 557

Raman Amplification for Telecom Optical Networks. Dominique Bayart Alcatel Lucent Bell Labs France, Research Center of Villarceaux

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