JOURNAL OF LATEX CLASS FILES, VOL. 6, NO. 1, JANUARY 2007
1
Transient Link Control Technique Applied to Optical Hybrid Amplifier (EDFA + DFRA) Cascades ´ Barbara Dumas and Ricardo Olivares
Abstract—For the first time to our knowledge, power transient control in Hybrid Amplifier (HA) cascades is analyzed by means of numerical simulation. Four hybrid configurations are investigated, considering DFRAs in both backward and forward pumping schemes, preceding and ahead of an EDFA. The link control technique was applied to the best and the worst configurations in terms of power excursion. When 17 out of 20 channels are dropped/added, the steady state power excursions of the surviving channels were reduced from 4.21 dB and 6.25 dB to 0.01 dB and 0 dB, for a single HA under configurations “EDFA + backward DFRA” and “forward DFRA + EDFA”, respectively. When a cascade of 12 HAs (1800 km) is studied, the steady state output power excursions were mitigated from 8.66 dB to 0.07 dB and 0.60 dB, for the same hybrid configurations, respectively.
to our knowledge, we investigate by means of numerical simulation, the transient response in cascades of HAs and the application of the link control technique in order to mitigate the power excursions. In section II, the description of four hybrid configurations is presented and the transient response along cascades of HAs under each hybrid configuration is analyzed. In section III, the link control technique is described and the simulation parameters are set. In section IV, this technique is applied to the best and the worst hybrid configurations (lower and larger power excursions) considering one amplification stage and cascades of 12 HAs. Finally, in section V, the conclusions of this work are presented.
Index Terms—WRONs, EDFAs, DFRAs, HAs, transient response.
II. T RANSIENT R ESPONSE OF HA C ASCADES A. HA configurations
I. I NTRODUCTION
H
ybrid amplifiers, composed of Erbium Doped Fiber Amplifiers (EDFAs) and Distributed Fiber Raman Amplifiers (DFRAs), have emerged as a promising solution in extending the span and transmission capacity of Dense Wavelength Division Multiplexed (DWDM) optical networks that already utilize EDFAs. Combining both EDFAs and DFRAs advantages (high gain and good power conversion efficiency by EDFAs and more flexible gain bandwidth design, low noise and good capacity to mitigate fiber nonlinearities by DFRAs [1], [2], [3] and [4]) makes the HA an advantageous component and economically attractive approach to compensate the optic fiber losses and those introduced by the intermediate nodes. In DWDM optical networks based on wavelength routing, HAs may be exposed to transport a variable number of channels, either due to network dynamic reconfigurations or due to the increase of the network capacity. In this scenario, optical amplifiers can present output power transients which represent a major limitation to the performance of DWDM networks. If some channels are dropped, the power of the surviving channels may surpass the threshold above where the fiber nonlinearities cannot be neglected any longer. If channels are added, the power of the surviving ones diminishes and may fall below the receiver sensitivity. In both cases the performance of these networks can be significantly degraded. Power transients and their control have been extensively studied in EDFA and DFRA cascades [5] and [6]. Nevertheless, the transient response of HAs has been treated discreetly and in limited scenarios [7], [8] and [9]. Particularly, there are no reported works about the transient response along HA cascades accumulative effects and neither about their control. Hence, in this work, for the first time Manuscript received April 19, 2005; revised January 11, 2007. B. Dumas and R. Olivares are with the Electronic Engineering Department, Universidad T´ecnica Federico Santa Mar´ıa, Valpara´ıso, Chile (e-mail:
[email protected],
[email protected]).
In this paper four hybrid configurations are analyzed. For two of these configurations the EDFA is located on first place followed by the DFRA (“EDFA + DFRA”). The other two configurations invert the order of the amplifiers (“DFRA + EDFA”). For both combinations backward (b) and forward (f) pumping schemes DFRAs are considered, as shown in Fig. 1. The propagation of 20 WDM channels evenly spaced (1 nm) from 1545 nm to 1565 nm is considered with an input power of Ps,in = 0 dBm/ch for every configuration. In each hybrid configuration the EDFA compensates, as a post-amplifier, 100 km of Standard Single-Mode Fiber (SMF) power losses, which are estimated to be 20 dB. The EDFA consists of a 12 m long Erbium Doped Fiber (EDF) pumped with 40 mW of power at a wavelength of 980 nm. Thus, the EDFA input power reaches PEDF A,in = −20 dBm/ch. Otherwise, the DFRA is designed to compensate 50 km of SMF power losses, with two pumps located at 1455 nm and 1463 nm. When the backward pumping scheme is considered, pumps with power levels at 130 mW and 60 mW are used; alternatively, if the pumping scheme is reversed to the forward direction, pumps are set at 200 mW and 65 mW, respectively. The DFRA input PDF RA,in corresponds to the EDFA output for “EDFA + DFRA” configurations and PDF RA,in = Ps,in for “DFRA + EDFA” configurations. The theoretical model used for the EDFA in the time domain is presented in [10]. This model neglects the Amplified Spontaneous Emission (ASE) noise, because while working in high saturation levels this noise is negligible in relation with the signal power. The theoretical model used for the DFRA is presented in [11]. This model considers the effects of attenuation, Rayleigh scattering and stimulated Raman scattering (gain and depletion of channels and pumps). Anti-Stokes and Stokes spontaneous scatterings are not considered, since they are negligible with the channel spacing used in these simulations (1 nm) [6]. The propagation equation of this model describes the power variation of signals and pumps regarding position and time.
JOURNAL OF LATEX CLASS FILES, VOL. 6, NO. 1, JANUARY 2007
2
(a)
(b)
(a)
(c)
(d) Fig. 1. Hybrid amplifier configurations. (a) “EDFA + DFRAb ”, (b) “EDFA + DFRAf ”, (c) “DFRAb + EDFA” and (d) “DFRAf + EDFA”.
Both models are solved using numerical integration techniques. For the EDFA model the fourth order Runge-Kutta method is considered. For the DFRA model the finite difference method is applied and the relaxation method is used when considering the backward pump propagation. B. Transient response To analyze the transient response in cascades of HAs, a 1800 km long link, which losses are compensated by 12 HAs (150 km each) under the four presented hybrid configurations, is considered. Fig. 2 shows the transient response of channel 7 (λ7 = 1551 nm, one of the three surviving channels) for the even amplification stages, for the four configurations shown in Fig.1, considering the drop/add of channels. A total of 20 WDM channels are introduced at time t = 0 ms, of which 17 are removed (channels 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 19 and 20) at time t = 1 ms and then re-added at time t = 2 ms. In this figure each curve starts to rise at time t = 1 ms; we have used this time as a reference, ignoring the propagation
(b) Fig. 2. Power excursion of the surviving channel 7 along the HA cascades. (a) “EDFA + DFRAb,f ” configurations and (b) “DFRAb,f + EDFA” configurations.
delay estimated to be 250 µs trough 50 km of Raman fiber. In this way, the kth amplification stage curve has been advanced k ∗ 250 µs. That is 500 µs for the second amplification stage, 1000 µs for the fourth amplification stage, and so on. The results are shown in terms of power excursion, that is any power variation experimented by the surviving channels (in this case of channel 7) with respect to their steady state value before the perturbation. In each curve it is possible to identify two clearly distinct regions: an initial disturbance or overshoot (transient region) followed by a zone in which power excursions reach the new steady state (steady state region). It can be seen that power excursions of channel 7 increase for both the transient and the steady state regions until the sixth and the fourth amplification stages, respectively, from which power excursions decrease (overshoots and steady state values). After the 17 channels are re-added, the
JOURNAL OF LATEX CLASS FILES, VOL. 6, NO. 1, JANUARY 2007
output power is re-established to the value before the drop of channels, for every hybrid configuration (steady state power excursions reach 0 dB after t = 2 ms). This behavior is explained through the long response time of EDFAs and backward pumped DFRAs. In addition, the input power from the second HA corresponds to the surviving channels with the transient characteristic accumulated by the previous amplification stages. Therefore, immediately after the drop of channels, the HA provides the power gain stimulated by the 20 channels to the 3 surviving channels, those which, having a higher power than the achieved at steady state (because of the increased power gain introduced by the previous amplification stage), reach larger power excursions. The maximum power that this overshoot can achieve is related to the maximum gain that the amplifier can provide under the stimulation of the 20 channels at steady state. Backward DFRA pumping scheme configurations overshoot values went from 6.86 dB and 7.06 dB to 9.34 dB and 9.40 dB, between the second and the sixth amplification stages, for configurations “EDFA + DFRAb ” and “DFRAb + EDFA”, respectively. While overshoots in forward DFRA hybrid configurations reached 8.54 dB and 8.55 dB in the fourth amplification stage, for configurations “EDFA + DFRAf ” and “DFRAf + EDFA”, respectively. Otherwise, the steady state output power depends on the power gain provided by the amplifiers, which depends on the input power of the surviving channels and the amplifier saturation level. After the first HA, the input power of the surviving channels is being modified constantly by the transient effects introduced by the previous amplification stages. Besides, after the drop of channels the total input power decreases and, with it, the amplifier saturation level is reduced. However, as the overshoots start to appear, the total input power increases, resulting in higher saturation. Once these two parameters stabilize, the power excursions of the surviving channels reach the steady state. Steady state power excursions increase along the cascade from 6.76 dB and 7.00 dB to 8.66 dB, between the second and the sixth amplification stages and then they remain constant for configurations “EDFA + DFRAb ” and “DFRAb + EDFA”, respectively. For configurations “EDFA + DFRAf ” and “DFRAf + EDFA” power excursions go from 7.78 dB and 8.15 dB to 8.66 dB between the third and the sixth amplification stages, after which they remain constant. Forward DFRA pumping scheme configurations present larger power excursions than those with backward DFRA pumping scheme, because the power gain is higher at the beginning of link. Furthermore, they are larger when the EDFA is the second amplifier of the configuration, since this amplifier is more sensitive to load changes than the DFRA for both pumping schemes. For instance, configurations “EDFA + DFRAb ” and “DFRAf + EDFA” present the lowest and largest power excursions between the second and the fourth amplification stages.
3
Wavelength Routed Nodes (WRN), where channels can be added or dropped, as is shown in Fig. 3. A control channel is inserted in the transmission band, at wavelength λc , before the first amplification stage. The control channel is dropped after last amplifier to avoid unnecessary load on the network. The control channel power is continuously adjusted by means of a feedback control circuit, so that the total power (the sum of the power of all the transported channels, even if one or more channels are dropped) at the input of the first HA is kept constant. In this way, the load on all amplifiers of the link is kept relatively constant and power transients are mitigated. Fig. 3 shows the link control schematic in a cascade of 12 HAs. The control channel, which is generated by the Laser Diode (L.D.), is introduced to the link through the first Wavelength Select Coupler (WSC1 ) before the first HA of the cascade and subsequently it is removed through WSC2 after the last HA. To regulate the control channel input power, the control circuit takes as reference the total input power sensed through a Photo-Detector (P.D.). Isolators (ISO) are used between every amplification stage to avoid pumps transfer to the control circuit.
Fig. 3.
Link control module schematic in a cascade of 12 HAs.
To apply the link control technique a ProportionalIntegrative (PI) electronic control to determine the control channel input power Pcc (t) regarding time t is implemented according to the feedback loop in (1). dPcc (t) dR(t) kp = R(t) + kp τi (1) dt τi dt Where kp and τi represent the gain of the proportional and the integrative errors, respectively. R(t) corresponds to the error function regarding time t as defined in (2). R(t) = |PT (t = 0) − PT (t)| Where PT (t) =
∑
(2)
Pi (t)
i
III. L INK C ONTROL T ECHNIQUE The link control technique, originally designed to mitigate transient effects in EDFAs [12] and lately in DFRAs [6], is here applied to cascades of HAs. It is worth mentioning that the word “link” refers to a network segment between two
is the total input power, including the control channel as a function of time t. kp and τi were set considering a 4 µs feedback loop response time (typically associated to real electronic components) and the Ziegler Nichols method [13], resulting kp = 1 and τi = 1 · 10−6 .
JOURNAL OF LATEX CLASS FILES, VOL. 6, NO. 1, JANUARY 2007
Even though the integrative control ensures a steady state error equals to zero, it does not guarantee that the steady state power excursions will be null for the surviving channels. The power gain associated to a signal does not depend exclusively on the amplifier saturation level, but on its wavelength, on its input power and on the other channels wavelength and input power. For this reason, the control channel was chosen in a wavelength whereas the steady state power gain corresponds to the average power gain of all the transported channels, that is channel 11 (λc = λ11 = 1555 nm). IV. R ESULTS A. Transient control in a single HA stage Fig. 4 shows the total power excursion (variation) at the first HA output, with and without link control protection, for configurations “EDFA + DFRAb ” and “DFRAf + EDFA” (see the left scale).
4
presents positive power excursions for both hybrid configurations. It can be seen a 12.55 dB power excursion overshoot for the “EDFA + DFRAb ” configuration, while steady state power excursions reached approximately 12.50 dB for both hybrid configurations. Immediately after the drop of channels, the control circuit modifies the control channel input power to absorb the total input power variation. Then both the surviving channels and the control channel receive the available power gain left by the dropped channels. The control channel presents a transient characteristic according to the hybrid configuration (control channel overshoot shown in the zoom for “EDFA + DFRAb ” configuration). This behavior is reflected in the residual total power excursion described in the previous paragraph. Afterwards, when steady state is reached, the control channel has absorbed the total input power variation (associated to the 17/20 dropped channels) by increasing its steady state power from −20 dBm to −7.45 dBm, corresponding to a 12.55 dB power excursion. As shown in Fig. 4, power excursions of channel 11 are very close to this value (12.50 dB). The steady state results depend on each HA power gain profile, slightly different for both configurations. For this reason, the available power gain distribution among the surviving channels and the control channel will be different according to the configuration. The control channel for the “EDFA + DFRAb ” configuration is absorbing more power gain than the required to compensate the total input power variation. As a result, the steady state total power excursion is larger for this configuration. Finally, after the dropped channels are re-added, the control channel reduces the total power excursion transient and the initial steady state value (0 dB) is reached. In addition, the power excursion of surviving channels is presented with (see the right scale) and without (see the left scale) link control protection in Fig. 5. Moreover, the control channel is shown in this figure to better explain these results (see the left scale).
Fig. 4. Total power excursion with and without link control protection and control channel power excursion at the first HA output, for “EDFA + DFRAb ” and “DFRAf + EDFA” configurations.
Figure 4 shows that transient effects are mitigated for both hybrid configurations, especially for the “DFRAf + EDFA” configuration. Total power excursion undershoots are reduced from −0.50 dB and −3.44 dB to −0.06 dB and −0.09 dB for configurations “EDFA + DFRAb ” and “DFRAf + EDFA”, respectively. It can be seen that after this undershoot, the EDFA + DFRAb ” configuration presents a 0.18 dB total power excursion overshoot followed by a mitigated steady state total power excursion from −0.22 dB to 0.13 dB. Otherwise, for the “DFRAf + EDFA” configuration, the steady state total power excursion is reduced from −2.10 dB to −0.05 dB, immediately after the power undershoot. When the dropped channels are re-added, the total power excursion experiments 0.27 dB and 1.23 dB power overshoots and after 0.25 ms and 0.41 ms the initial steady state value (0 dB) is reached, for the “EDFA + DFRAb ” and “DFRAf + EDFA”, respectively. To explain the residual total power excursion, the control channel (λ11 -control channel) is also shown in Fig. 4 considering the right scale. After the drop of channels, this channel
Fig. 5. Power excursion of the surviving channels (λ7 and λ15 ) and the control channel (λ11 ), at the first HA output with and without link control protection for the “EDFA + DFRAb ” (top) and the “DFRAf + EDFA” (bottom) configurations.
Once applied the link control technique, the surviving
JOURNAL OF LATEX CLASS FILES, VOL. 6, NO. 1, JANUARY 2007
channels 7 and 15 (λ7 = 1551 nm and λ15 = 1559 nm) have considerably reduced its power excursions for both configurations. On the top of this figure results for the “EDFA + DFRAb ” configuration are shown. Immediately after the drop of channels, channels 7 and 15 present 0.04 dB and 0.01 dB residual power excursions, respectively. It also can be seen that steady state power excursions are mitigated from 4.21 dB and 3.41 dB to −0.04 dB and −0.06 dB for channels 7 and 15, respectively. Besides, on the bottom of this figure results for the “DFRAf + EDFA” configuration are presented. For this configuration, residual power excursions reached 0.08 dB and 0.04 dB and the steady state values went from 6.25 dB and 5.54 dB to 0 dB and −0.11 dB for channels 7 and 15, respectively. On one hand, the surviving channel residual power excursions can be explained through the control channel power variation, since its transient power dynamic depends on the HA response time. The control channel initial variation presented on the “EDFA + DFRAb ” configuration is reflected on smaller and slower power excursion overshoots for the surviving channels. A larger control channel initial variation causes a faster input power changes absorption, restricting the residual power excursions of the surviving channels. Moreover, these residual power excursions are slower compared to those of the “DFRAf + EDFA” configuration, since the HA response time is longer (walkoff). On the other hand, the steady state power excursions are explained through the amplifier power gain profile. Both configurations have a power gain profile whereas the longer wavelengths receive less power gain than the shorter ones. In addition, the power gain slope (power gain profile v/s wavelength) is higher for the “DFRAf + EDFA” configuration. The wavelength and the input power (set by the control circuit) of the control channel, the HA saturation level and the power gain profile will determine what proportion of the available power gain left by the dropped channels will be received by the control channel. For both configurations the spectral position and the input power of the control channel is the same, however the saturation level and the power gain profile is different. For instance, the “EDFA + DFRAb ” configuration is less saturated than the “DFRAf + EDFA” configuration, resulting a control channel steady state power excursion slightly larger (the control channel is absorbing more power gain than the required to compensate the total input power variation). For this reason, the power excursions of the surviving channels are negative. Besides, the power excursion of channel 7 is larger than that of channel 15, since the power gain profile slope is negative. Otherwise, for “DFRAf + EDFA” configuration, the power excursion of channel 7 is completely mitigated, but channel 15 presents a power excursion even larger than the “EDFA + DFRAb ” configuration surviving channels. This effect is explained through the higher power gain profile slope of the “DFRAf + EDFA” configuration. B. Power transient control in HA cascades The transient response is now analyzed along cascades of 12 HAs under the configurations “EDFA + DFRAb ” and “DFRAf + EDFA”, when the link control technique is applied. In Fig. 6 power excursions of channel 7 for the even amplification stages for both hybrid configurations are
5
shown. To better analyze, these results will be compared to those obtained on section II (without link control protection).
Fig. 6. Power excursion of channel 7 along cascades of 12 HAs with link control protection, for the “EDFA + DFRAb ” (top) and the “DFRAf + EDFA” (bottom) configurations.
It can be seen that when applying link control protection to cascades under the “EDFA + DFRAb ” configuration, the properties described on section II (top of Fig. 2(a)) remain, but in a much lower intensity. For instance, both the initial disturbances and the steady state regions can be identified on the top of Fig. 2(a), which are intensified along the cascade. Residual power excursions (peaks) went from 0.05 dB to 0.08 dB, while steady state power excursions went from −0.04 dB to 0.07 dB, between the second and the twelfth amplification stages. In the worst case, corresponding to the sixth amplification stage, the power excursion (peak) is reduced from 9.34 dB to 0.07 dB. While the maximum steady state power excursion (twelfth amplification stage) is decreased from 8.66 dB to 0.07 dB. Otherwise, when applying link control protection to cascades under the “DFRAf + EDFA” configuration, residual power excursions last until the fourth amplification stage (0.12 dB). Note that under the “DFRAf + EDFA” configuration without link control protection (bottom of Fig. 2(b)), power excursions do not present overshoots and residual power excursions are even higher than those under the “EDFA + DFRAb ” configuration. After the fourth amplification stage, power excursions become larger and faster along the cascade, since the DFRAf mitigates the residual power excursions. Steady state power excursions went from 0.04 dB to 0.60 dB, between the second and the twelfth amplification stages. In the worst case, corresponding to the twelfth amplification stage, the steady state power excursion is reduced from 8.66 dB to 0.60 dB. In contrast to the transient response analyzed for a single stage of hybrid amplification, along cascades of 12 HAs , the link control technique is more efficient for the “EDFA + DFRAb ” configuration than the “DFRAf + EDFA” configuration. Basically, because this configuration is more sensitive to changes in the number of the transported channels. Total power excursions do not remain constant at
JOURNAL OF LATEX CLASS FILES, VOL. 6, NO. 1, JANUARY 2007
each amplification stage, because power excursions of the surviving channels grow under any variation, causing higher total power excursions, and so on. V. C ONCLUSION The transient response of optical HAs has been analyzed under an extreme scenario of drop/add of channels. DFRAs in both backward and forward pumping schemes have been considered preceding and ahead of an EDFA. Forward DFRA hybrid configurations presented larger and faster power excursions, especially when DFRAf is the first amplifier of the configuration. These transient effects were accumulated when the HAs were cascaded. It was noted that cascades of amplifiers with longer response times, such as EDFAs, DFRAs and HAs (both last with backward DFRA pumping scheme), have shown transient responses where it is possible to identify an initial disturbance followed by a steady state condition. Immediately after the drop of channels, while the amplifiers are still providing the power gain stimulated by the 20 channels, the 3 surviving channels increase their power excursions generating overshoot disturbances. After the second amplifier, these channels will further increase their power excursions, because of the transient effects introduced by the previous amplification stages. The link control technique was described and applied to cascades of HAs under configurations “EDFA + DFRAb ” and “DFRAf + EDFA”. This technique allows the total power excursion to remain relatively constant along the cascade, by introducing a control channel to absorb any power variation in the cascade input. Results were analyzed in terms of the total power excursions (and the control channel power changes) after the first amplification stage and channel 7 power excursions along the cascade. Total power excursions also presented initial disturbances and steady state regions and both were mitigated for both hybrid configurations, especially for the “DFRAf + EDFA” configuration. The residual total power excursions were explained through the control channel power variation, since it is modified by the control circuit to absorb the total input power excursions after the drop of channels. Then both the surviving channels and the control channel receive the available power gain left by the dropped channels. The initial disturbances were determined by the configuration response time, while the steady state characteristics were defined by the configuration power gain profile. The transient effects of the surviving channels were accumulated along the cascade (in a much smaller scale than without link control protection), because power gain does not depend exclusively on the amplifier saturation level (controlled by this technique) but also on every channel’s wavelength and input power. It was noted that the link control protection was more efficient for the “EDFA + DFRAb ” configuration. In the worst case, corresponding to the sixth amplification stage, the power excursion (peak) is reduced from 9.34 dB to 0.07 dB. A CKNOWLEDGMENT The authors would like to thank the partial support received from the UTFSM project DGIP-231229.
6
R EFERENCES [1] C. R. Giles and E. Desurvire, “Modeling Erbium Doped Fiber Amplifiers”, IEEE Journal of Lightwave Technology, vol. 9, pp. 271-283, 1991. [2] M. N. Islam, “Raman Amplifiers for Telecommunications”, IEEE Journal of Selected Topics in Quantum Electronics, vol. 8, pp. 548-559, 2002. [3] V. E. Perlin and H. Winful, “On Distributed Raman Amplification for Ultrabroad-Band Long Haul WDM Systems”, IEEE Journal of Lightwave Technology, vol. 20, pp. 409-416, 2002. [4] C. Rivera, R. Olivares, M. T. M. Rocco Giraldi, A. P. L´opez Barbero, M. J. Pontes, M. E. S. Segatto, M. A. G. Martinez and J. O. Cris´ostomo Weyl Costa, “Numerical Simulations and Experimental Results of a Hybrid EDFA-Raman Amplifier”, International Microwave and Optoelectronics Conference (IMOC 2009), Brazil, 2009. [5] R. Olivares, “A Comparative Study of Techniques to Control Power Transients in Optical WDM Networks”, 10th European Conference on Networks & Optical Communications, England, 2005. [6] V. Pincheira, M. Soto and R. Olivares, “Per-band Link Control Transients Protection in Distributed Fiber Raman Amplifier Cascades”, International Microwave and Optoelectronics Conference (IMOC 2009), Brazil, 2009. [7] J. H. Lee, Y. M. Chang, Y. G. Han, H. Chung, S. H. Kim and S. B. Lee, “A Detailed Experimental Study on Single-Pump Raman/EDFA Hybrid Amplifiers: Static, Dynamic and System Performance Comparison”, IEEE Journal of Lightwave Technology, vol. 23, pp. 3484-3493, 2005. [8] S. H. Chang, H. S. Chung, H. J. Lee and K. Kim, “Suppression of Transient Phenomena in Hybrid Raman/EDFA Hybrid Amplifier”, IEEE Photonics Technology Letters, vol. 17, pp. 1004-1006, 2005. [9] J. H. Lee, Y. M. Chang, Y. G. Han, S. H. Kim and S. B. Lee, “Dynamic Properties of Single-Pump, Dispersion-compensating Hybrid Amplifier Recycling Residual Raman Pump”, Optics Express, vol. 12, pp. 6594-6599, 2004. [10] S. R. Chinn, “Simplified Modeling of Transients in GainClamped Erbium Doped Fiber Amplifiers”, Journal of Lightwave Technology, vol. 16, pp. 1095-1100, 1998. ´ [11] M. Karasek and M. Menif, “Channel Addition/Removal Response in All Optical Lumped Raman Amplifiers”, IEEE Journal of Lightwave Technology, vol. 20, pp. 1680-1687, 2002. [12] J. L. Zyskind, A. K. Srivastava, Y. Sun, J. C. Ellson, G. W. Newsome, R. W. Tkach, A. R. Chraplyvy, J. W. Sulhoff, T. A. Strasser, J. R. Pedrazzani and C. Wolf, “Fast-Link control Protection of Surviving Channels in Multi-wavelength Optical Networks”, IEEE Photonics Technology Letters, vol. 9, pp. 1667-1669, 1990. [13] G. C. Goodwin, S. F. Graebe and M. Salgado, “Control System Design”, pp. 160-164, 2000.
