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Protection of surviving channels in pump-controlled gain-locked Raman fibre amplifier
1 September 2002
Optics Communications 210 (2002) 57–65 www.elsevier.com/locate/optcom
Protection of surviving channels in pump-controlled gain-locked Raman fibre amplifier M. Kar asek a,*, M. Menif b,1 a
b
Institute of Radio Engineering and Electronics, Academy of Sciences of the Czech Republic, Chaberska 57, 18251 Prague, Czech Republic Department of Electrical and Computer Engineering, Centre for Optics, Photonics and Lasers (COPL), Laval University, Qu ebec, Canada G1K 7P4 Received 10 April 2001; received in revised form 10 June 2002; accepted 14 June 2002
Abstract The authors present results of numerical analysis on transient gain response to channel addition/removal in a counter-directionally pumped Raman fibre amplifier (RFA) with a pump-controlled gain-locking feedback loop. A large signal numerical model which incorporates time variation effects, downstream propagation of multiple signals, upstream propagation of pump and both downstream and upstream propagation of amplified spontaneous emission has been used for the analysis. To lock the gain of the RFA for variable channel loading, the input pump power must be varied. Negative-feedback control derived from a monitoring channel output power has been introduced in the model. It follows from the theoretical investigation that the surviving-channel-power excursion in a 10 dB RFA due to removal/addition of six channels in an eight-channel multiwavelength system can be reduced to less than 0.1 dB when the pump-power-feedback parameters are properly selected. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Modelling; Wavelength division multiplexing; Optical fibre amplifiers and Raman scattering
1. Introduction Rapid growth of communications traffic and the development of high-power compact semiconductor laser diode pumps have boosted the research on Raman fibre amplifiers (RFAs). By
*
Corresponding author. Tel.: +1 420-2-66773-507; fax: +1 420-2-84680-222. E-mail addresses: [email protected] (M. Kara´sek), [email protected] (M. Menif). 1 Tel.: +1 418-656-2906; fax: +1 418-656-3159
proper selection of wavelengths and powers of pump sources, RFA can exhibit wider amplification bandwidth and flexible centre wavelength in comparison with erbium-doped fibre amplifiers [1], [2]. One hundred nanometer bandwidth flat-gain RFA pumped and gain equalized by 12-wavelength-channel WDM laser diode unit has been reported in [3]. Wavelength-based routing has been proposed as a promising approach towards transparent alloptical WDM networking. When conventional fibre amplifiers are used, such networks would be vulnerable to transient inter-channel cross-gain
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modulation when they undergo dynamic reconfigurations [4]. Because optical amplifiers saturate on a total-power basis, addition or removal of channels in a wavelength routing multi-access WDM network will tend to perturb channels at other wavelengths that share all or part of the route. When the network is reconfigured and wavelength channels are added or dropped, crossgain modulation in fibre amplifiers will induce power transients in the surviving channels that can cause serious service impairment. Attention has been focused primarily on signal-power transients in concatenated highly pumped, deeply saturated erbium-doped fibre amplifiers (EDFAs) [5–7]. Several schemes have been suggested to control the unwanted power excursions of surviving channels in EDFAs. Fast pump control in a two-stage EDFA was demonstrated, [8,9]. A photodetector was used to sense the power transients in the surviving signal and provided the feedback-control signal for the pump laser diode current. The two stages of the EDFA were monitored and controlled separately. The speed of the dynamic control exceeded that reported earlier [10]. The fast link control reported in [11] was based on an addition of a control channel before the first optical amplifier in a link. The power of the control channel was adjusted by a fast feedforward loop which holds constant the total power of all transmitted signal channels and the control channel at the input to the first EDFA. This way, constant loading of all fibre amplifiers in the link was maintained independent of channel addition/removal. The all-optical gain control has also been widely studied, [12–14]. Allowing lasing action at a designated wavelength different from signal wavelengths in an EDFA clamps signal gain regardless of signal-input-power levels. This solution requires additional optical elements to form the laser cavity which generally impairs the noise performance. It has been shown in a recent study that excellent suppression of both transient and steady-state-signal-power fluctuations due to channel addition/removal is achieved without additional measures if the concatenated EDFAs are strongly inverted [15]. Little attention has so far been paid to transient effects in RFA. In [16], transient effects in satu-
rated Raman amplifier caused by input-power fluctuations have been reported. The Raman gain medium was a counter-directionally pumped 13.9 km long piece of dispersion compensating fibre (DCF), the input signal was square wave modulated at 1 kHz, either partially or with 100% modulation depth, and the time evolution of output signal was recorded. A leading-edge-outputpower overshoot lasting for approximately 50 ls has been observed and attributed to unsaturated RFA gain. The strong power of the signal depleted the pump so that the remaining signal pulse did not experience the same high gain as the leading edge of the signal pulse. An accurate description of the transient effect has been achieved by a dynamic numerical model of RFA. A control scheme for suppression of transients in both lumped and distributed RFAs has been demonstrated in [17]. Proportional-integral-derivative (PID) control circuit was implemented to vary the counter-directional pump power, the control signal was derived either from the surviving channel output power, or from the both the surviving and total output power. When the control was off, Raman gain fluctuations on the surviving channels ranged from 0.35 to 1.2 dB as the drop/total ratios ranged from 4/8 to 20/24 in the distributed RFA. The control algorithm kept gain fluctuations on surviving channels < 0:06 dB. Analytical expressions, basic rules and physical interpretation of transient phenomena in discrete RFA were presented in [18]. In this article we analyze the recently proposed and experimentally tested RFA gain-locking technique based on surviving-channel-power monitoring [17]. The analysis is based on the application of a comprehensive large-signal numerical model which incorporates temporal properties of RFA and can take into account both the downstream and upstream propagation of pump, signal and ASE powers. In order to minimize the correlation between the states of polarization of signal and pumps, counter-directional pumping scheme is assumed. The gain-locking algorithm based on proportional-integral-differential control of pump power has been implemented numerically. We have extended the results presented in [17] by analyzing the sensitivity of the gain-locking system to the
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selection of feedback-loop gain coefficients and verified the applicability of the gain-locking system to multi-pump, multi-channel wide-band RFA. It will be shown that the same feedback-loop parameters give excellent suppression of survivingchannel-power fluctuations even when different number of WDM channels is dropped/added and that at least two monitoring channels must be used in multi-pump RFA to achieve sufficient suppression of power fluctuations.
2. Numerical model and results The dynamic model used for the simulation is similar to the steady-state model of RFA derived in [19]. Generation and propagation of spontaneous emission noise was taken into account in accordance with [20]. When backward Rayleigh scattering, temperature-dependent spontaneous Raman emission and wavelength dependence of fibre loss and group velocity are taken into consideration, the propagation equations for forward and backward propagating pumps, signals, and spectral components of amplified spontaneous emission powers, P þ ðz; t; mÞ, P ðz; t; mÞ, describing their evolution in space and time acquire the form [20]: oP ðz; t; mÞ 1 oP ðz; t; mÞ oz Vg ðmÞ ot ¼ aðmÞP ðz; t; mÞ cðmÞP ðz; t; mÞ X gR ðm nÞ P ðz; t; mÞ Keff Aeff n>m ½P ðz; t; nÞ þ P ðz; t; nÞ
X gR ðm nÞ ½P ðz; t; nÞ þ P ðz; t; nÞ
hm Aeff n>m 1 1 þ hðnmÞ=kT Dm P ðz; t; mÞ e 1 X m gR ðm nÞ ½P ðz; t; nÞ þ P ðz; t; nÞ
n K A eff eff n
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where Vg ðmÞ is the frequency-dependent group velocity, aðmÞ is the fibre background loss, cðmÞ the Rayleigh back scattering coefficient, gR ðm nÞ the Raman gain coefficient between waves with frequency m and n, Keff is the polarization factor between pumps and Stokes signals, Aeff the effective interaction area of the fibre, h is the Planck’s constant, k is the Boltzman’s constant and T the absolute temperature of the fibre. In steady-state, time derivatives in the system of coupled propagation Eq. (1) disappear. The steady-state solution of propagation equations involved in RFA simulation introduces a two boundary value problem. Due to the backward propagating ASE powers and counter-directional pumping scheme, an iterative forward and backward integration of propagation equations must be used. We applied the fourth-order Runge– Kutta subroutine for forward and backward integration. The iteration is started with a forward integration of signals and forward propagating ASE spectral components. The backward pumps and backward ASE powers are set to zero. At each backward integration the final results P þ ðz ¼ L; mÞ of the previous forward integration, together with the boundary conditions for backward pump and backward ASE powers are used as starting conditions. Similarly, the results of the previous backward integration P ðz ¼ 0; mÞ together with the boundary conditions for signal channels and forward ASE are used as starting conditions for each next forward integration. The iteration process is stopped when, during two successive forward integrations, gain of a selected signal channel does not change by more than 0.05%. Time evolution of pumps, signals and amplified spontaneous emission waves has been performed by direct integration of Eq. (1) starting with the steady-state solution for longitudinal distributions of individual powers along the Raman fibre. To avoid possible oscillations of the solution in the time domain, care must be taken in the selection of bin widths used in the space, Dz, and time, Dt, discretization schemes. Stable solution has been obtained when the time bin Dt is equal or smaller than the propagation time through the space bin, Dt 6 Dz=Vg . In order to determine rise/fall times of the surviving channel power transients with
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sufficient resolution, we kept the ratio of time and space bins Dt=Dz ¼ 4 109 ½s=m independent of the Raman fibre length. Practical implementation of the RFA that uses the output power of one of the surviving channels as a control signal is shown schematically in Fig. 1. In order to lock the gain of the RFA for variable channel loading, the backward pump power, Ppin , must bee varied. Negative-feedback control derived from the output power of one of the surviving channels, Psur ðtÞ, has been introduced. In a network, the single channel that is monitored via a directional coupler, optical band pass filter and photodetector might be a carrier that is not one of the add/drop channels or might be a nearby telemetry channel. It has been found that a single proportional, integral or derivative feedback function does not give satisfactory control. Stable behaviour has generally been achieved with a combination of proportional and differential feedback (known in feedback-control theory as PD control) Ppin ðt þ dtÞ ¼ Ppin ðtÞ þ Cp ½Psur ðtÞ Psur ð0Þ
þ Cd
d ½Psur ðtÞ Psur ð0Þ ; dt
ð2Þ
where Psur ð0Þ represents the stationary value of the selected surviving channel output power when all intended channels are amplified and Cp , Cd represent the gains of the proportional and differential errors used in the negative-feedback system. Cp and Cd must be carefully selected to achieve fast elimination of surviving channel fluctuations without unwanted oscillations. Starting values of
Fig. 1. Schematic diagram of RFA with pump-powercontrolled gain-locking system
Cp and Cd have been determined using the Ziegler– Nichols method [21]. First, Cd has been set to zero and Cp increased, step by step, until steady-state oscillations of the surviving channel at the amplifier output have been reached. Denoting the corresponding proportional gain constant as Cpkr and the oscillation frequency as f kr ¼ 1=T kr , the starting values are given by Cp ¼ 0:6 Cpkr , Cd ¼ 0:075 Cp T kr =dt. Optimum values of Cp ; Cd are determined according to acceptable survivingchannel-power excursions and differ slightly from the starting values. Our numerical model of RFA is based on the solution of coupled nonlinear partial differential Eq. (1) that include pump-to-pump, pump-tosignal, and signal-to-signal Raman interactions, pump depletion due to Raman energy transfer, Rayleigh backscattering, wavelength-dependent fibre loss, spontaneous emission noise and thermal noise. It is not easy to identify the influence of the individual physical phenomena on the transients of surviving channels in multi-pump RFA fed by several tens of WDM channels. In order to demonstrate the performance of pump-controlled gain-locked RFA, we will consider a single-pump amplifier consisting of dispersion-shifted fibre (DSF) fed by eight signal channels. The wavelength and power of the counter-directional pump are assumed to be kp ¼ 1450 nm and 800 mW, the signals are placed between 1546 and 1553 nm with 1 nm spacing, the input signal power is )3 dBm/ channel. Some of the eight channels are 100% square wave modulated with frequency fm ¼ 500 Hz and 50% duty-cycle to simulate channel addition/removal, the signal at 1546 nm is selected as a monitoring channel of the negative-feedback loop. The optical spectrum at the output of the RFA is shown in Fig. 2 for the case that all eight channels are on. The ASE power contained in 0.2 nm slots is displayed. Spectral dependence of net gain and of optical signal-to-noise ratio is shown in Fig. 3. The gain of the eight channels ranges between 12.9 and 13.6 dB, the optical signal-tonoise ration (OSNR) is better than 41 dB. Fig. 4 shows the output-power variation of the monitoring channel, DP1546 nm , as a function of time when 2, 4, or 6 out of 8 channels are switched off (at t ¼ 0:5 ms) and on again (at t ¼ 1:5 ms) and the
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Fig. 2. Optical spectrum at the output of RFA: LDSF ¼ 40 km, ¼ 800 mW, Psin ¼ 3 dBm/channel (ASE kp ¼ 1450 nm, Ppin power contained in 0.2 nm slot is displayed).
Fig. 3. Spectral dependence of gain and optical signal-to-noise ¼ 800 mW, ratio of RFA: LDSF ¼ 40 km, kp ¼ 1450 nm, Ppin Psin ¼ 3 dBm/channel.
feedback control is not operating. When the last two channels (1552 and 1553 nm) are dropped, the gain of the 1546 nm channel increases in an exponential fashion, the steady-state-signal-power increase reaches DP1546 nm ¼ 0:48 dB and the risetime (10–90% of the maximum value) is equal to Trt ¼ 189 ls. When 4 or 6 out of 8 channels are switched off the steady-state-power increase grows to 1.1 and 1.98 dB, respectively. The corresponding risetimes are 203 and 224 ls. The onset of the surviving-channel-power transient is delayed by the propagation delay, s, of the 40 km of DSF fibre, s ¼ 193 ls. During the simulation of the gain-locking feedback-loop, pump power is modified in accordance with the Eq. (2) at each time step when the
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Fig. 4. Surviving-channel-power fluctuation as a function of time when 2, 4, or 6 out of 8 channels are dropped/added: control loop switched off.
output power of the monitoring channel changes. Fig. 5 plots the time evolution of DP1546 nm immediately after 2, 4, or 6 out of 8 channels are switched off at t ¼ 500 ls and the control feedbackloop is switched on. The parameters of the loop have been set to Cp ¼ 10, Cd ¼ 2 104 . The maximum power excursions are now 0.025, 0.053 and 0.08 dB when 2, 4 or 6 out of 8 channels are switched off, respectively. The feedback-loop brings back the signal level to the original value within 80 ls even when 6 out of 8 channels are dropped. Fig. 6 shows the time evolution of the input pump power immediately after 2, 4 or 6 out of 8 channels are switched off at t ¼ 500 ls. For
Fig. 5. Output-power variation at k ¼ 1546 nm as a function of time immediately after 2, 4 or 6 out of 8 channels are switched off at t ¼ 500 ls: control loop switched on, Cp ¼ 10, Cd ¼ 2 104 .
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Fig. 6. Input-pump-power variation as a function of time immediately after 2, 4 or 6 out of 8 channels are switched off at t ¼ 500 ls: control loop switched on, Cp ¼ 10, Cd ¼ 2 104 .
practical implementation of the gain-locked RFA it can be deduced from this figure that the feedback circuitry must be able to process fall/rise times <30 ls. One period of the monitoring channel output-power fluctuation and the corresponding input pump-power evolution in case that 6 out of 8 channels are dropped/added is plotted in Fig. 7 (Cp ¼ 10, Cd ¼ 2 104 ). It is seen that after the initial pump-power undershoot at t 718 ls the monitoring channel output power seems to be almost constant, but the feedbackloop control keeps the pump power decreasing until new steady-state-pump-power distribution along the transmission fibre is established. This takes twice the propagation delay, 2 s, so that at
Fig. 7. Surviving-channel-power fluctuation and input-pumppower variation as a function of time when 6 out of 8 channels are switched off at t ¼ 500 ls and on again at t ¼ 1500 ls: control loop switched on, Cp ¼ 10, Cd ¼ 2 104 .
t 1074 ls starts another fast change in pump power (smaller in amplitude) which is reflected in the surviving channel output power as a secondary fluctuation. Symmetrical behaviour has been observed when channels were added. These pumppower transients in the gain-locked RFA were recorded experimentally (see Fig. 4, [17]) and can be attributed to non-negligible light propagation time through the transmission fibre. Sensitivity of the gain-locking system to the selection of feedback-loop gain constants Cp , Cd , has been investigated for the case that 6 out of 8 channels are switched off/on. Fig. 8 illustrates the effect of the differential-gain constant, Cd , on the power excursion of the RFA at 1546 nm. As expected, when increasing the Cd , the peak value of the surviving-channel-power excursion decreases and the oscillatory response of the feedback loop disappears. Sufficiently fast electronics must, however, be used as the fall-/risetime of the pump laser drive current becomes shorter. Fig. 9 plots the evolution of Ppin ðtÞ. The fall time (10–90% of the minimum value) is 26.4, 24.0 and 20.4 ls for Cd ¼ 0:6 104 , 1:2 104 and 2:4 104 , respectively. The effect of the proportional-gain coefficient, Cp , on the output-power fluctuations of the monitoring channel is illustrated in Fig. 10. It is seen that the peak-power excursion is not very sensitive to Cp and that for a given Cd ¼ 2 104 , the proportional gain constant can be selected
Fig. 8. Output-power variation at k ¼ 1546 nm as a function of time immediately after 6 out of 8 channels are switched off at t ¼ 500 ls: control loop switched on, Cp ¼ 10, Cd as a parameter.
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Fig. 9. Input-pump-power variation as a function of time immediately after 6 out of 8 channels are switched off at t ¼ 500 ls: control loop switched on, Cp ¼ 10, Cd as a parameter.
Fig. 10. Output-power variation at k ¼ 1546 nm as a function of time immediately after 6 out of 8 channels are switched off at t ¼ 500 ls: control loop switched on, Cd ¼ 2 104 , Cp as a parameter.
which brings the surviving channel power to its original value in the shortest possible time without oscillations. Corresponding pump-power variation as a function of time immediately after 6 out of 8 channels are switched off is shown in Fig. 11. At the end, we will show that cross-gain modulation can seriously affect surviving channels in gain-flattened multiple-pump RFAs designed for WDM applications. We have considered a distributed RFA with flat gain in 100 nm wavelength range, reported in [22]. The amplifier consists of L ¼ 45 km of dispersion-shifted single-mode fibre counter-directionally pumped by eight laser diodes
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Fig. 11. Input-pump-power variation as a function of time immediately after 6 out of 8 channels are switched off at t ¼ 500 ls: control loop switched on, Cd ¼ 2 104 , Cp as a parameter.
at wavelengths 1416, 1421, 1426, 1432, 1440, 1456, 1473, and 1502 nm with powers of 125, 130, 125, 120, 100, 90, 80, and 70 mW, respectively. We consider 100 WDM channels starting at 1520 nm with 1 nm spacing and input power of )3 dBm/ channel. We calculated a net gain of the amplifier between 2.7 and 3.9 dB, the optical signal-to-noise ratio (OSNR) varied from 37.5 dB at 1520 nm to 42.5 dB at 1619 nm (ASE power contained in 0.2 nm slots has been considered). Let us now assume that the last 50 channels (1570–1619 nm) are 100% square wave modulated with frequency fm ¼ 500 Hz and 50% duty-cycle. Fig. 12 shows the calculated power variation at the
Fig. 12. Surviving-channel-power fluctuation as a function of time when 50 out of 100 channels are dropped/added: 8 pump RFA [22], control loop switched off.
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output of the RFA as a function of time for three surviving channels at 1520, 1544 and 1568 nm when the last 50 channels are switched off (at t0 ¼ 0:5 ms) and on again (at t1 ¼ 1:5 ms). The steady-state power fluctuation reaches 1.45 dB for channels at 1520 and 1568 nm and 1.25 dB for the 1554 nm channel. Rise and fall times of surviving channel power transients are wavelength dependent. It multi-pump, multi-channel RFA, pump-topump, signal-to-signal power transfers and pump depletion are rather complex. Fig. 13 shows the distribution of counter-direction pump power at individual wavelengths along the DSF fibre. It is seen that shorter-wavelength pumps contribute their power to longer-wavelengths ones which makes the application of the fast pump-power control more complicated that in the case of single pump RFA. It was impossible to achieve effective suppression of surviving channel power fluctuations using one monitoring channel only to control all eight pump sources. With respect to ease of implementation of the pump-controlled gainlocking system, we resorted to two control signals, each controlling half of the pump sources. Fig. 14 depicts time evolution of power fluctuation of surviving channels at 1520, 1544 and 1568 nm after 50 out of 100 channels have been dropped at t ¼ 500 ls (compare with Fig. 12, without pump control). The first monitoring channel controlling the first four pumps at 1416, 1421, 1426, and 1432 nm was placed at 1520, the second at 1540 nm
Fig. 14. Surviving-channel-power fluctuation as a function of time when 50 out of 100 channels are dropped/added: 8 pump RFA [22], control loop switched on, Cp ¼ 10, Cd ¼ 2:4 104 .
Fig. 15. Input-pump-power variation as a function of time immediately after 50 out of 100 channels are switched off at t ¼ 500 ls: control loop switched on, Cp ¼ 10, Cd ¼ 2:4 104 .
controlled the remaining 4 pumps. The parameters of the feedback loop have been set to Cp ¼ 10, Cd ¼ 2:4 104 . Corresponding pump-power variation of pump sources at 1416, 1432 and 1502 nm as a function of time immediately after 50 out of 100 channels are switched off is shown in Fig. 15.
3. Conclusion
Fig. 13. Power evolution of backward propagating pumps: 8 pump RFA [22].
We have presented a theoretical analysis of surviving channel protection in a pump-controlled gain-locked RFA. The analysis is based on an application of a numerical model that incorporates
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time variation effects in distributed RFA and solves the time-dependent propagation equations for multiple signals, counter-directionally propagating pump and both downstream and upstream propagating spectral components of amplified spontaneous emission. The effect of switching off and on 2, 4 and 6 out of 8 WDM channels in an RFA composed of 40 km of DSF fibre counterdirectionally pumped at 1450 nm with 800 mW without and with the gain-locking feedback loop has been compared. Surviving-channel-power fluctuations as high as 2 dB can be expected when 6 out of 8 channels are dropped/added and the gain-locking loop is disabled. It has been found that a single proportional, integral or derivative feedback function does not give satisfactory pump-power control. Stable behaviour has generally been achieved with a combination of proportional and differential feedback. The effect of feedback-loop parameters on the surviving channel response has been investigated. If the proportional- and differential-gain coefficients of the loop are properly selected, the surviving-channel-power excursion can be kept below 0.1 dB, without any oscillations and independent of the number of dropped/added channels. We have verified that the pump-controlled gainlocking system may be used in multi-pump wideband RFA under the assumption that more than one monitoring channel is used. Detailed study of the best position of monitoring channels will be a subject of further simulations.
Acknowledgements This research has been partly supported by the Grant Agency of the Academy of Sciences of Czech Republic under project number A2067202 and in part by a grant from the Natural Science and Engineering Research Council of Canada and by Quebec Telephone.
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Optics Communications 210 (2002) 57–65 www.elsevier.com/locate/optcom
Protection of surviving channels in pump-controlled gain-locked Raman fibre amplifier M. Kar asek a,*, M. Menif b,1 a
b
Institute of Radio Engineering and Electronics, Academy of Sciences of the Czech Republic, Chaberska 57, 18251 Prague, Czech Republic Department of Electrical and Computer Engineering, Centre for Optics, Photonics and Lasers (COPL), Laval University, Qu ebec, Canada G1K 7P4 Received 10 April 2001; received in revised form 10 June 2002; accepted 14 June 2002
Abstract The authors present results of numerical analysis on transient gain response to channel addition/removal in a counter-directionally pumped Raman fibre amplifier (RFA) with a pump-controlled gain-locking feedback loop. A large signal numerical model which incorporates time variation effects, downstream propagation of multiple signals, upstream propagation of pump and both downstream and upstream propagation of amplified spontaneous emission has been used for the analysis. To lock the gain of the RFA for variable channel loading, the input pump power must be varied. Negative-feedback control derived from a monitoring channel output power has been introduced in the model. It follows from the theoretical investigation that the surviving-channel-power excursion in a 10 dB RFA due to removal/addition of six channels in an eight-channel multiwavelength system can be reduced to less than 0.1 dB when the pump-power-feedback parameters are properly selected. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Modelling; Wavelength division multiplexing; Optical fibre amplifiers and Raman scattering
1. Introduction Rapid growth of communications traffic and the development of high-power compact semiconductor laser diode pumps have boosted the research on Raman fibre amplifiers (RFAs). By
*
Corresponding author. Tel.: +1 420-2-66773-507; fax: +1 420-2-84680-222. E-mail addresses: [email protected] (M. Kara´sek), [email protected] (M. Menif). 1 Tel.: +1 418-656-2906; fax: +1 418-656-3159
proper selection of wavelengths and powers of pump sources, RFA can exhibit wider amplification bandwidth and flexible centre wavelength in comparison with erbium-doped fibre amplifiers [1], [2]. One hundred nanometer bandwidth flat-gain RFA pumped and gain equalized by 12-wavelength-channel WDM laser diode unit has been reported in [3]. Wavelength-based routing has been proposed as a promising approach towards transparent alloptical WDM networking. When conventional fibre amplifiers are used, such networks would be vulnerable to transient inter-channel cross-gain
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modulation when they undergo dynamic reconfigurations [4]. Because optical amplifiers saturate on a total-power basis, addition or removal of channels in a wavelength routing multi-access WDM network will tend to perturb channels at other wavelengths that share all or part of the route. When the network is reconfigured and wavelength channels are added or dropped, crossgain modulation in fibre amplifiers will induce power transients in the surviving channels that can cause serious service impairment. Attention has been focused primarily on signal-power transients in concatenated highly pumped, deeply saturated erbium-doped fibre amplifiers (EDFAs) [5–7]. Several schemes have been suggested to control the unwanted power excursions of surviving channels in EDFAs. Fast pump control in a two-stage EDFA was demonstrated, [8,9]. A photodetector was used to sense the power transients in the surviving signal and provided the feedback-control signal for the pump laser diode current. The two stages of the EDFA were monitored and controlled separately. The speed of the dynamic control exceeded that reported earlier [10]. The fast link control reported in [11] was based on an addition of a control channel before the first optical amplifier in a link. The power of the control channel was adjusted by a fast feedforward loop which holds constant the total power of all transmitted signal channels and the control channel at the input to the first EDFA. This way, constant loading of all fibre amplifiers in the link was maintained independent of channel addition/removal. The all-optical gain control has also been widely studied, [12–14]. Allowing lasing action at a designated wavelength different from signal wavelengths in an EDFA clamps signal gain regardless of signal-input-power levels. This solution requires additional optical elements to form the laser cavity which generally impairs the noise performance. It has been shown in a recent study that excellent suppression of both transient and steady-state-signal-power fluctuations due to channel addition/removal is achieved without additional measures if the concatenated EDFAs are strongly inverted [15]. Little attention has so far been paid to transient effects in RFA. In [16], transient effects in satu-
rated Raman amplifier caused by input-power fluctuations have been reported. The Raman gain medium was a counter-directionally pumped 13.9 km long piece of dispersion compensating fibre (DCF), the input signal was square wave modulated at 1 kHz, either partially or with 100% modulation depth, and the time evolution of output signal was recorded. A leading-edge-outputpower overshoot lasting for approximately 50 ls has been observed and attributed to unsaturated RFA gain. The strong power of the signal depleted the pump so that the remaining signal pulse did not experience the same high gain as the leading edge of the signal pulse. An accurate description of the transient effect has been achieved by a dynamic numerical model of RFA. A control scheme for suppression of transients in both lumped and distributed RFAs has been demonstrated in [17]. Proportional-integral-derivative (PID) control circuit was implemented to vary the counter-directional pump power, the control signal was derived either from the surviving channel output power, or from the both the surviving and total output power. When the control was off, Raman gain fluctuations on the surviving channels ranged from 0.35 to 1.2 dB as the drop/total ratios ranged from 4/8 to 20/24 in the distributed RFA. The control algorithm kept gain fluctuations on surviving channels < 0:06 dB. Analytical expressions, basic rules and physical interpretation of transient phenomena in discrete RFA were presented in [18]. In this article we analyze the recently proposed and experimentally tested RFA gain-locking technique based on surviving-channel-power monitoring [17]. The analysis is based on the application of a comprehensive large-signal numerical model which incorporates temporal properties of RFA and can take into account both the downstream and upstream propagation of pump, signal and ASE powers. In order to minimize the correlation between the states of polarization of signal and pumps, counter-directional pumping scheme is assumed. The gain-locking algorithm based on proportional-integral-differential control of pump power has been implemented numerically. We have extended the results presented in [17] by analyzing the sensitivity of the gain-locking system to the
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selection of feedback-loop gain coefficients and verified the applicability of the gain-locking system to multi-pump, multi-channel wide-band RFA. It will be shown that the same feedback-loop parameters give excellent suppression of survivingchannel-power fluctuations even when different number of WDM channels is dropped/added and that at least two monitoring channels must be used in multi-pump RFA to achieve sufficient suppression of power fluctuations.
2. Numerical model and results The dynamic model used for the simulation is similar to the steady-state model of RFA derived in [19]. Generation and propagation of spontaneous emission noise was taken into account in accordance with [20]. When backward Rayleigh scattering, temperature-dependent spontaneous Raman emission and wavelength dependence of fibre loss and group velocity are taken into consideration, the propagation equations for forward and backward propagating pumps, signals, and spectral components of amplified spontaneous emission powers, P þ ðz; t; mÞ, P ðz; t; mÞ, describing their evolution in space and time acquire the form [20]: oP ðz; t; mÞ 1 oP ðz; t; mÞ oz Vg ðmÞ ot ¼ aðmÞP ðz; t; mÞ cðmÞP ðz; t; mÞ X gR ðm nÞ P ðz; t; mÞ Keff Aeff n>m ½P ðz; t; nÞ þ P ðz; t; nÞ
X gR ðm nÞ ½P ðz; t; nÞ þ P ðz; t; nÞ
hm Aeff n>m 1 1 þ hðnmÞ=kT Dm P ðz; t; mÞ e 1 X m gR ðm nÞ ½P ðz; t; nÞ þ P ðz; t; nÞ
n K A eff eff n
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where Vg ðmÞ is the frequency-dependent group velocity, aðmÞ is the fibre background loss, cðmÞ the Rayleigh back scattering coefficient, gR ðm nÞ the Raman gain coefficient between waves with frequency m and n, Keff is the polarization factor between pumps and Stokes signals, Aeff the effective interaction area of the fibre, h is the Planck’s constant, k is the Boltzman’s constant and T the absolute temperature of the fibre. In steady-state, time derivatives in the system of coupled propagation Eq. (1) disappear. The steady-state solution of propagation equations involved in RFA simulation introduces a two boundary value problem. Due to the backward propagating ASE powers and counter-directional pumping scheme, an iterative forward and backward integration of propagation equations must be used. We applied the fourth-order Runge– Kutta subroutine for forward and backward integration. The iteration is started with a forward integration of signals and forward propagating ASE spectral components. The backward pumps and backward ASE powers are set to zero. At each backward integration the final results P þ ðz ¼ L; mÞ of the previous forward integration, together with the boundary conditions for backward pump and backward ASE powers are used as starting conditions. Similarly, the results of the previous backward integration P ðz ¼ 0; mÞ together with the boundary conditions for signal channels and forward ASE are used as starting conditions for each next forward integration. The iteration process is stopped when, during two successive forward integrations, gain of a selected signal channel does not change by more than 0.05%. Time evolution of pumps, signals and amplified spontaneous emission waves has been performed by direct integration of Eq. (1) starting with the steady-state solution for longitudinal distributions of individual powers along the Raman fibre. To avoid possible oscillations of the solution in the time domain, care must be taken in the selection of bin widths used in the space, Dz, and time, Dt, discretization schemes. Stable solution has been obtained when the time bin Dt is equal or smaller than the propagation time through the space bin, Dt 6 Dz=Vg . In order to determine rise/fall times of the surviving channel power transients with
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sufficient resolution, we kept the ratio of time and space bins Dt=Dz ¼ 4 109 ½s=m independent of the Raman fibre length. Practical implementation of the RFA that uses the output power of one of the surviving channels as a control signal is shown schematically in Fig. 1. In order to lock the gain of the RFA for variable channel loading, the backward pump power, Ppin , must bee varied. Negative-feedback control derived from the output power of one of the surviving channels, Psur ðtÞ, has been introduced. In a network, the single channel that is monitored via a directional coupler, optical band pass filter and photodetector might be a carrier that is not one of the add/drop channels or might be a nearby telemetry channel. It has been found that a single proportional, integral or derivative feedback function does not give satisfactory control. Stable behaviour has generally been achieved with a combination of proportional and differential feedback (known in feedback-control theory as PD control) Ppin ðt þ dtÞ ¼ Ppin ðtÞ þ Cp ½Psur ðtÞ Psur ð0Þ
þ Cd
d ½Psur ðtÞ Psur ð0Þ ; dt
ð2Þ
where Psur ð0Þ represents the stationary value of the selected surviving channel output power when all intended channels are amplified and Cp , Cd represent the gains of the proportional and differential errors used in the negative-feedback system. Cp and Cd must be carefully selected to achieve fast elimination of surviving channel fluctuations without unwanted oscillations. Starting values of
Fig. 1. Schematic diagram of RFA with pump-powercontrolled gain-locking system
Cp and Cd have been determined using the Ziegler– Nichols method [21]. First, Cd has been set to zero and Cp increased, step by step, until steady-state oscillations of the surviving channel at the amplifier output have been reached. Denoting the corresponding proportional gain constant as Cpkr and the oscillation frequency as f kr ¼ 1=T kr , the starting values are given by Cp ¼ 0:6 Cpkr , Cd ¼ 0:075 Cp T kr =dt. Optimum values of Cp ; Cd are determined according to acceptable survivingchannel-power excursions and differ slightly from the starting values. Our numerical model of RFA is based on the solution of coupled nonlinear partial differential Eq. (1) that include pump-to-pump, pump-tosignal, and signal-to-signal Raman interactions, pump depletion due to Raman energy transfer, Rayleigh backscattering, wavelength-dependent fibre loss, spontaneous emission noise and thermal noise. It is not easy to identify the influence of the individual physical phenomena on the transients of surviving channels in multi-pump RFA fed by several tens of WDM channels. In order to demonstrate the performance of pump-controlled gain-locked RFA, we will consider a single-pump amplifier consisting of dispersion-shifted fibre (DSF) fed by eight signal channels. The wavelength and power of the counter-directional pump are assumed to be kp ¼ 1450 nm and 800 mW, the signals are placed between 1546 and 1553 nm with 1 nm spacing, the input signal power is )3 dBm/ channel. Some of the eight channels are 100% square wave modulated with frequency fm ¼ 500 Hz and 50% duty-cycle to simulate channel addition/removal, the signal at 1546 nm is selected as a monitoring channel of the negative-feedback loop. The optical spectrum at the output of the RFA is shown in Fig. 2 for the case that all eight channels are on. The ASE power contained in 0.2 nm slots is displayed. Spectral dependence of net gain and of optical signal-to-noise ratio is shown in Fig. 3. The gain of the eight channels ranges between 12.9 and 13.6 dB, the optical signal-tonoise ration (OSNR) is better than 41 dB. Fig. 4 shows the output-power variation of the monitoring channel, DP1546 nm , as a function of time when 2, 4, or 6 out of 8 channels are switched off (at t ¼ 0:5 ms) and on again (at t ¼ 1:5 ms) and the
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Fig. 2. Optical spectrum at the output of RFA: LDSF ¼ 40 km, ¼ 800 mW, Psin ¼ 3 dBm/channel (ASE kp ¼ 1450 nm, Ppin power contained in 0.2 nm slot is displayed).
Fig. 3. Spectral dependence of gain and optical signal-to-noise ¼ 800 mW, ratio of RFA: LDSF ¼ 40 km, kp ¼ 1450 nm, Ppin Psin ¼ 3 dBm/channel.
feedback control is not operating. When the last two channels (1552 and 1553 nm) are dropped, the gain of the 1546 nm channel increases in an exponential fashion, the steady-state-signal-power increase reaches DP1546 nm ¼ 0:48 dB and the risetime (10–90% of the maximum value) is equal to Trt ¼ 189 ls. When 4 or 6 out of 8 channels are switched off the steady-state-power increase grows to 1.1 and 1.98 dB, respectively. The corresponding risetimes are 203 and 224 ls. The onset of the surviving-channel-power transient is delayed by the propagation delay, s, of the 40 km of DSF fibre, s ¼ 193 ls. During the simulation of the gain-locking feedback-loop, pump power is modified in accordance with the Eq. (2) at each time step when the
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Fig. 4. Surviving-channel-power fluctuation as a function of time when 2, 4, or 6 out of 8 channels are dropped/added: control loop switched off.
output power of the monitoring channel changes. Fig. 5 plots the time evolution of DP1546 nm immediately after 2, 4, or 6 out of 8 channels are switched off at t ¼ 500 ls and the control feedbackloop is switched on. The parameters of the loop have been set to Cp ¼ 10, Cd ¼ 2 104 . The maximum power excursions are now 0.025, 0.053 and 0.08 dB when 2, 4 or 6 out of 8 channels are switched off, respectively. The feedback-loop brings back the signal level to the original value within 80 ls even when 6 out of 8 channels are dropped. Fig. 6 shows the time evolution of the input pump power immediately after 2, 4 or 6 out of 8 channels are switched off at t ¼ 500 ls. For
Fig. 5. Output-power variation at k ¼ 1546 nm as a function of time immediately after 2, 4 or 6 out of 8 channels are switched off at t ¼ 500 ls: control loop switched on, Cp ¼ 10, Cd ¼ 2 104 .
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Fig. 6. Input-pump-power variation as a function of time immediately after 2, 4 or 6 out of 8 channels are switched off at t ¼ 500 ls: control loop switched on, Cp ¼ 10, Cd ¼ 2 104 .
practical implementation of the gain-locked RFA it can be deduced from this figure that the feedback circuitry must be able to process fall/rise times <30 ls. One period of the monitoring channel output-power fluctuation and the corresponding input pump-power evolution in case that 6 out of 8 channels are dropped/added is plotted in Fig. 7 (Cp ¼ 10, Cd ¼ 2 104 ). It is seen that after the initial pump-power undershoot at t 718 ls the monitoring channel output power seems to be almost constant, but the feedbackloop control keeps the pump power decreasing until new steady-state-pump-power distribution along the transmission fibre is established. This takes twice the propagation delay, 2 s, so that at
Fig. 7. Surviving-channel-power fluctuation and input-pumppower variation as a function of time when 6 out of 8 channels are switched off at t ¼ 500 ls and on again at t ¼ 1500 ls: control loop switched on, Cp ¼ 10, Cd ¼ 2 104 .
t 1074 ls starts another fast change in pump power (smaller in amplitude) which is reflected in the surviving channel output power as a secondary fluctuation. Symmetrical behaviour has been observed when channels were added. These pumppower transients in the gain-locked RFA were recorded experimentally (see Fig. 4, [17]) and can be attributed to non-negligible light propagation time through the transmission fibre. Sensitivity of the gain-locking system to the selection of feedback-loop gain constants Cp , Cd , has been investigated for the case that 6 out of 8 channels are switched off/on. Fig. 8 illustrates the effect of the differential-gain constant, Cd , on the power excursion of the RFA at 1546 nm. As expected, when increasing the Cd , the peak value of the surviving-channel-power excursion decreases and the oscillatory response of the feedback loop disappears. Sufficiently fast electronics must, however, be used as the fall-/risetime of the pump laser drive current becomes shorter. Fig. 9 plots the evolution of Ppin ðtÞ. The fall time (10–90% of the minimum value) is 26.4, 24.0 and 20.4 ls for Cd ¼ 0:6 104 , 1:2 104 and 2:4 104 , respectively. The effect of the proportional-gain coefficient, Cp , on the output-power fluctuations of the monitoring channel is illustrated in Fig. 10. It is seen that the peak-power excursion is not very sensitive to Cp and that for a given Cd ¼ 2 104 , the proportional gain constant can be selected
Fig. 8. Output-power variation at k ¼ 1546 nm as a function of time immediately after 6 out of 8 channels are switched off at t ¼ 500 ls: control loop switched on, Cp ¼ 10, Cd as a parameter.
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Fig. 9. Input-pump-power variation as a function of time immediately after 6 out of 8 channels are switched off at t ¼ 500 ls: control loop switched on, Cp ¼ 10, Cd as a parameter.
Fig. 10. Output-power variation at k ¼ 1546 nm as a function of time immediately after 6 out of 8 channels are switched off at t ¼ 500 ls: control loop switched on, Cd ¼ 2 104 , Cp as a parameter.
which brings the surviving channel power to its original value in the shortest possible time without oscillations. Corresponding pump-power variation as a function of time immediately after 6 out of 8 channels are switched off is shown in Fig. 11. At the end, we will show that cross-gain modulation can seriously affect surviving channels in gain-flattened multiple-pump RFAs designed for WDM applications. We have considered a distributed RFA with flat gain in 100 nm wavelength range, reported in [22]. The amplifier consists of L ¼ 45 km of dispersion-shifted single-mode fibre counter-directionally pumped by eight laser diodes
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Fig. 11. Input-pump-power variation as a function of time immediately after 6 out of 8 channels are switched off at t ¼ 500 ls: control loop switched on, Cd ¼ 2 104 , Cp as a parameter.
at wavelengths 1416, 1421, 1426, 1432, 1440, 1456, 1473, and 1502 nm with powers of 125, 130, 125, 120, 100, 90, 80, and 70 mW, respectively. We consider 100 WDM channels starting at 1520 nm with 1 nm spacing and input power of )3 dBm/ channel. We calculated a net gain of the amplifier between 2.7 and 3.9 dB, the optical signal-to-noise ratio (OSNR) varied from 37.5 dB at 1520 nm to 42.5 dB at 1619 nm (ASE power contained in 0.2 nm slots has been considered). Let us now assume that the last 50 channels (1570–1619 nm) are 100% square wave modulated with frequency fm ¼ 500 Hz and 50% duty-cycle. Fig. 12 shows the calculated power variation at the
Fig. 12. Surviving-channel-power fluctuation as a function of time when 50 out of 100 channels are dropped/added: 8 pump RFA [22], control loop switched off.
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output of the RFA as a function of time for three surviving channels at 1520, 1544 and 1568 nm when the last 50 channels are switched off (at t0 ¼ 0:5 ms) and on again (at t1 ¼ 1:5 ms). The steady-state power fluctuation reaches 1.45 dB for channels at 1520 and 1568 nm and 1.25 dB for the 1554 nm channel. Rise and fall times of surviving channel power transients are wavelength dependent. It multi-pump, multi-channel RFA, pump-topump, signal-to-signal power transfers and pump depletion are rather complex. Fig. 13 shows the distribution of counter-direction pump power at individual wavelengths along the DSF fibre. It is seen that shorter-wavelength pumps contribute their power to longer-wavelengths ones which makes the application of the fast pump-power control more complicated that in the case of single pump RFA. It was impossible to achieve effective suppression of surviving channel power fluctuations using one monitoring channel only to control all eight pump sources. With respect to ease of implementation of the pump-controlled gainlocking system, we resorted to two control signals, each controlling half of the pump sources. Fig. 14 depicts time evolution of power fluctuation of surviving channels at 1520, 1544 and 1568 nm after 50 out of 100 channels have been dropped at t ¼ 500 ls (compare with Fig. 12, without pump control). The first monitoring channel controlling the first four pumps at 1416, 1421, 1426, and 1432 nm was placed at 1520, the second at 1540 nm
Fig. 14. Surviving-channel-power fluctuation as a function of time when 50 out of 100 channels are dropped/added: 8 pump RFA [22], control loop switched on, Cp ¼ 10, Cd ¼ 2:4 104 .
Fig. 15. Input-pump-power variation as a function of time immediately after 50 out of 100 channels are switched off at t ¼ 500 ls: control loop switched on, Cp ¼ 10, Cd ¼ 2:4 104 .
controlled the remaining 4 pumps. The parameters of the feedback loop have been set to Cp ¼ 10, Cd ¼ 2:4 104 . Corresponding pump-power variation of pump sources at 1416, 1432 and 1502 nm as a function of time immediately after 50 out of 100 channels are switched off is shown in Fig. 15.
3. Conclusion
Fig. 13. Power evolution of backward propagating pumps: 8 pump RFA [22].
We have presented a theoretical analysis of surviving channel protection in a pump-controlled gain-locked RFA. The analysis is based on an application of a numerical model that incorporates
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time variation effects in distributed RFA and solves the time-dependent propagation equations for multiple signals, counter-directionally propagating pump and both downstream and upstream propagating spectral components of amplified spontaneous emission. The effect of switching off and on 2, 4 and 6 out of 8 WDM channels in an RFA composed of 40 km of DSF fibre counterdirectionally pumped at 1450 nm with 800 mW without and with the gain-locking feedback loop has been compared. Surviving-channel-power fluctuations as high as 2 dB can be expected when 6 out of 8 channels are dropped/added and the gain-locking loop is disabled. It has been found that a single proportional, integral or derivative feedback function does not give satisfactory pump-power control. Stable behaviour has generally been achieved with a combination of proportional and differential feedback. The effect of feedback-loop parameters on the surviving channel response has been investigated. If the proportional- and differential-gain coefficients of the loop are properly selected, the surviving-channel-power excursion can be kept below 0.1 dB, without any oscillations and independent of the number of dropped/added channels. We have verified that the pump-controlled gainlocking system may be used in multi-pump wideband RFA under the assumption that more than one monitoring channel is used. Detailed study of the best position of monitoring channels will be a subject of further simulations.
Acknowledgements This research has been partly supported by the Grant Agency of the Academy of Sciences of Czech Republic under project number A2067202 and in part by a grant from the Natural Science and Engineering Research Council of Canada and by Quebec Telephone.
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