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Analysis of semiconductor optical amplifier based double-stage all-optical wavelength converter with improved extinction ratio
Optics Communications 241 (2004) 391–397 www.elsevier.com/locate/optcom
Analysis of semiconductor optical amplifier based double-stage all-optical wavelength converter with improved extinction ratio F. Ginovart *, J.C. Simon Groupement dÕInte´reˆt Scientifique ÔFOTONÕ, Laboratoire dÕOptronique, Ecole Nationale Supe´rieure de Sciences Applique´es et de Technologie, CNRS/UMR 6082, 6 rue de Ke´rampont, 22305 Lannion, France Received 5 March 2004; received in revised form 11 July 2004; accepted 21 July 2004
Abstract We theoretically study the temporal dynamics of a semiconductor optical amplifier (SOA) based double-stage wavelength converter in co-propagative configuration. The impact of the SOA number in the device is analyzed. In this work, we are concerned with the gain recovery time shortening while keeping a low level of noise. We also study the pump and probe power influence on a 10 Gbit/s NRZ sequence output extinction ratio and undertake a systematic study when varying the input extinction ratio. 2004 Elsevier B.V. All rights reserved. Keywords: Semiconductor optical amplifier; All-optical regeneration
1. Introduction Semiconductor optical amplifier (SOA) will be a key element in future all-optical networks, thanks to its properties. SOA gain saturation effects are used in numerous all-optical processing applications based on cross-gain and cross-phase modulations such as wavelength conversion, switching
*
Corresponding author. Fax: +33296370199. E-mail address: [email protected] (F. Ginovart).
and pulse regeneration [1,2]. Also, SOA based devices, and in particular cascaded SOA, have been studied with different configurations [2–9]. Here, we theoretically analyze a SOA based double-stage wavelength converter in co-propagative configuration. Its sketch is pictured in Fig. 1. The principle of operation consists of injecting the pump simultaneously in all amplifiers, while the cw probe crosses the amplifiers in series. The injected pump into the second stage SOA is in phase with the probe output of the first stage SOA. In this way, the extinction ratios of the converted
0030-4018/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.07.050
392
F. Ginovart, J.C. Simon / Optics Communications 241 (2004) 391–397
Pump (data)
Probe (CW)
SOA 2
SOA 1 A
Fig. 1. Sketch of the SOA double stage wavelength converter.
signal are multiplied. The second SOA injected probe power is adjusted, thanks to a variable attenuator (attenuation: A). In our calculations, the filter is supposed to be perfect and only the probe is injected into the second SOA. So, amplified spontaneous emission (ASE) effects are only taken into account in the dynamics of each SOA. After briefly describing the temporal SOA gain dynamics model, we study the double-stage SOA gain dynamics to give an understanding analysis of the influence of the SOA number in the device on the gain recovery and show the conditions which allow to shorten it while keeping a low level of noise. For this purpose, we study the noise transmission of the device. Next, we consider a 10 Gbit/s NRZ sequence. The analysis of the influence of the injected pump and probe power on its extinction ratio is undertaken. This study shows how the SOA based double-stage can be used as an all-optical 2R regenerator.
2. SOA model A temporal SOA gain dynamics model including pump and probe propagation, as well as amplified forward and backward spontaneous emission has been presented in [10,11]. Material gain and
spontaneous emission are calculated from [12]. Both double stage SOA are identical. Here, we assume that SOA facets reflectivity is negligible and that all the injected current contributes completely to the population inversion in the active zone. We also assume that transverse effects are negligible, since carrier scattering length is much longer than waveguide size and, thus, carrier density is uniform in transverse cross-sections. We give in Table 1 the constant modeling parameters which have been used.
3. Gain dynamics and noise transmission analysis In this part, the injected pump pulse duration is 2.1 ps. 3.1. Gain dynamics analysis 3.1.1. The injected probe power is the same for both SOA In Fig. 2(a), we plot the single and double-stage wavelength converter output normalized probe power versus time. The pump power is 3 dBm and the probe power is 10 dBm. To simplify the analysis, A is adjusted in order to get the same injected probe power in each SOA. We see that gain compression is increasing with the number of SOA. To model this feature, we look for the multi-stage gain function. Let us write G(Ps,1, Pp) as the first SOA gain which depends on the pump power Pp and on the injected probe power Ps,1. Then, the probe pulse at the entrance of the second SOA is P s;2 ¼ P s;1 AGðP s;1 ; P p Þ
ð1Þ
so the double-stage gain seen by the injected probe Ps,1 will be G(Ps,1, Pp)AG(Ps,2, Pp). This product gain function explains as to why in Fig. 2(a), the
Table 1 Parameters used in the model SOA length: 1170 lm Rectangular guide: 0.5 · 0.4 lm2 Injected current: I = 278 mA Probe wavelength: 1530 nm Pump wavelength: 1540 nm
Confinement factor: C = 0.5 Peak gain wavelength value: 1540 nm Auger recombination coefficient: C = 4 · 1029 cm6 s1 Spontaneous recombination coefficient: B = 1.2 · 109 cm3 s1
F. Ginovart, J.C. Simon / Optics Communications 241 (2004) 391–397
Fig. 2. Single and double stage output normalized probe power versus time. The probe power injected into each SOA is: (a) 10 and (b) 0 dBm. The pump power is 3 dBm. The attenuation A is: (a) 27.4 and (b) 18.9 dB.
gain compression is much more important when increasing the SOA number in the device. Let us see why gain recovery is faster when increasing the SOA number in the device. When the pump is crossing the second SOA, the gain is depleted and if the pump arrival is synchronized with the probeÕs one, the probe extinction ratios are multiplied. The differences between the dynamics occurring in the first and second SOA are only due to the probe power. In effect, let us recall that in our analysis, all SOA are identical and the injected pump is the same for both SOA. After the pump crossing, the ASE and carrier density are depleted. At this time, the second SOA sees a probe power increasing from its bottom value due to the first SOA gain compression to its steady-state value. The attenuation A is adjusted so that the probe steady state value is 10 dBm. So, the second SOA experiences a probe power much weaker than the first SOA which sees a constant probe power (10 dBm). Thus, there is a competition between gain recovery and carrier density depletion due to the probe in the first SOA. On the other hand, as the probe power is much weaker in the second SOA, the carrier density is less depleted and the spontaneous emission can be amplified quicklier boosting in turn the carrier density recovery [10,11]. As a matter of fact, we can notice that
393
the slope of the probe in the recovery process is sharper when using two SOA. In Fig. 2(b), the two SOA output normalized probe powers versus time are plotted when the probe power is 0 dBm. When increasing the probe power, the gain is compressed and so the pump sees less gain. Since its power has not been increased, the gain compression becomes lower: pump and probe waves are in competition. In Fig. 3, the gain recovery time versus injected probe power is plotted for different injected pump powers. Here, we define the gain recovery time as the time difference between the two times corresponding to 10% and 90% steady-state gain values above the bottom gain value. The injected probe power is the same for both SOA. As expected, the gain recovery time is shortening when increasing the injected probe power. This is due to the fact that the effective carrier lifetime depends also on the stimulated emission rate induced by the probe power. For a given injected probe power, when increasing pump power, gain recovery time is increasing since gain compression is higher, e.g., carrier density and ASE are more depleted. From Fig. 3, we see that short gain recovery time, suitable for high-speed all-optical regeneration, corresponds to a relatively strong injected probe
Fig. 3. Gain recovery time versus injected probe power for different injected pump powers. The injected probe power is the same for both SOA. The dashed and solid lines correspond, respectively, to the single and double stage.
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power in a double-stage wavelength converter. However, the probe power should always be less than the pump power in order to have a significant gain compression and for the gain recovery time to benefit from the double-stage configuration. 3.1.2. The injected probe powers are different for both SOA On Fig. 4, we plot the single and double stage wavelength converter output normalized probe power versus time when the injected probe power varies between the first and second SOA. Like above, since the pump and the probe waves are in competition, the gain compression is lower when using a stronger probe power. In Fig. 5, double stage gain recovery time versus second SOA injected probe power is plotted when considering three 1st SOA injected probe powers: 30, 3 and 0 dBm. We can see that for weak second SOA injected probe powers (roughly less than 10 dBm), there is no striking difference. In effect, in this case the probe injected into the second SOA is weak, thus there is no competition between gain recovery and carrier density depletion. But for higher probe powers (more than 5 dBm), the probe power is strong enough to deplete carrier density. In this case, the bottom value due to the
Fig. 5. Double stage SOA gain rise time versus second SOA injected probe power.
first SOA gain compression explains the difference appearing between very weak injected probe powers (30 dBm corresponding to a small-signal regime) and stronger probe powers which compress the SOA gain (3 and 0 dBm). So, a short double-stage gain recovery time is obtained for a relatively strong first and second SOA injected probe power. 3.2. Noise transmission analysis
Fig. 4. Single and double output normalized probe power versus time. The probe power injected into the first SOA is 3 dBm, into the second SOA: (a) 10 and (b) 0 dBm. The pump power is 3 dBm. The attenuation A is: (a) 28.5 and (b) 18.7 dB.
In Fig. 6(a) is plotted the transmission of the device against the input pump power for the three stages. As expected, the slope of the transmission function becomes steeper as the number of SOA increases which leads to a better device for all-optical regeneration purposes. In effect, a noisy input signal whose Ô0Õ bit power is below 20 dBm and whose Ô1Õ bit power is above 0 dBm will be transformed in a signal with no noise on the the Ô1Õ: the noise on the input Ô0Õ bit is cancelled, thanks to the saturation of the transmission for weak input power. Since there is no saturation for high input power, the noise on the input Ô1Õ bit will be transformed into a noise on the output Ô0Õ bit. Nevertheless, the steeper the transmission, the more reduced will be the amplitude of this transformed noise. In Fig. 6(b), the noise transmission factor defined as
F. Ginovart, J.C. Simon / Optics Communications 241 (2004) 391–397
Fig. 6. Transmission and noise transmission factor versus input power. The dashed and solid lines correspond, respectively, to the single and double stage.
NTF ¼
P in dT T ðP in Þ dP in
ð2Þ
is plotted. T stands for the transmission function and Pin for the input pump power. This factor characterizes the noise transmission, since an input power Pin with a noise dPin will be transformed into an output power transmission factor T(Pin) with a transformed noise dT [6]. A good nonlinear gate is notably characterized by |NTF| < 1. Thus, increasing the SOA number leads to deterioration of the NTF. So, a careful choice of the input power has to be done in order to get a good double-stage.
4. NRZ signal wavelength conversion analysis Next, we consider the 10 Gbits/s NRZ sequence 110100101101011. Each bit has its maximum or minimum power varying around an average value, the amplitude of fluctuations does not exceed 10%. In Fig. 7 we plot the input sequence and single and double-stage wavelength converters output sequences. We observe that the extinction ratio is better when increasing the SOA number in the double-stage wavelength converter. It is not surprising since it has been observed in the previous part with a single pulse. So, this feature can be well understood with the double-stage gain function. In
395
Fig. 7. Input pump power versus time with 6 dB of extinction ratio (up). Output probe power versus time when the injected probe power is 500 lW in each SOA (down). The dashed and solid lines correspond respectively to the single and double stage. The attenuation A is 21.9 dB.
effect, let us write GðP s;1 ; P ip Þ as the single SOA gain which depends on the ÔiÕ pulse (Ô1Õ or Ô0Õ) of the pump power Pp and on the injected probe power Ps,1. Then, the probe Ô1Õ and Ô0Õ bits at the entrance of the second SOA are ( 1 P s;3 ¼ P s;1 AGðP s;1 ; P 0p Þ; ð3Þ P 0s;3 ¼ P s;1 AGðP s;1 ; P 1p Þ; and the double-stage gain seen by the injected probe gain Ps,1 will be for a Ô0Õ bit GðP s;1 ; P 1p ÞAGðP 0s;2 ; P 1p Þ and GðP s;1 ; P 0p ÞAGðP 1s;2 ; P 0p Þ for a Ô1Õ bit. A product gain function is obtained and explains the better extinction ratio improvement when increasing the SOA number in the doublestage device. In Fig. 8, we have plotted the single and doublestage output normalized (with respect to its bottom value) probe power corresponding to Fig. 7 versus time. Since the input extinction ratio is 6 dB, we immediately see that, as it is known, a single SOA does not improve the extinction ratio and that the double-stage device leads to a quite good extinction ratio improvement. Let us look now at the pump and probe powers influence on the extinction ratio improvement when varying the input extinction ratio. In Figs.
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9 and 10, single and double-stage output sequence extinction ratio variations are plotted against input extinction ratio. In Fig. 9, we let the injected pump power vary while keeping fixed the injected probe power to 0.5 mW. The injected pump powers are set to 0.25, 0.5, 1 and 2 mW. When the pump power is increasing, the carrier density depletion is more
important thus leading to a higher gain compression which in turn gives a better extinction ratio. And in effect, we see that whatever the SOA number is, the extinction ratio is increasing with the pump power. Of course, as it has already been shown, the more SOA in the device, the better the extinction ratio. We also notice a saturation effect with respect to the input extinction ratio, depending on the pump power. In Fig. 10, the injected probe power is varying with a fixed injected pump power. The probe powers are set to 1 lW, 0.1, 0.5 and 1 mW with a pump power of 0.5 mW. We see once more that increasing the SOA number leads to get a higher output extinction ratio. We also notice that increasing probe power lets the output extinction ratio improvement to decrease. In effect, as we have already seen in Fig. 2, increasing injected probe power leads to gain compression decreasing since the probe and pump waves are in competition. Once again, we also notice the saturation effect with respect to the input extinction ratio, depending on the ratio between pump and probe powers. It is clear that the double-stage device allows both high speed and good extinction ratio opera-
Fig. 9. Extinction ratio variations when the injected probe power is 0.5 mW in each SOA. The dashed and solid lines correspond, respectively, to the single and double stage. The attenuation A is 21.9 dB.
Fig. 10. Extinction ratio variations when the injected pump power is 0.5 mW. The dashed and solid lines correspond, respectively, to the single and double stage. The attenuation A is: (a) 5.5, (b) 20.8, (c) 21.9 and (d) 22.1 dB.
Fig. 8. Output normalized probe power versus time corresponding to Fig. 7.
F. Ginovart, J.C. Simon / Optics Communications 241 (2004) 391–397
tion depending on the pump and probe power as well as the input extinction ratio.
5. Conclusion We have presented a theoretical analysis of a SOA double-stage wavelength converter in comparison with a single stage. We have shown how this wavelength converter can improve characteristics which are important for high-speed all-optical wavelength conversion: gain recovery time can reach a few ps when increasing the SOA number in the device. The counterpart of adding SOA is to get a stronger noise transmission factor on the output Ô0Õ symbols: a trade-off has to be done and a careful choice of pump and probe powers is needed. Studying a 10 Gbit/s NRZ sequence, we have also shown that a great extinction ratio improvement can be obtained. For a realistic range of input extinction ratio between 6 and 8 dB, we have seen that an improvement of around 7 dB for a double-stage can be reached. Finally, we have shown that the multi-stage wavelength converter with accurate choice of the different parameters can be used as an all-optical 2R extinction ratio regenerator.
397
Acknowledgments This work was supported by Ministe`re de la Recherche et des Nouvelles Technologies, Conseil Re´gional de Bretagne, and FEDER.
References [1] C. Janz, OFCÕ00, Baltimore, MD, USA, 7–10 March 2000. [2] K.E. Stubkjaer, IEEE J. Select. Top. Quantum Electron. 6 (2000) 1428. [3] A. Hamie´, A. Sharaiha, M. Gue´gan, B. Pucel, IEEE PTL 14 (2002) 1439. [4] J.H. Kim, K.R. Oh, H.S. Kim, K. Cho, IEEE PTL 12 (2000) 513. [5] J. Yu, X. Zheng, P. Jeppesen, Opt. Commun. 178 (2000) 309. [6] D. Wolfson, IEEE Photon. Technol. Lett. 11 (1999) 1494. [7] J. Yu, P. Jeppesen, J. Lightwave Technol. 19 (2001) 614. [8] A. Sharaiha, A. Hamie, J. Lightwave Technol. 22 (2004) 850. [9] J.C. Simon, L. Lablonde, I. Valiente, L. Bille`s, P. Lamouler, OFCÕ95, San-Jose, USA, 1995, Postdeadline paper PD15-2. [10] F. Ginovart, J.C. Simon, I. Valiente, Opt. Commun. 199 (2001) 111. [11] F. Ginovart, J.C. Simon, J. Opt. A 4 (2002) 283. [12] S.L. Chuang, J. OÕGorman, A.F.J. Levi, IEEE J. Quantum Electron. 29 (1993) 1631.
Analysis of semiconductor optical amplifier based double-stage all-optical wavelength converter with improved extinction ratio F. Ginovart *, J.C. Simon Groupement dÕInte´reˆt Scientifique ÔFOTONÕ, Laboratoire dÕOptronique, Ecole Nationale Supe´rieure de Sciences Applique´es et de Technologie, CNRS/UMR 6082, 6 rue de Ke´rampont, 22305 Lannion, France Received 5 March 2004; received in revised form 11 July 2004; accepted 21 July 2004
Abstract We theoretically study the temporal dynamics of a semiconductor optical amplifier (SOA) based double-stage wavelength converter in co-propagative configuration. The impact of the SOA number in the device is analyzed. In this work, we are concerned with the gain recovery time shortening while keeping a low level of noise. We also study the pump and probe power influence on a 10 Gbit/s NRZ sequence output extinction ratio and undertake a systematic study when varying the input extinction ratio. 2004 Elsevier B.V. All rights reserved. Keywords: Semiconductor optical amplifier; All-optical regeneration
1. Introduction Semiconductor optical amplifier (SOA) will be a key element in future all-optical networks, thanks to its properties. SOA gain saturation effects are used in numerous all-optical processing applications based on cross-gain and cross-phase modulations such as wavelength conversion, switching
*
Corresponding author. Fax: +33296370199. E-mail address: [email protected] (F. Ginovart).
and pulse regeneration [1,2]. Also, SOA based devices, and in particular cascaded SOA, have been studied with different configurations [2–9]. Here, we theoretically analyze a SOA based double-stage wavelength converter in co-propagative configuration. Its sketch is pictured in Fig. 1. The principle of operation consists of injecting the pump simultaneously in all amplifiers, while the cw probe crosses the amplifiers in series. The injected pump into the second stage SOA is in phase with the probe output of the first stage SOA. In this way, the extinction ratios of the converted
0030-4018/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.07.050
392
F. Ginovart, J.C. Simon / Optics Communications 241 (2004) 391–397
Pump (data)
Probe (CW)
SOA 2
SOA 1 A
Fig. 1. Sketch of the SOA double stage wavelength converter.
signal are multiplied. The second SOA injected probe power is adjusted, thanks to a variable attenuator (attenuation: A). In our calculations, the filter is supposed to be perfect and only the probe is injected into the second SOA. So, amplified spontaneous emission (ASE) effects are only taken into account in the dynamics of each SOA. After briefly describing the temporal SOA gain dynamics model, we study the double-stage SOA gain dynamics to give an understanding analysis of the influence of the SOA number in the device on the gain recovery and show the conditions which allow to shorten it while keeping a low level of noise. For this purpose, we study the noise transmission of the device. Next, we consider a 10 Gbit/s NRZ sequence. The analysis of the influence of the injected pump and probe power on its extinction ratio is undertaken. This study shows how the SOA based double-stage can be used as an all-optical 2R regenerator.
2. SOA model A temporal SOA gain dynamics model including pump and probe propagation, as well as amplified forward and backward spontaneous emission has been presented in [10,11]. Material gain and
spontaneous emission are calculated from [12]. Both double stage SOA are identical. Here, we assume that SOA facets reflectivity is negligible and that all the injected current contributes completely to the population inversion in the active zone. We also assume that transverse effects are negligible, since carrier scattering length is much longer than waveguide size and, thus, carrier density is uniform in transverse cross-sections. We give in Table 1 the constant modeling parameters which have been used.
3. Gain dynamics and noise transmission analysis In this part, the injected pump pulse duration is 2.1 ps. 3.1. Gain dynamics analysis 3.1.1. The injected probe power is the same for both SOA In Fig. 2(a), we plot the single and double-stage wavelength converter output normalized probe power versus time. The pump power is 3 dBm and the probe power is 10 dBm. To simplify the analysis, A is adjusted in order to get the same injected probe power in each SOA. We see that gain compression is increasing with the number of SOA. To model this feature, we look for the multi-stage gain function. Let us write G(Ps,1, Pp) as the first SOA gain which depends on the pump power Pp and on the injected probe power Ps,1. Then, the probe pulse at the entrance of the second SOA is P s;2 ¼ P s;1 AGðP s;1 ; P p Þ
ð1Þ
so the double-stage gain seen by the injected probe Ps,1 will be G(Ps,1, Pp)AG(Ps,2, Pp). This product gain function explains as to why in Fig. 2(a), the
Table 1 Parameters used in the model SOA length: 1170 lm Rectangular guide: 0.5 · 0.4 lm2 Injected current: I = 278 mA Probe wavelength: 1530 nm Pump wavelength: 1540 nm
Confinement factor: C = 0.5 Peak gain wavelength value: 1540 nm Auger recombination coefficient: C = 4 · 1029 cm6 s1 Spontaneous recombination coefficient: B = 1.2 · 109 cm3 s1
F. Ginovart, J.C. Simon / Optics Communications 241 (2004) 391–397
Fig. 2. Single and double stage output normalized probe power versus time. The probe power injected into each SOA is: (a) 10 and (b) 0 dBm. The pump power is 3 dBm. The attenuation A is: (a) 27.4 and (b) 18.9 dB.
gain compression is much more important when increasing the SOA number in the device. Let us see why gain recovery is faster when increasing the SOA number in the device. When the pump is crossing the second SOA, the gain is depleted and if the pump arrival is synchronized with the probeÕs one, the probe extinction ratios are multiplied. The differences between the dynamics occurring in the first and second SOA are only due to the probe power. In effect, let us recall that in our analysis, all SOA are identical and the injected pump is the same for both SOA. After the pump crossing, the ASE and carrier density are depleted. At this time, the second SOA sees a probe power increasing from its bottom value due to the first SOA gain compression to its steady-state value. The attenuation A is adjusted so that the probe steady state value is 10 dBm. So, the second SOA experiences a probe power much weaker than the first SOA which sees a constant probe power (10 dBm). Thus, there is a competition between gain recovery and carrier density depletion due to the probe in the first SOA. On the other hand, as the probe power is much weaker in the second SOA, the carrier density is less depleted and the spontaneous emission can be amplified quicklier boosting in turn the carrier density recovery [10,11]. As a matter of fact, we can notice that
393
the slope of the probe in the recovery process is sharper when using two SOA. In Fig. 2(b), the two SOA output normalized probe powers versus time are plotted when the probe power is 0 dBm. When increasing the probe power, the gain is compressed and so the pump sees less gain. Since its power has not been increased, the gain compression becomes lower: pump and probe waves are in competition. In Fig. 3, the gain recovery time versus injected probe power is plotted for different injected pump powers. Here, we define the gain recovery time as the time difference between the two times corresponding to 10% and 90% steady-state gain values above the bottom gain value. The injected probe power is the same for both SOA. As expected, the gain recovery time is shortening when increasing the injected probe power. This is due to the fact that the effective carrier lifetime depends also on the stimulated emission rate induced by the probe power. For a given injected probe power, when increasing pump power, gain recovery time is increasing since gain compression is higher, e.g., carrier density and ASE are more depleted. From Fig. 3, we see that short gain recovery time, suitable for high-speed all-optical regeneration, corresponds to a relatively strong injected probe
Fig. 3. Gain recovery time versus injected probe power for different injected pump powers. The injected probe power is the same for both SOA. The dashed and solid lines correspond, respectively, to the single and double stage.
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power in a double-stage wavelength converter. However, the probe power should always be less than the pump power in order to have a significant gain compression and for the gain recovery time to benefit from the double-stage configuration. 3.1.2. The injected probe powers are different for both SOA On Fig. 4, we plot the single and double stage wavelength converter output normalized probe power versus time when the injected probe power varies between the first and second SOA. Like above, since the pump and the probe waves are in competition, the gain compression is lower when using a stronger probe power. In Fig. 5, double stage gain recovery time versus second SOA injected probe power is plotted when considering three 1st SOA injected probe powers: 30, 3 and 0 dBm. We can see that for weak second SOA injected probe powers (roughly less than 10 dBm), there is no striking difference. In effect, in this case the probe injected into the second SOA is weak, thus there is no competition between gain recovery and carrier density depletion. But for higher probe powers (more than 5 dBm), the probe power is strong enough to deplete carrier density. In this case, the bottom value due to the
Fig. 5. Double stage SOA gain rise time versus second SOA injected probe power.
first SOA gain compression explains the difference appearing between very weak injected probe powers (30 dBm corresponding to a small-signal regime) and stronger probe powers which compress the SOA gain (3 and 0 dBm). So, a short double-stage gain recovery time is obtained for a relatively strong first and second SOA injected probe power. 3.2. Noise transmission analysis
Fig. 4. Single and double output normalized probe power versus time. The probe power injected into the first SOA is 3 dBm, into the second SOA: (a) 10 and (b) 0 dBm. The pump power is 3 dBm. The attenuation A is: (a) 28.5 and (b) 18.7 dB.
In Fig. 6(a) is plotted the transmission of the device against the input pump power for the three stages. As expected, the slope of the transmission function becomes steeper as the number of SOA increases which leads to a better device for all-optical regeneration purposes. In effect, a noisy input signal whose Ô0Õ bit power is below 20 dBm and whose Ô1Õ bit power is above 0 dBm will be transformed in a signal with no noise on the the Ô1Õ: the noise on the input Ô0Õ bit is cancelled, thanks to the saturation of the transmission for weak input power. Since there is no saturation for high input power, the noise on the input Ô1Õ bit will be transformed into a noise on the output Ô0Õ bit. Nevertheless, the steeper the transmission, the more reduced will be the amplitude of this transformed noise. In Fig. 6(b), the noise transmission factor defined as
F. Ginovart, J.C. Simon / Optics Communications 241 (2004) 391–397
Fig. 6. Transmission and noise transmission factor versus input power. The dashed and solid lines correspond, respectively, to the single and double stage.
NTF ¼
P in dT T ðP in Þ dP in
ð2Þ
is plotted. T stands for the transmission function and Pin for the input pump power. This factor characterizes the noise transmission, since an input power Pin with a noise dPin will be transformed into an output power transmission factor T(Pin) with a transformed noise dT [6]. A good nonlinear gate is notably characterized by |NTF| < 1. Thus, increasing the SOA number leads to deterioration of the NTF. So, a careful choice of the input power has to be done in order to get a good double-stage.
4. NRZ signal wavelength conversion analysis Next, we consider the 10 Gbits/s NRZ sequence 110100101101011. Each bit has its maximum or minimum power varying around an average value, the amplitude of fluctuations does not exceed 10%. In Fig. 7 we plot the input sequence and single and double-stage wavelength converters output sequences. We observe that the extinction ratio is better when increasing the SOA number in the double-stage wavelength converter. It is not surprising since it has been observed in the previous part with a single pulse. So, this feature can be well understood with the double-stage gain function. In
395
Fig. 7. Input pump power versus time with 6 dB of extinction ratio (up). Output probe power versus time when the injected probe power is 500 lW in each SOA (down). The dashed and solid lines correspond respectively to the single and double stage. The attenuation A is 21.9 dB.
effect, let us write GðP s;1 ; P ip Þ as the single SOA gain which depends on the ÔiÕ pulse (Ô1Õ or Ô0Õ) of the pump power Pp and on the injected probe power Ps,1. Then, the probe Ô1Õ and Ô0Õ bits at the entrance of the second SOA are ( 1 P s;3 ¼ P s;1 AGðP s;1 ; P 0p Þ; ð3Þ P 0s;3 ¼ P s;1 AGðP s;1 ; P 1p Þ; and the double-stage gain seen by the injected probe gain Ps,1 will be for a Ô0Õ bit GðP s;1 ; P 1p ÞAGðP 0s;2 ; P 1p Þ and GðP s;1 ; P 0p ÞAGðP 1s;2 ; P 0p Þ for a Ô1Õ bit. A product gain function is obtained and explains the better extinction ratio improvement when increasing the SOA number in the doublestage device. In Fig. 8, we have plotted the single and doublestage output normalized (with respect to its bottom value) probe power corresponding to Fig. 7 versus time. Since the input extinction ratio is 6 dB, we immediately see that, as it is known, a single SOA does not improve the extinction ratio and that the double-stage device leads to a quite good extinction ratio improvement. Let us look now at the pump and probe powers influence on the extinction ratio improvement when varying the input extinction ratio. In Figs.
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9 and 10, single and double-stage output sequence extinction ratio variations are plotted against input extinction ratio. In Fig. 9, we let the injected pump power vary while keeping fixed the injected probe power to 0.5 mW. The injected pump powers are set to 0.25, 0.5, 1 and 2 mW. When the pump power is increasing, the carrier density depletion is more
important thus leading to a higher gain compression which in turn gives a better extinction ratio. And in effect, we see that whatever the SOA number is, the extinction ratio is increasing with the pump power. Of course, as it has already been shown, the more SOA in the device, the better the extinction ratio. We also notice a saturation effect with respect to the input extinction ratio, depending on the pump power. In Fig. 10, the injected probe power is varying with a fixed injected pump power. The probe powers are set to 1 lW, 0.1, 0.5 and 1 mW with a pump power of 0.5 mW. We see once more that increasing the SOA number leads to get a higher output extinction ratio. We also notice that increasing probe power lets the output extinction ratio improvement to decrease. In effect, as we have already seen in Fig. 2, increasing injected probe power leads to gain compression decreasing since the probe and pump waves are in competition. Once again, we also notice the saturation effect with respect to the input extinction ratio, depending on the ratio between pump and probe powers. It is clear that the double-stage device allows both high speed and good extinction ratio opera-
Fig. 9. Extinction ratio variations when the injected probe power is 0.5 mW in each SOA. The dashed and solid lines correspond, respectively, to the single and double stage. The attenuation A is 21.9 dB.
Fig. 10. Extinction ratio variations when the injected pump power is 0.5 mW. The dashed and solid lines correspond, respectively, to the single and double stage. The attenuation A is: (a) 5.5, (b) 20.8, (c) 21.9 and (d) 22.1 dB.
Fig. 8. Output normalized probe power versus time corresponding to Fig. 7.
F. Ginovart, J.C. Simon / Optics Communications 241 (2004) 391–397
tion depending on the pump and probe power as well as the input extinction ratio.
5. Conclusion We have presented a theoretical analysis of a SOA double-stage wavelength converter in comparison with a single stage. We have shown how this wavelength converter can improve characteristics which are important for high-speed all-optical wavelength conversion: gain recovery time can reach a few ps when increasing the SOA number in the device. The counterpart of adding SOA is to get a stronger noise transmission factor on the output Ô0Õ symbols: a trade-off has to be done and a careful choice of pump and probe powers is needed. Studying a 10 Gbit/s NRZ sequence, we have also shown that a great extinction ratio improvement can be obtained. For a realistic range of input extinction ratio between 6 and 8 dB, we have seen that an improvement of around 7 dB for a double-stage can be reached. Finally, we have shown that the multi-stage wavelength converter with accurate choice of the different parameters can be used as an all-optical 2R extinction ratio regenerator.
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Acknowledgments This work was supported by Ministe`re de la Recherche et des Nouvelles Technologies, Conseil Re´gional de Bretagne, and FEDER.
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