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The global analysis for an all-optical gain-clamped L-band erbium-doped fiber amplifier using a single fiber Bragg grating
Optics Communications 224 (2003) 73–80 www.elsevier.com/locate/optcom
The global analysis for an all-optical gain-clamped L-band erbium-doped fiber amplifier using a single fiber Bragg grating Zexuan Qiang *, Xiang Wu, Sailing He, Zukang Lu State Key Laboratory for Modern Optical Instrumentation, Department of Optical Engineering, Zhejiang University, Hangzhou 310027, PR China Received 9 January 2003; received in revised form 15 May 2003; accepted 2 July 2003
Abstract Based on the Giles model with ASE, modeling for all-optical gain-clamped L-band EDFA using a single fiber Bragg grating (FBG) is built. The influence of the configuration, the pump wavelength, the Bragg wavelength, the reflectivity, the length of erbium doped fiber (EDF) and the pump power to the gain-clamped characteristics is studied. Finally, a set of parameters for a gain-clamped L-band EDFA with flat-gain band is given. Ó 2003 Published by Elsevier B.V. PACS: 42.55.Wd; 42.60.Da; 42.81.)i Keywords: Erbium doped fiber amplifier; L-band; All-optical gain clamped; Fiber grating; Gain
1. Introduction The L-band erbium-doped fiber amplifiers (EDFAs) have attracted much attention [1–4] since they can effectively increase the transmission bandwidth from the conventional C band to the 1570–1605 nm range. In addition to wider operation, EDFAs also need gain control because they are sensitive to transient cross saturation induced by random bursts and signal add/drops under
*
Corresponding author. Tel.: +8657187951185; +8657187951214. E-mail address: [email protected] (Z. Qiang).
fax:
0030-4018/$ - see front matter Ó 2003 Published by Elsevier B.V. doi:10.1016/S0030-4018(03)01723-1
network reconfiguration. Recently, Harun et al. [5] experimentally proposed a new all-optical gainclamping method using a single fiber Bragg grating (FBG). There may exist other possible configurations, which have not been studied. Some commercially available simulators do not work well in L-band. Therefore, it is necessary to investigate this new EDFA in more details. In this paper, we study gain-clamped capability, effects of various configurations, pumping wavelength, Bragg wavelength, reflectivity, and the length of EDF on the EDFA performances. An optimal L-band gain-clamped EDFA configuration and amplifier parameters, which can provide a flat-gain band simultaneously, are proposed through a numerical simulation.
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The paper is organized as follows: In Section 2 the four basic configurations of all-optical gainclamped L-band EDFA using a single FBG are presented and the mathematical models based on the two-level model of Giles and Desurvire are described. Gain-clamped capabilities and the different EDFA parameters are numerically analyzed and discussed in Section 3. We discuss the effect of signal add/drop from network reconfiguration in Section 4. Finally, the paper is summarized and the optimal EDFA configuration with the corresponding optimal parameters is presented in Section 5.
2. Theoretical modeling 2.1. EDFA configurations In general, there are three kinds of pumping schemes, such as forward pumping, backward pumping and bi-directional pumping. The former two pumping schemes are considered only in this paper in order to make the structure more compact. Four basic assembled configurations are configured for the all-optical gain-clamped L-band EDFA using a single FBG as shown in Fig. 1.
Fig. 1(a) shows the structure reported in [5], in which a portion of the backward ASE is reflected. Fig. 1(b) corresponds to the case, in which a portion of the forward ASE is reflected. The structures using backward pumping are shown in Figs. 1(c) and (d). Fig. 1(c) corresponds to the case, in which a portion of the backward ASE is reflected. Fig. 1(d) corresponds to the case, in which a portion of the forward ASE is reflected. 2.2. Model The gain-clamped EDFA pumped by 980 or 1480 nm laser can be modeled as the two-level model of Giles and Desurvire [6]. According to the two-level model of with ASE, the propagation equation for each light field (with index k) is dPk ðzÞ n2 n2 ¼ uk ðak þ gk Þ Pk ðzÞ þ uk gk mhvk Dvk dz nt nt uk ðak þ lk ÞPk ðzÞ; ð1Þ where Pk ðzÞ is the light power at position z in the frequency bandwidth Dvk , Dvk equals the frequency step which is about 125 GHz for the spectral bandwidth of 1 nm, uk is +1 for a forwardpropagating field and )1 for a backward-propagating field, ak , gk , and lk represent the spectral attenuation, gain and background loss of the considered EDF, respectively, and the factor m equals 2 due to the two polarization states of the lowest order mode. The population ratio n2 =nt for the upper energy level is P n2 ððP þ ðzÞ þ Pk ðzÞÞak =hvk fÞ P k þk ; ¼ nt 1 þ k ððPk ðzÞ þ Pk ðzÞÞðak þ gk Þ=hvk fÞ ð2Þ Pksat ðak
gk Þ=hvk
where f ¼ þ is the saturation parameter which can be obtained from a measurement of the fiber saturation power. Note that only the splice loss (SL) for the reflected light by fiber Bragg grating is considered. The boundary conditions for all-optical gainclamped EDFA using a single fiber Bragg grating can be expressed as Fig. 1. Various possible configurations for a gain-clamped L-band EDFA with a single fiber Bragg grating.
Psþ ð0Þ ¼ Pin ; Pkþ ð0Þ ¼ 0; Pk ðLÞ ¼ 0 ðk 6¼ s; k 6¼ f Þ
ð3Þ
Z. Qiang et al. / Optics Communications 224 (2003) 73–80 2
2
Pfþ ð0Þ ¼ Pf ð0ÞRð1 l1 Þ ð1 l2 Þ ;
Pf ðLÞ ¼ 0; ð4Þ
or Pfþ ð0Þ ¼ 0;
2
2
Pf ðLÞ ¼ Pfþ ðLÞRð1 l1 Þ ð1 l2 Þ ; ð5Þ
where L is the length of erbium-doped fiber, R the reflectivity of fiber Bragg grating, l1 the SL between FBG and WDM, l2 the SL between the FBG and the EDF or that between the WDM and the EDF, Pf the power of lasing light, and Ps the power of signal light. It should be noted that Eq. (4) is the boundary condition for the configurations (a) and (c), Eq. (5) is the boundary condition for configurations (b) and (d), and l1 equals 0 for configurations (b) and (c). The signal noise figure and gain are defined by 1 PASE NF ¼ 10 log10 þ ; ð6Þ G hv G Dv G ¼ 10 log10 ðPsignal-out =Psignal-in Þ ððPsignal-out þ PASE Þ PASE Þ ¼ 10 log10 ; ð7Þ Psignal-in where h is PlanckÕs constant, v is the optical frequency, PASE is the ASE power measured in the bandwidth Dv. According to Eqs. (1), (2), (6), (7) and the corresponding boundary conditions, the gain and noise figure of all-optical gain-clamped Lband EDFA using a single FBG can be evaluated. A commercial erbium doped fiber (type: MP 980) is used in our simulation. The absorption and emis-
Fig. 2. Wavelength dependence of a and g used in the simulation.
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sion spectra are shown in Fig. 2. The other parameters for the EDFs are set as follows: cutoff wavelength kc ¼ 842 nm, absorption coefficient að980 nmÞ ¼ 4:57 dB/m, emission coefficient g ð980 nmÞ ¼ 0 dB/m, að1530 nmÞ ¼ 5:86 dB/m, background loss l ¼ 0:91 dB/km, and bandwidth Dv ¼ 125 GHz.
3. Calculation result and discussion 3.1. The influence of configurations and pump wavelengths An important parameter to estimate the gainclamped capability is the critical input power Pc , which is corresponding to the amplifier gain drop 0.2 dB from the maximum small signal gain. The gain-clamped capability is getting better with increasing Pc . The area, where the input power is less than the critical maximum input power, is defined as gain-clamped area. EDFAs can be well pumped by 980 or 1480 nm laser without excited state absorption (ESA). So, it is very important to choose an optimal structure and the corresponding pumping wavelength. Fig. 3 shows the relationship of the gain and noise figure as the input signal power increases for various configurations and pump wavelengths, where the length, L, is 50 m, the lasing wavelength, kf , is 1555 nm, the reflectivity of FBG, R, is 99%, the signal wavelength, ks , is 1570 nm, the loss, l1 , is 0.02 dB and l2 is 0.13 dB, and the pump power, Pp , is 120 mW. In Fig. 3(a), curve 1 describes the gain of configuration (a) pumped by 980 nm lasers. Pc1 is the critical input signal power for configuration (a) pumped by 980 nm lasers. The other curves and the corresponding critical input powers are characterized similar to the above. Figs. 3(a) and (b) show the relationships between the gain and the input signal power when the pump wavelengths, kp , are 980 and 1480 nm, respectively. Figs. 3(c) and (d) show the relationship between the noise figure and the input signal power when the pump wavelengths are 980 and 1480 nm, respectively. In Fig. 3(a), the simulation result shows that the gains are clamped with larger input power for structures (a) and (d). These
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Fig. 3. Gain or noise figure for various pump wavelength and fiber Bragg grating location.
simulation results are found to be in good agreement with the experimental ones in [5]. The modeling can be used to analyze the influence on gain-clamped capability for the other structures and the parameters such as reflectivity of FBG, Bragg wavelength, length of EDF, pump power and pump wavelength. As shown in Figs. 3(a) and (b), it is clear that the maximum critical input power Pc , whether the pump wavelength is 980 or 1480 nm, can be obtained by the configuration (d). In Figs. 3(c) and (d), the noise figures of the configurations (c) and (d) are more than 8.3 dB. They cannot satisfy the requirement for DWDM systems since the typical value of the noise figure for communication is 5 dB. Therefore, the configurations (c) and (d) are not suitable for DWDM systems and they will not be taken into account in the following discussion. In the gain-clamped area, the gain of configuration (b) is always higher than
that of configuration (a) whether the pump wavelength is 980 nm or 1480 nm, as shown in Figs. 3(a) and (b). The noise figure of structure (b) is larger than that of structure (a) with evident ripple, whether the pump wavelength is 980 or 1480 nm. It should be noted that the noise figure of configuration (b) pumped by 1480 nm laser is larger than 5 dB, which cannot satisfy the system requirement. In addition, the critical input signal power Pc of configuration (a) pumped by 1480 nm laser and the corresponding gain are larger than those of configuration (a) pumped by 980 nm laser, of which the noise figure is a bit larger. At the gainclamped area, the noise figure of configuration (a) pumped by 1480 nm laser keeps at a constant level less than 4.2 dB, which can satisfy the requirement for system communication. As discussed above, the large gain and low noise with large Pc can be obtained using configuration
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(a) pumped by 1480 nm laser. Therefore, only this configuration is considered in the following discussion.
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gain is the smallest. Due to the fairly large critical input power and gain, the case of 1562-nm Bragg wavelength is investigated in the following discussions.
3.2. The influence of Bragg wavelength of fiber Bragg grating
3.3. The influence of reflectivity of fiber grating
The gain and noise figure, as the input signal power increases for various Bragg wavelengths, are shown in Fig. 4, where L is 50 m, R is 99%, Pp is 120 mW, ks is 1570 nm, and the loss is the same as in the above discussion and fixed in the following discussion. It is shown that the gain of EDFA cannot be clamped when kf < 1535 nm or kf ¼ 1610 nm. In addition, the small signal gain with Bragg gratings at 1535 nm is larger than those at 1525 and 1610 nm, since the a and g at 1535 nm is larger than those at 1525 and 1610 nm. The critical input power increases with increasing the Bragg wavelength, i.e., Pc;1535 < Pc;1550 < Pc;1555 < Pc;1565 . The difference between Pc;1565 and Pc;1555 is about 6 dB. The difference of the small signal gain between curves 6 and 5 of Fig. 4(a) is about 4 dB. The curves of noise figure with Bragg wavelength of 1550, 1555, and 1565 nm are overlapped together and keep at a constant level in the gain-clamped area. In addition, the noise figures for 1535, 1525, and 1610 nm are larger than those for 1550, 1555, and 1565 nm. As discussed above, it is obviously shown that the critical input power with 1565-nm Bragg wavelength is the largest while the corresponding
Fig. 5 shows the gain and noise figure, as the input signal power increases for various reflectivities, where L is 50 m, kf is 1562 nm, Pp is 120 mW, and ks is 1570 nm. The set of curves on the top in Fig. 5(a) show the relationships between gain and input power for various reflectivities, and they correspond to the reflectivity 0%, 20%, 40%, 60%, 80% and 99% from the top down. The set of curves in Fig. 5(b) from top down correspond to the reflectivity 0%, 99%, 80%, 60%, 40% and 20%. The gain of L-band EDFA cannot be clamped when the reflectivity equals 0. The critical input signal power increases with increasing the reflectivity, while the gain decreases. From the figure, one can see that the gain can be clamped so far as the reflectivity is equal to 20%. The differences of the critical input power and corresponding gain in the gain-clamped area, between curves 5 and 6 of Fig. 5(a) are both about 0.3 dB. In addition, with increasing the reflectivity, the noise figure increases but is less than 4.2 dB. As discussed above, the case of 60% reflectivity can give relatively large Pc , corresponding large gain and low noise figure. Therefore, it is investigated in the following discussion.
Fig. 4. Gain and noise figure as the input signal power increases for various Bragg wavelengths.
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Fig. 5. Gain and noise figure as the input signal power increases for various reflectivities of Bragg wavelength at 1562 nm.
3.4. The influence of the length of erbium-doped fiber and pump power So far, the length of EDF and the pump power is fixed at 50 m and 120 mW, respectively. In general, L-band EDFA can give intrinsically flatness about 1 dB by adjusting the length of EDF [7]. There is an optimal length for this gainclamped EDFA using a single FBG, which is similar to the conventional EDFAs. The pump power will change by its aging effect and the influence of ambient temperature. It is, thus, necessary to study the relationship between the EDFA parameters and gain-clamped capability. The gain and noise figure, as the input signal power increases for various lengths of EDF, are shown in Fig. 6. It is obvious that the gain and the noise figure increase with increasing the length while the critical input power decreases. The largest critical input power and the lowest noise figure can be obtained in the case of 50 m. However, a gain spectrum with 1 dB flatness cannot be obtained when the length of EDF is 50 m, as the result shown in [5]. Fig. 7 shows the relationship between the gain bandwidth of the gain-clamped L-band EDFA and the length of EDF when the Bragg wavelength is 1565 nm, the reflectivity is 99%, the pump wavelength is 1480 nm, and the pump power is 120 mW. As shown in the figure, there are maximum values for 1, 2 and 3 dB bandwidth, respectively, when the length of EDF equals 140 m and the operating
Fig. 6. Gain and noise figure as the input signal power increases for various lengths of EDF.
Fig. 7. Gain bandwidth of the gain-clamped L-band EDFA for various lengths of EDF.
Z. Qiang et al. / Optics Communications 224 (2003) 73–80
wavelength ranges from 1570 to 1610 nm. It indicates that 140-m length is the optimal length to achieve a flat gain spectrum for the gain-clamped EDFA using a single FBG. 50-m length is not suitable to obtain a flatness about 1 dB and it is found to be in good agreement with the experimental result in [5]. The case of 1565-nm Bragg wavelength, 99% reflectivity, and 140-m length of EDF is, thus, considered in the following discussion to obtain the adequate capability including fairly large Pc , corresponding large gain, low noise figure and flat gain spectrum. Fig. 8 shows the gain and noise figure as the input signal power increases for various pump powers. With increasing the pump power, the gain and the critical input signal power increase while the
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noise figure decreases. The difference in noise figure is very small. The gain difference at the gain-clamped area is almost the same when the pump power is beyond 190 mW. For example, the gain difference between the case of 190 mW and the case of 260 mW is only about 0.11 dB, while the difference of corresponding critical input signal power is about 1.1 dB. In addition, in this gain-clamped scheme using a single FBG, more pump power is necessary to have the same clamped output compared to a typical gainclamped L-band EDFA using an additional laser cavity. Therefore, the case of 260-mW-pump power is chosen.
4. The influence of channels add/drop
Fig. 8. Gain and noise figure as the input signal power increases for various pump powers.
As discussed above, a good set of parameters for a gain-clamped L-band EDFA with a flat-gain band are obtained. L is 140 m, kp is 1480 nm, Pp is 260 mw, kf is 1565 nm, R is 99%, and the structure (a) is considered. The gain and noise figure for multi-channel signals with different wavelengths are shown in Fig. 9. The signal wavelengths range from 1570 to 1610 nm. The input power of each channel is )20 dBm. We change the number of surviving channels to simulate the dynamic reconfiguration of networks. The 1590-nm channel is used to study the influence of the add/drop of channels in the following discussion. Fig. 9(a)
Fig. 9. Gain and noise figure for multi-channel signals (with different wavelengths).
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shows the relationship between the gain and the channel wavelength. When there is only a surviving channel, the gain spectrum without a FBG is not flat and the gain spectrum with a FBG keeps constant. The flatness of gain spectrum, DF , is about 0.8 dB when the wavelength ranges from 1573 to 1603 nm. When the number of surviving channels increases to 11 and the first channel is 1570-nm channel and the channel spacing is 4 nm, the gain spectrum without a FBG declines rapidly and the gain difference, DG1590 , is about 2.7 dB. The gain spectrum with a FBG almost keeps constant and DF increases only about 0.3 dB and DG1590 is about 0.3 dB. When the number of surviving channels increases to 21 and the first channel is 1570-nm channel and the channel spacing is 2 nm, the gain spectrum without a FBG continues to decline rapidly and DG1590 is getting larger about 4.3 dB. The gain spectrum with a FBG begins to decline obviously and DF is about 2.2 dB and DG1590 is about 0.8 dB. It is obvious that the gain-clamped ability will be weakened with increasing the surviving channels. A flat-gain band, which is less than 1 dB, can be achieved when the number of surviving channels is less than 11. It indicates that the EDFA adding a single FBG can clamp the gain with a flat-gain band simultaneously, which coincides with the experimental result in [7]. It has been also shown that the gain spectrum and the gain could not be clamped without a FBG. Fig. 9(b) shows the relationship between noise figure and the channel wavelength. It has been shown that the noise figure changes indistinctively with the channel add/drop of input power after adding a single FBG and the noise
figure of the EDFA without FBG decreases with increasing the number of surviving channels. 5. Conclusion Based on the Giles model with ASE, modeling for a gain-clamped L-band EDFA using a single FBG is set up. The four basic structures are globally analyzed and finally the structure (a) is recommended. We theoretically study the relationships between the all-optical gain-clamped capability and the influence factors such as the pump wavelength, the Bragg wavelength, the reflectivity, the length of EDF and the pump power. Key parameters for a gain-clamped L-band EDFA over 30 nm (1573– 1603 nm) with less than )1 dB flatness are obtained. The gain-clamped L-band EDFA would be optimized to achieve better performance by using, e.g., a genetic algorithm in the further work. References [1] J.F. Massicott, R. Wyatt, B.J. Ainsile, et al., Electron 26 (14) (1990) 1038. [2] J. Lee, U.C. Ryu, S.J. Ahn, et al., IEEE Photon. Technol. Lett. 11 (1) (1999) 42. [3] M.A. Mahdi, F.R.M. Adikan, P. Poopalan, et al., Opt. Commun. 176 (3) (2000) 125. [4] S.W. Harun, P. Poopalan, H. Ahmad, IEEE Photon. Technol. Lett. 14 (3) (2002) 296. [5] S.W. Harun, S.K. Low, P. Poopalan, et al., IEEE Photon. Technol. Lett. 14 (3) (2002) 293. [6] C.R. Giles, E.D. Desurvire, J. Lightwave Technol. 9 (2) (1991) 271. [7] J.M. Oh, H.B. Choi, D. Lee, et al., IEEE Photon. Technol. Lett. 14 (9) (2002) 1258.
The global analysis for an all-optical gain-clamped L-band erbium-doped fiber amplifier using a single fiber Bragg grating Zexuan Qiang *, Xiang Wu, Sailing He, Zukang Lu State Key Laboratory for Modern Optical Instrumentation, Department of Optical Engineering, Zhejiang University, Hangzhou 310027, PR China Received 9 January 2003; received in revised form 15 May 2003; accepted 2 July 2003
Abstract Based on the Giles model with ASE, modeling for all-optical gain-clamped L-band EDFA using a single fiber Bragg grating (FBG) is built. The influence of the configuration, the pump wavelength, the Bragg wavelength, the reflectivity, the length of erbium doped fiber (EDF) and the pump power to the gain-clamped characteristics is studied. Finally, a set of parameters for a gain-clamped L-band EDFA with flat-gain band is given. Ó 2003 Published by Elsevier B.V. PACS: 42.55.Wd; 42.60.Da; 42.81.)i Keywords: Erbium doped fiber amplifier; L-band; All-optical gain clamped; Fiber grating; Gain
1. Introduction The L-band erbium-doped fiber amplifiers (EDFAs) have attracted much attention [1–4] since they can effectively increase the transmission bandwidth from the conventional C band to the 1570–1605 nm range. In addition to wider operation, EDFAs also need gain control because they are sensitive to transient cross saturation induced by random bursts and signal add/drops under
*
Corresponding author. Tel.: +8657187951185; +8657187951214. E-mail address: [email protected] (Z. Qiang).
fax:
0030-4018/$ - see front matter Ó 2003 Published by Elsevier B.V. doi:10.1016/S0030-4018(03)01723-1
network reconfiguration. Recently, Harun et al. [5] experimentally proposed a new all-optical gainclamping method using a single fiber Bragg grating (FBG). There may exist other possible configurations, which have not been studied. Some commercially available simulators do not work well in L-band. Therefore, it is necessary to investigate this new EDFA in more details. In this paper, we study gain-clamped capability, effects of various configurations, pumping wavelength, Bragg wavelength, reflectivity, and the length of EDF on the EDFA performances. An optimal L-band gain-clamped EDFA configuration and amplifier parameters, which can provide a flat-gain band simultaneously, are proposed through a numerical simulation.
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The paper is organized as follows: In Section 2 the four basic configurations of all-optical gainclamped L-band EDFA using a single FBG are presented and the mathematical models based on the two-level model of Giles and Desurvire are described. Gain-clamped capabilities and the different EDFA parameters are numerically analyzed and discussed in Section 3. We discuss the effect of signal add/drop from network reconfiguration in Section 4. Finally, the paper is summarized and the optimal EDFA configuration with the corresponding optimal parameters is presented in Section 5.
2. Theoretical modeling 2.1. EDFA configurations In general, there are three kinds of pumping schemes, such as forward pumping, backward pumping and bi-directional pumping. The former two pumping schemes are considered only in this paper in order to make the structure more compact. Four basic assembled configurations are configured for the all-optical gain-clamped L-band EDFA using a single FBG as shown in Fig. 1.
Fig. 1(a) shows the structure reported in [5], in which a portion of the backward ASE is reflected. Fig. 1(b) corresponds to the case, in which a portion of the forward ASE is reflected. The structures using backward pumping are shown in Figs. 1(c) and (d). Fig. 1(c) corresponds to the case, in which a portion of the backward ASE is reflected. Fig. 1(d) corresponds to the case, in which a portion of the forward ASE is reflected. 2.2. Model The gain-clamped EDFA pumped by 980 or 1480 nm laser can be modeled as the two-level model of Giles and Desurvire [6]. According to the two-level model of with ASE, the propagation equation for each light field (with index k) is dPk ðzÞ n2 n2 ¼ uk ðak þ gk Þ Pk ðzÞ þ uk gk mhvk Dvk dz nt nt uk ðak þ lk ÞPk ðzÞ; ð1Þ where Pk ðzÞ is the light power at position z in the frequency bandwidth Dvk , Dvk equals the frequency step which is about 125 GHz for the spectral bandwidth of 1 nm, uk is +1 for a forwardpropagating field and )1 for a backward-propagating field, ak , gk , and lk represent the spectral attenuation, gain and background loss of the considered EDF, respectively, and the factor m equals 2 due to the two polarization states of the lowest order mode. The population ratio n2 =nt for the upper energy level is P n2 ððP þ ðzÞ þ Pk ðzÞÞak =hvk fÞ P k þk ; ¼ nt 1 þ k ððPk ðzÞ þ Pk ðzÞÞðak þ gk Þ=hvk fÞ ð2Þ Pksat ðak
gk Þ=hvk
where f ¼ þ is the saturation parameter which can be obtained from a measurement of the fiber saturation power. Note that only the splice loss (SL) for the reflected light by fiber Bragg grating is considered. The boundary conditions for all-optical gainclamped EDFA using a single fiber Bragg grating can be expressed as Fig. 1. Various possible configurations for a gain-clamped L-band EDFA with a single fiber Bragg grating.
Psþ ð0Þ ¼ Pin ; Pkþ ð0Þ ¼ 0; Pk ðLÞ ¼ 0 ðk 6¼ s; k 6¼ f Þ
ð3Þ
Z. Qiang et al. / Optics Communications 224 (2003) 73–80 2
2
Pfþ ð0Þ ¼ Pf ð0ÞRð1 l1 Þ ð1 l2 Þ ;
Pf ðLÞ ¼ 0; ð4Þ
or Pfþ ð0Þ ¼ 0;
2
2
Pf ðLÞ ¼ Pfþ ðLÞRð1 l1 Þ ð1 l2 Þ ; ð5Þ
where L is the length of erbium-doped fiber, R the reflectivity of fiber Bragg grating, l1 the SL between FBG and WDM, l2 the SL between the FBG and the EDF or that between the WDM and the EDF, Pf the power of lasing light, and Ps the power of signal light. It should be noted that Eq. (4) is the boundary condition for the configurations (a) and (c), Eq. (5) is the boundary condition for configurations (b) and (d), and l1 equals 0 for configurations (b) and (c). The signal noise figure and gain are defined by 1 PASE NF ¼ 10 log10 þ ; ð6Þ G hv G Dv G ¼ 10 log10 ðPsignal-out =Psignal-in Þ ððPsignal-out þ PASE Þ PASE Þ ¼ 10 log10 ; ð7Þ Psignal-in where h is PlanckÕs constant, v is the optical frequency, PASE is the ASE power measured in the bandwidth Dv. According to Eqs. (1), (2), (6), (7) and the corresponding boundary conditions, the gain and noise figure of all-optical gain-clamped Lband EDFA using a single FBG can be evaluated. A commercial erbium doped fiber (type: MP 980) is used in our simulation. The absorption and emis-
Fig. 2. Wavelength dependence of a and g used in the simulation.
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sion spectra are shown in Fig. 2. The other parameters for the EDFs are set as follows: cutoff wavelength kc ¼ 842 nm, absorption coefficient að980 nmÞ ¼ 4:57 dB/m, emission coefficient g ð980 nmÞ ¼ 0 dB/m, að1530 nmÞ ¼ 5:86 dB/m, background loss l ¼ 0:91 dB/km, and bandwidth Dv ¼ 125 GHz.
3. Calculation result and discussion 3.1. The influence of configurations and pump wavelengths An important parameter to estimate the gainclamped capability is the critical input power Pc , which is corresponding to the amplifier gain drop 0.2 dB from the maximum small signal gain. The gain-clamped capability is getting better with increasing Pc . The area, where the input power is less than the critical maximum input power, is defined as gain-clamped area. EDFAs can be well pumped by 980 or 1480 nm laser without excited state absorption (ESA). So, it is very important to choose an optimal structure and the corresponding pumping wavelength. Fig. 3 shows the relationship of the gain and noise figure as the input signal power increases for various configurations and pump wavelengths, where the length, L, is 50 m, the lasing wavelength, kf , is 1555 nm, the reflectivity of FBG, R, is 99%, the signal wavelength, ks , is 1570 nm, the loss, l1 , is 0.02 dB and l2 is 0.13 dB, and the pump power, Pp , is 120 mW. In Fig. 3(a), curve 1 describes the gain of configuration (a) pumped by 980 nm lasers. Pc1 is the critical input signal power for configuration (a) pumped by 980 nm lasers. The other curves and the corresponding critical input powers are characterized similar to the above. Figs. 3(a) and (b) show the relationships between the gain and the input signal power when the pump wavelengths, kp , are 980 and 1480 nm, respectively. Figs. 3(c) and (d) show the relationship between the noise figure and the input signal power when the pump wavelengths are 980 and 1480 nm, respectively. In Fig. 3(a), the simulation result shows that the gains are clamped with larger input power for structures (a) and (d). These
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Fig. 3. Gain or noise figure for various pump wavelength and fiber Bragg grating location.
simulation results are found to be in good agreement with the experimental ones in [5]. The modeling can be used to analyze the influence on gain-clamped capability for the other structures and the parameters such as reflectivity of FBG, Bragg wavelength, length of EDF, pump power and pump wavelength. As shown in Figs. 3(a) and (b), it is clear that the maximum critical input power Pc , whether the pump wavelength is 980 or 1480 nm, can be obtained by the configuration (d). In Figs. 3(c) and (d), the noise figures of the configurations (c) and (d) are more than 8.3 dB. They cannot satisfy the requirement for DWDM systems since the typical value of the noise figure for communication is 5 dB. Therefore, the configurations (c) and (d) are not suitable for DWDM systems and they will not be taken into account in the following discussion. In the gain-clamped area, the gain of configuration (b) is always higher than
that of configuration (a) whether the pump wavelength is 980 nm or 1480 nm, as shown in Figs. 3(a) and (b). The noise figure of structure (b) is larger than that of structure (a) with evident ripple, whether the pump wavelength is 980 or 1480 nm. It should be noted that the noise figure of configuration (b) pumped by 1480 nm laser is larger than 5 dB, which cannot satisfy the system requirement. In addition, the critical input signal power Pc of configuration (a) pumped by 1480 nm laser and the corresponding gain are larger than those of configuration (a) pumped by 980 nm laser, of which the noise figure is a bit larger. At the gainclamped area, the noise figure of configuration (a) pumped by 1480 nm laser keeps at a constant level less than 4.2 dB, which can satisfy the requirement for system communication. As discussed above, the large gain and low noise with large Pc can be obtained using configuration
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(a) pumped by 1480 nm laser. Therefore, only this configuration is considered in the following discussion.
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gain is the smallest. Due to the fairly large critical input power and gain, the case of 1562-nm Bragg wavelength is investigated in the following discussions.
3.2. The influence of Bragg wavelength of fiber Bragg grating
3.3. The influence of reflectivity of fiber grating
The gain and noise figure, as the input signal power increases for various Bragg wavelengths, are shown in Fig. 4, where L is 50 m, R is 99%, Pp is 120 mW, ks is 1570 nm, and the loss is the same as in the above discussion and fixed in the following discussion. It is shown that the gain of EDFA cannot be clamped when kf < 1535 nm or kf ¼ 1610 nm. In addition, the small signal gain with Bragg gratings at 1535 nm is larger than those at 1525 and 1610 nm, since the a and g at 1535 nm is larger than those at 1525 and 1610 nm. The critical input power increases with increasing the Bragg wavelength, i.e., Pc;1535 < Pc;1550 < Pc;1555 < Pc;1565 . The difference between Pc;1565 and Pc;1555 is about 6 dB. The difference of the small signal gain between curves 6 and 5 of Fig. 4(a) is about 4 dB. The curves of noise figure with Bragg wavelength of 1550, 1555, and 1565 nm are overlapped together and keep at a constant level in the gain-clamped area. In addition, the noise figures for 1535, 1525, and 1610 nm are larger than those for 1550, 1555, and 1565 nm. As discussed above, it is obviously shown that the critical input power with 1565-nm Bragg wavelength is the largest while the corresponding
Fig. 5 shows the gain and noise figure, as the input signal power increases for various reflectivities, where L is 50 m, kf is 1562 nm, Pp is 120 mW, and ks is 1570 nm. The set of curves on the top in Fig. 5(a) show the relationships between gain and input power for various reflectivities, and they correspond to the reflectivity 0%, 20%, 40%, 60%, 80% and 99% from the top down. The set of curves in Fig. 5(b) from top down correspond to the reflectivity 0%, 99%, 80%, 60%, 40% and 20%. The gain of L-band EDFA cannot be clamped when the reflectivity equals 0. The critical input signal power increases with increasing the reflectivity, while the gain decreases. From the figure, one can see that the gain can be clamped so far as the reflectivity is equal to 20%. The differences of the critical input power and corresponding gain in the gain-clamped area, between curves 5 and 6 of Fig. 5(a) are both about 0.3 dB. In addition, with increasing the reflectivity, the noise figure increases but is less than 4.2 dB. As discussed above, the case of 60% reflectivity can give relatively large Pc , corresponding large gain and low noise figure. Therefore, it is investigated in the following discussion.
Fig. 4. Gain and noise figure as the input signal power increases for various Bragg wavelengths.
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Fig. 5. Gain and noise figure as the input signal power increases for various reflectivities of Bragg wavelength at 1562 nm.
3.4. The influence of the length of erbium-doped fiber and pump power So far, the length of EDF and the pump power is fixed at 50 m and 120 mW, respectively. In general, L-band EDFA can give intrinsically flatness about 1 dB by adjusting the length of EDF [7]. There is an optimal length for this gainclamped EDFA using a single FBG, which is similar to the conventional EDFAs. The pump power will change by its aging effect and the influence of ambient temperature. It is, thus, necessary to study the relationship between the EDFA parameters and gain-clamped capability. The gain and noise figure, as the input signal power increases for various lengths of EDF, are shown in Fig. 6. It is obvious that the gain and the noise figure increase with increasing the length while the critical input power decreases. The largest critical input power and the lowest noise figure can be obtained in the case of 50 m. However, a gain spectrum with 1 dB flatness cannot be obtained when the length of EDF is 50 m, as the result shown in [5]. Fig. 7 shows the relationship between the gain bandwidth of the gain-clamped L-band EDFA and the length of EDF when the Bragg wavelength is 1565 nm, the reflectivity is 99%, the pump wavelength is 1480 nm, and the pump power is 120 mW. As shown in the figure, there are maximum values for 1, 2 and 3 dB bandwidth, respectively, when the length of EDF equals 140 m and the operating
Fig. 6. Gain and noise figure as the input signal power increases for various lengths of EDF.
Fig. 7. Gain bandwidth of the gain-clamped L-band EDFA for various lengths of EDF.
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wavelength ranges from 1570 to 1610 nm. It indicates that 140-m length is the optimal length to achieve a flat gain spectrum for the gain-clamped EDFA using a single FBG. 50-m length is not suitable to obtain a flatness about 1 dB and it is found to be in good agreement with the experimental result in [5]. The case of 1565-nm Bragg wavelength, 99% reflectivity, and 140-m length of EDF is, thus, considered in the following discussion to obtain the adequate capability including fairly large Pc , corresponding large gain, low noise figure and flat gain spectrum. Fig. 8 shows the gain and noise figure as the input signal power increases for various pump powers. With increasing the pump power, the gain and the critical input signal power increase while the
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noise figure decreases. The difference in noise figure is very small. The gain difference at the gain-clamped area is almost the same when the pump power is beyond 190 mW. For example, the gain difference between the case of 190 mW and the case of 260 mW is only about 0.11 dB, while the difference of corresponding critical input signal power is about 1.1 dB. In addition, in this gain-clamped scheme using a single FBG, more pump power is necessary to have the same clamped output compared to a typical gainclamped L-band EDFA using an additional laser cavity. Therefore, the case of 260-mW-pump power is chosen.
4. The influence of channels add/drop
Fig. 8. Gain and noise figure as the input signal power increases for various pump powers.
As discussed above, a good set of parameters for a gain-clamped L-band EDFA with a flat-gain band are obtained. L is 140 m, kp is 1480 nm, Pp is 260 mw, kf is 1565 nm, R is 99%, and the structure (a) is considered. The gain and noise figure for multi-channel signals with different wavelengths are shown in Fig. 9. The signal wavelengths range from 1570 to 1610 nm. The input power of each channel is )20 dBm. We change the number of surviving channels to simulate the dynamic reconfiguration of networks. The 1590-nm channel is used to study the influence of the add/drop of channels in the following discussion. Fig. 9(a)
Fig. 9. Gain and noise figure for multi-channel signals (with different wavelengths).
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shows the relationship between the gain and the channel wavelength. When there is only a surviving channel, the gain spectrum without a FBG is not flat and the gain spectrum with a FBG keeps constant. The flatness of gain spectrum, DF , is about 0.8 dB when the wavelength ranges from 1573 to 1603 nm. When the number of surviving channels increases to 11 and the first channel is 1570-nm channel and the channel spacing is 4 nm, the gain spectrum without a FBG declines rapidly and the gain difference, DG1590 , is about 2.7 dB. The gain spectrum with a FBG almost keeps constant and DF increases only about 0.3 dB and DG1590 is about 0.3 dB. When the number of surviving channels increases to 21 and the first channel is 1570-nm channel and the channel spacing is 2 nm, the gain spectrum without a FBG continues to decline rapidly and DG1590 is getting larger about 4.3 dB. The gain spectrum with a FBG begins to decline obviously and DF is about 2.2 dB and DG1590 is about 0.8 dB. It is obvious that the gain-clamped ability will be weakened with increasing the surviving channels. A flat-gain band, which is less than 1 dB, can be achieved when the number of surviving channels is less than 11. It indicates that the EDFA adding a single FBG can clamp the gain with a flat-gain band simultaneously, which coincides with the experimental result in [7]. It has been also shown that the gain spectrum and the gain could not be clamped without a FBG. Fig. 9(b) shows the relationship between noise figure and the channel wavelength. It has been shown that the noise figure changes indistinctively with the channel add/drop of input power after adding a single FBG and the noise
figure of the EDFA without FBG decreases with increasing the number of surviving channels. 5. Conclusion Based on the Giles model with ASE, modeling for a gain-clamped L-band EDFA using a single FBG is set up. The four basic structures are globally analyzed and finally the structure (a) is recommended. We theoretically study the relationships between the all-optical gain-clamped capability and the influence factors such as the pump wavelength, the Bragg wavelength, the reflectivity, the length of EDF and the pump power. Key parameters for a gain-clamped L-band EDFA over 30 nm (1573– 1603 nm) with less than )1 dB flatness are obtained. The gain-clamped L-band EDFA would be optimized to achieve better performance by using, e.g., a genetic algorithm in the further work. References [1] J.F. Massicott, R. Wyatt, B.J. Ainsile, et al., Electron 26 (14) (1990) 1038. [2] J. Lee, U.C. Ryu, S.J. Ahn, et al., IEEE Photon. Technol. Lett. 11 (1) (1999) 42. [3] M.A. Mahdi, F.R.M. Adikan, P. Poopalan, et al., Opt. Commun. 176 (3) (2000) 125. [4] S.W. Harun, P. Poopalan, H. Ahmad, IEEE Photon. Technol. Lett. 14 (3) (2002) 296. [5] S.W. Harun, S.K. Low, P. Poopalan, et al., IEEE Photon. Technol. Lett. 14 (3) (2002) 293. [6] C.R. Giles, E.D. Desurvire, J. Lightwave Technol. 9 (2) (1991) 271. [7] J.M. Oh, H.B. Choi, D. Lee, et al., IEEE Photon. Technol. Lett. 14 (9) (2002) 1258.