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Performance comparison for RZ-DPSK signal in DCF-based and CFBG-based dispersive transmission system
ARTICLE IN PRESS
Optik
Optics
Optik 119 (2008) 441–445 www.elsevier.de/ijleo
Performance comparison for RZ-DPSK signal in DCF-based and CFBG-based dispersive transmission system Chen Yong, Cao Jihong, Qin Xi, Zhang Feng, Jian Shuisheng Institute of Lightwave Technology, Beijing Jiaotong University, Beijing 100044, PR China Received 27 July 2006; accepted 13 December 2006
Abstract The impact of the phase noise induced by self-phase modulation and intrachannel nonlinear effect for return-to-zero differential phase-shift keying (RZ-DPSK) in long haul 40 Gb/s transmission systems where dispersion is compensated by chirped fiber Bragg grating (CFBG) is analyzed and numerical evaluated, and it is compared with what is derived from the conventional DCF-based phase-modulated system. Our work also provides a clear physical picture of how the transmission performance is affected by CFBG, which is instructive for further research on CFBG compensated phase-modulated formats. r 2007 Elsevier GmbH. All rights reserved. Keywords: Differential phase-shift keying (DPSK); Chirped fiber Bragg grating; Nonlinear phase noise; Intrachannel nonlinear effect
1. Introduction Due to the 3-dB receiver sensitivity improvement to on–off keying (OOK) and larger tolerance to fiber nonlinearities than OOK signal, the differential phaseshift keying signal has been studied extensively in highspeed long-haul lightwave transmissions. Most DPSK experiments use return-to-zero (RZ) short pulse which launches a constant-intensity pulse train with phase modulated to each RZ pulse, and it is considered as a constant envelope modulation format in digital communication. It is propitious to nonlinearity constraint in lightwave transmission [1–5]. As we know, the refractive index of the fiber is modulated by fluctuating optical power created by the amplified spontaneous emission (ASE) noise through the Kerr effect, which is called self-phase modulation Corresponding author.
E-mail address: smartfi[email protected] (C. Yong). 0030-4026/$ - see front matter r 2007 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2006.12.014
(SPM)-induced nonlinear phase noise. It gives rise to phase fluctuations at the receiver. As [4] shown, nonlinear phase noise is the major degradation for DPSK signals. For 40 Gb/s signal in dispersive fiber link, the pulse-to-pulse interaction gives intrachannel cross-phase modulation (IXPM) and four-wave mixing (IFWM) caused from each temporal short pulse broadens fast by chromatic dispersion and overlaps with each other [6,7]. IXPM induces timing jitter of the transmitted pulse. Fortunately, in the constant RZ-DPSK pulse train transmission timing jitter induced identical phase modulation to all pulses, which does not affect DPSK signal. However, IFWM adds ghost pulses with random additive phase to each RZ pulse resulting in phase chaos distorting the performance of the phase modulated system. Much work has been done to investigate these negative effects to the RZ-DPSK system, but they were all conducted in the dispersion compensating fiber (DCF) employing system. Chirped fiber Bragg grating is known as an effective dispersion
ARTICLE IN PRESS 442
C. Yong et al. / Optik 119 (2008) 441–445
compensator and applied in OOK system widely [8], whereas few research work was done on CFBG employing DPSK system in-depth. In this paper, the impact of the nonlinear phase noise and intrachannel nonlinear effect for CFBG-based RZ-DPSK in long haul 40 Gb/s transmission systems is analyzed and numerically evaluated, and the result is also compared with what is derived from the conventional DCF-based system. Here we try to provide a clear physical picture of how the transmission performance is affected by CFBG in phasemodulated system, and how to optimize the system performance with the characteristic of CFBG. We believe the discussion in this paper will be instructive for further transmission research with CFBG compensated phasemodulated formats. It is the first time, to the best of our knowledge, the performance of the DPSK with CFBG dispersion compensation is forwarded in detail.
2. Impact of SPM-induced nonlinear phase noise Consider a transmission link using phase-shift keying signal, wherein a monochromatic optical field of constant power is modulated by imposing it on a phase shift of either 0 or p radian during each bit period. The accumulated ASE noise from the cascading EDFAs will impair the optical signal-to-noise ratio (OSNR) resulting in the most obstacle to long-haul transmission. In this paper only two degrees of freedom (DOFs) of the noise field from EDFA is taken into account. For an N-span fiber link with the length of L to per span fiber with normalized launched field E0. In [4], the OSNR at the receiver input end was given by rSNR ¼ E o
Leff 1 1 Gðln GÞ2 , L nsp hv0 ðG 1ÞDV f aNL G 1
the transmitted bit rate. So almost 160 GHz is sufficient for the routine 40 Gb/s system. That is, from Eq. (1) we can affirm that in this bandwidth-limited CFBG-based system rSNR is improved greatly. In the phase-modulated transmission system, the standard deviation of the phase noise at the receiver is used to investigate the transmission performance, and the linear phase noise which caused from the ASE of EDFA merely can be expressed as [4] hdsL i2 ¼
1 . 2rSNR
(2)
The variance of the phase fluctuations produced by the interaction between the amplitude ASE fluctuations and the SPM effect was usually taken for nonlinear phase noise. For an actual valuable transmission system rSNR 1, the nonlinear phase noise is given by [4] 2 2 fNL 2 1 2 fNL 2 hdsNL i ¼ rSNR þ , (3) 6 3 rSNR ðrSNR þ 12Þ2 3 where the nonlinear phase shift fNL ¼ gLeff ðE 20 þ Pn Þ ¼ gLeff E 20 þ nsp hv0 ðG 1ÞDV f . (4) From the analysis in Eqs. (1)–(4), we came to some conclusions: (1) Both the linear phase noise and the nonlinear phase noise are in inverse proportion to the rSNR, that means in the CFBG-based bandwidth constraint system, proper bandwidth will help to decrease phase noises. (2) In most situations, we take the ASE of the EDFA as Gauss distribution and from Eq. (4) we can educe: h i 2 2 fNL / ðDV f Þ2 and hdsNL i2 / fNL =DV f / ðDV f Þ3
(1)
where the fiber link has an attenuation coefficient of a, and the Leff ¼ (1exp(aL))/a is the effective nonlinear length per span. G is the gain for every optical amplifier mounted along the fiber link, and here we suppose every amplifier has the same gain. The spectral density of ASE noise is given by nsphv0(G1), and in Eq. (1) DVf is the bandwidth of the transmission system which is an important parameter for DCF-based and CFBG-based system performance evaluating thereinafter. In the traditional DCF-based system, no accessional filter but the final one preceding receiver is applied along the fiber link, where DVf denotes the bandwidth of the EDFA which is about 35 nm (44 THz). Whereas, CFBG can filter the ASE distributing out-of-band of the grating profited from its bandpass-filter character, which help to maintain the OSNR effectively so as to extend the transmission distance. From experiential conclusion, the bandwidth of 4B is enough for CFBG-based system whatever modulation format was adopted, and here B is
So the nonlinear phase noise is in proportion to the cube of DVf. That is, in the CFBG-based system where the system link was restricted in properly transmitted bandwidth by CFBG hdsNL i2 will be decreased greatly. We simulated the CFBG-based and the DCF-based system performance whose schematic diagram and simulated result was shown in Fig. 1. The standard single-mode fiber (SMF) and the DCF fiber have an attenuation coefficient of 0.2 and 0.5 dB/km, respectively, 5 dB insert loss for CFBG. With a bit interval of 25 ps, DPSK signal has a data rate of 40 Gb/s. The initial pulsewidth is 8 ps, for a duty cycle of about 0.33. The whole simulated link is 1100 km, corresponding to 55 km for each span. The dispersion coefficient is 17 ps/km/nm for SMF and 85 ps/km/nm for DCF, respectively. EDFA was the solo form of amplifier employed in system to equalize power distribution. Traditionally, the impact of nonlinear phase noise to DPSK signals is investigated based on the variance of the phase. As a non-Gaussian random variable for
ARTICLE IN PRESS C. Yong et al. / Optik 119 (2008) 441–445
a
60
5
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Input Power (mW)
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DCF
80
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2 1.5 1
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12 0
8 6
80 10 0
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60 40
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Fig. 1. Transmitted Q-value fluctuates with the input power and noise figure of EDFA in (a) DCF-based and (b) CFBGbase DPSK system.
phase noise, DPSK system performance cannot be completely characterized by conventional Q-value evaluated method applied in OOK system [8]. Various methods to evaluate the Q-value of DPSK signal have been studied [1–3]. Here we adopt the method referred in [1] to calculate Q-value of DPSK system. From the simulated results shown in Fig. 1, we found: (i) 1.95 mW input power is the optimum launched power in this DCF-based simulated system. At this launched power level, the total nonlinear phase shift produced by the signal power is DCF fNL ¼ gSNF P0 LSMF eff þ gDCF P0 expðaSMF LÞLeff
¼ 0:95 ðradÞ.
3. Impact of the phase noise from intrachannel nonlinearity
80
80 SMF
10 Input Power (mW)
the bandpass-filter and low nonlinear effect of CFBG. The higher power input, the greater OSNR of the signal will be gotten within the nonlinear effect acceptable scope in optical transmission system. (ii) Comparing Fig. 1(a) and (b) it can be seem that although the performance will be decreased with the increasing of the noise figure of EDFA employed in both systems. The input power around the optimum point in the CFBG-based system has great noise tolerance than that in DCF-based system, which means the transmission distance will be extended and more stabile transmission performance will be achieved.
60
4.5
443
ð5Þ
It is up to the conclusion in [4] that the minimum error rate was gotten when the signal power produces a total nonlinear phase shift is approximate to 1 rad. But in CFBG-based system the optimum launched power is almost 7.5 mW that will produce 3.2 rad nonlinear phase shift, and the high input power tolerance benefited from
When RZ pulses broaden by chromatic dispersion and overlap with each other, intrachannel nonlinear effect including IXPM and IFWM is more dominant than interchannel ones. As a constant pulse train in DPSK system, IFWM adds ghost pulses to each DPSK pulse to impose pulses different phase jitter, resulting in intrachannel nonlinearity phase noise as it is mentioned above. Along the fiber link, the pulse peak power difference between z ¼ L and 0 can be written as 2 Z z 2 pffiffiffi T T DPq;r ðzÞ ¼ 2P20 g 0 aðBÞ 0 FðzÞ 0 FðBÞ " # 2 2 T 0 T Bit 2 2 exp ðq þ r Þ FðBÞ 2 ! GðzÞT 2Bit sin ð6Þ qr DCq;r dx, FðBÞ 2 where the GðzÞ ¼ b2 z is used to denote the dispersion distribution map, and the other parameters in this equation is described below: FðzÞ ¼ T 20 iGðzÞ, aðzÞ ¼ expð2azÞ. Here T0 is the temporal pulsewidth. Supposing the transmitted data is pseudo random binary serial (PRBS) and the noise derived from EDFA accumulating along the link is Gauss distribution, the mean of the nonlinear phase noise hdsNL i ¼ 0. The variance of the phase fluctuations can be expressed as hdsNL i2 ¼ 14ðgLeff DPq;r Þ2 .
(7)
Taking Eq. (7) into Eq. (3) phase noise induced by intrachannel nonlinearity can be calculated simply. Fig. 2 shows the simulated result of the transmission performance fluctuates with the input power and dispersion compensation shift in DCF-based and CFBG-base DPSK system, respectively. And intrachannel nonlinear effect was taken into account here. Most of the parameters for simulation in this section are the same with those in previous section but the dispersion map along the link is symmetric managed here. According to
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considered in these theoretical researches could not be ignored in practical fiber link. In Fig. 2(a) it is seen clearly that the best system performance is achieved at the DCS deviating from 0.5 in both systems. But in CFBG-based system the best performance will be gotten in more wide scope when the DCS is around 0.5. Secondly, the input power tolerance is greater in CFBGbased system than in DCF-based system, and more OSNR will be expected to get in CFBG employed system. Thirdly, the discrepant stability in two systems was shown in Fig. 2. The Q-value of the system in DCFbased system fluctuates continually with the change of the input power and DCS, which was shown in Fig. 2(a) clearly. But in Fig. 2(b), the gotten Q-value will maintain stabilization in spite of the input power or DCS fluctuating within a certain scope.
4. Conclusion
Fig. 2. Transmission performance fluctuates with the input power and dispersion compensation shift in (a) DCF-based and (b) CFBG-base DPSK system when intrachannel nonlinear effect was taken into account.
Eq. (6), the sign of b2 determines the fluctuation of the peak power, i.e., if the accumulated GVD is inverse periodically energy transfer for each pulse will be reverse accordingly. That is, the variation of amplitude shift of a pulse can be eliminated in the subsequent link sections with alternated accumulated GVD. Here we define the concept of dispersion compensation shift (DCS). Let the length of the first span SMF be L1 and the length of the immediate DCF be L2, so the DCS is denoted as DCS ¼
DSMF L1 . DDCF L2
(8)
From the simulation result shown in Fig. 2 we will find some valuable results. Firstly, in the DCF-based system 50% precompensation of dispersion increases instead of reducing IFWM induced phase noise, which is consistent with the conclusion put forward in Ref. [2]. This result is different from many theoretical researches, and the reason for it is that the loss of the fiber that was not
We compared the performance of RZ-DPSK formats for long haul transmission over SMF with DCF and CFBG compensation by numerical simulations, respectively. CFBG is propitious to the linear phase and nonlinear phase noise suppressing, and better tolerance to the phase noise caused by intrachannel nonlinear effects. But in practical phase modulated systems, few work was implemented by CFBG, and the most obstacle for it is the impact of group-delay ripple of the grating originating from its nonideal fabricated technique which was analyzed in some papers [9]. The rule for the impact on nonideal characters of the grating in the phase modulated system is difficult to draw in theory. In conclusions, CFBG dispersion compensation is an attractive technique for long haul high-speed phasemodulated transmission, and more work will be done to find out the rule of dispersion compensation by CFBG in practical phase-modulated transmission so as to progress it.
Acknowledgements This work was supported by the National Natural science Foundation of China (nos. 60337010 and 60437010).
References [1] H. Keang-Po, W. Hsi-Cheng, Comparison of nonlinear phase noise and intrachannel four-wave mixing for rz-dpsk signals in dispersive transmission systems, IEEE Photon. Technol. Lett. 17 (2005) 1426–1428. [2] H. Keang-Po, Error probability of DPSK signals with intrachannel four-wave mixing in highly dispersive transmission systems, IEEE Photon. Technol. Lett. 17 (2005) 789–791.
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[3] C. Xu, L. Xiang, W. Xing, Differential phase-shift keying for high spectral efficiency optical transmissions, IEEE J. Sel. Top. Quant. Electron. 10 (2004) 281–293. [4] J.P. Gordon, L.F. Mollenauer, Phase noise in photonic communications-systems using linear-amplifiers, Opt. Lett. 15 (1990) 1351–1353. [5] K. Hoon, Cross-phase-modulation-induced nonlinear phase noise in wdm direct-detection dpsk systems, J. Lightwave Technol. 21 (2003) 1770–1774. [6] S. Kumar, Intrachannel four-wave mixing in dispersion managed rz systems, IEEE Photon. Technol. Lett. 13 (2001) 800–802.
445
[7] S. Kumar, J.C. Mauro, S. Raghavan, D.Q. Chowdhury, Intrachannel nonlinear penalties in dispersion-managed transmission systems, IEEE J. Sel. Top. Quant. Electron. 8 (2002) 626–631. [8] C. Yong, C. Jihong, C. Ting, J. Shuisheng, Advanced modulation formats for long-haul optical-transmission systems with dispersion compensation by chirped FBG, Microwave Opt. Technol. Lett. 48 (2006) 344–347. [9] L. Xiang, L.F. Mollenauer, W. Xing, Impact of groupdelay ripple in transmission systems including phasemodulated formats, IEEE Photon. Technol. Lett. 16 (2004) 305–307.
Optik
Optics
Optik 119 (2008) 441–445 www.elsevier.de/ijleo
Performance comparison for RZ-DPSK signal in DCF-based and CFBG-based dispersive transmission system Chen Yong, Cao Jihong, Qin Xi, Zhang Feng, Jian Shuisheng Institute of Lightwave Technology, Beijing Jiaotong University, Beijing 100044, PR China Received 27 July 2006; accepted 13 December 2006
Abstract The impact of the phase noise induced by self-phase modulation and intrachannel nonlinear effect for return-to-zero differential phase-shift keying (RZ-DPSK) in long haul 40 Gb/s transmission systems where dispersion is compensated by chirped fiber Bragg grating (CFBG) is analyzed and numerical evaluated, and it is compared with what is derived from the conventional DCF-based phase-modulated system. Our work also provides a clear physical picture of how the transmission performance is affected by CFBG, which is instructive for further research on CFBG compensated phase-modulated formats. r 2007 Elsevier GmbH. All rights reserved. Keywords: Differential phase-shift keying (DPSK); Chirped fiber Bragg grating; Nonlinear phase noise; Intrachannel nonlinear effect
1. Introduction Due to the 3-dB receiver sensitivity improvement to on–off keying (OOK) and larger tolerance to fiber nonlinearities than OOK signal, the differential phaseshift keying signal has been studied extensively in highspeed long-haul lightwave transmissions. Most DPSK experiments use return-to-zero (RZ) short pulse which launches a constant-intensity pulse train with phase modulated to each RZ pulse, and it is considered as a constant envelope modulation format in digital communication. It is propitious to nonlinearity constraint in lightwave transmission [1–5]. As we know, the refractive index of the fiber is modulated by fluctuating optical power created by the amplified spontaneous emission (ASE) noise through the Kerr effect, which is called self-phase modulation Corresponding author.
E-mail address: smartfi[email protected] (C. Yong). 0030-4026/$ - see front matter r 2007 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2006.12.014
(SPM)-induced nonlinear phase noise. It gives rise to phase fluctuations at the receiver. As [4] shown, nonlinear phase noise is the major degradation for DPSK signals. For 40 Gb/s signal in dispersive fiber link, the pulse-to-pulse interaction gives intrachannel cross-phase modulation (IXPM) and four-wave mixing (IFWM) caused from each temporal short pulse broadens fast by chromatic dispersion and overlaps with each other [6,7]. IXPM induces timing jitter of the transmitted pulse. Fortunately, in the constant RZ-DPSK pulse train transmission timing jitter induced identical phase modulation to all pulses, which does not affect DPSK signal. However, IFWM adds ghost pulses with random additive phase to each RZ pulse resulting in phase chaos distorting the performance of the phase modulated system. Much work has been done to investigate these negative effects to the RZ-DPSK system, but they were all conducted in the dispersion compensating fiber (DCF) employing system. Chirped fiber Bragg grating is known as an effective dispersion
ARTICLE IN PRESS 442
C. Yong et al. / Optik 119 (2008) 441–445
compensator and applied in OOK system widely [8], whereas few research work was done on CFBG employing DPSK system in-depth. In this paper, the impact of the nonlinear phase noise and intrachannel nonlinear effect for CFBG-based RZ-DPSK in long haul 40 Gb/s transmission systems is analyzed and numerically evaluated, and the result is also compared with what is derived from the conventional DCF-based system. Here we try to provide a clear physical picture of how the transmission performance is affected by CFBG in phasemodulated system, and how to optimize the system performance with the characteristic of CFBG. We believe the discussion in this paper will be instructive for further transmission research with CFBG compensated phasemodulated formats. It is the first time, to the best of our knowledge, the performance of the DPSK with CFBG dispersion compensation is forwarded in detail.
2. Impact of SPM-induced nonlinear phase noise Consider a transmission link using phase-shift keying signal, wherein a monochromatic optical field of constant power is modulated by imposing it on a phase shift of either 0 or p radian during each bit period. The accumulated ASE noise from the cascading EDFAs will impair the optical signal-to-noise ratio (OSNR) resulting in the most obstacle to long-haul transmission. In this paper only two degrees of freedom (DOFs) of the noise field from EDFA is taken into account. For an N-span fiber link with the length of L to per span fiber with normalized launched field E0. In [4], the OSNR at the receiver input end was given by rSNR ¼ E o
Leff 1 1 Gðln GÞ2 , L nsp hv0 ðG 1ÞDV f aNL G 1
the transmitted bit rate. So almost 160 GHz is sufficient for the routine 40 Gb/s system. That is, from Eq. (1) we can affirm that in this bandwidth-limited CFBG-based system rSNR is improved greatly. In the phase-modulated transmission system, the standard deviation of the phase noise at the receiver is used to investigate the transmission performance, and the linear phase noise which caused from the ASE of EDFA merely can be expressed as [4] hdsL i2 ¼
1 . 2rSNR
(2)
The variance of the phase fluctuations produced by the interaction between the amplitude ASE fluctuations and the SPM effect was usually taken for nonlinear phase noise. For an actual valuable transmission system rSNR 1, the nonlinear phase noise is given by [4] 2 2 fNL 2 1 2 fNL 2 hdsNL i ¼ rSNR þ , (3) 6 3 rSNR ðrSNR þ 12Þ2 3 where the nonlinear phase shift fNL ¼ gLeff ðE 20 þ Pn Þ ¼ gLeff E 20 þ nsp hv0 ðG 1ÞDV f . (4) From the analysis in Eqs. (1)–(4), we came to some conclusions: (1) Both the linear phase noise and the nonlinear phase noise are in inverse proportion to the rSNR, that means in the CFBG-based bandwidth constraint system, proper bandwidth will help to decrease phase noises. (2) In most situations, we take the ASE of the EDFA as Gauss distribution and from Eq. (4) we can educe: h i 2 2 fNL / ðDV f Þ2 and hdsNL i2 / fNL =DV f / ðDV f Þ3
(1)
where the fiber link has an attenuation coefficient of a, and the Leff ¼ (1exp(aL))/a is the effective nonlinear length per span. G is the gain for every optical amplifier mounted along the fiber link, and here we suppose every amplifier has the same gain. The spectral density of ASE noise is given by nsphv0(G1), and in Eq. (1) DVf is the bandwidth of the transmission system which is an important parameter for DCF-based and CFBG-based system performance evaluating thereinafter. In the traditional DCF-based system, no accessional filter but the final one preceding receiver is applied along the fiber link, where DVf denotes the bandwidth of the EDFA which is about 35 nm (44 THz). Whereas, CFBG can filter the ASE distributing out-of-band of the grating profited from its bandpass-filter character, which help to maintain the OSNR effectively so as to extend the transmission distance. From experiential conclusion, the bandwidth of 4B is enough for CFBG-based system whatever modulation format was adopted, and here B is
So the nonlinear phase noise is in proportion to the cube of DVf. That is, in the CFBG-based system where the system link was restricted in properly transmitted bandwidth by CFBG hdsNL i2 will be decreased greatly. We simulated the CFBG-based and the DCF-based system performance whose schematic diagram and simulated result was shown in Fig. 1. The standard single-mode fiber (SMF) and the DCF fiber have an attenuation coefficient of 0.2 and 0.5 dB/km, respectively, 5 dB insert loss for CFBG. With a bit interval of 25 ps, DPSK signal has a data rate of 40 Gb/s. The initial pulsewidth is 8 ps, for a duty cycle of about 0.33. The whole simulated link is 1100 km, corresponding to 55 km for each span. The dispersion coefficient is 17 ps/km/nm for SMF and 85 ps/km/nm for DCF, respectively. EDFA was the solo form of amplifier employed in system to equalize power distribution. Traditionally, the impact of nonlinear phase noise to DPSK signals is investigated based on the variance of the phase. As a non-Gaussian random variable for
ARTICLE IN PRESS C. Yong et al. / Optik 119 (2008) 441–445
a
60
5
SMF
Input Power (mW)
4
60
DCF
80
3.5
80
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2 1.5 1
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40 20
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80
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12 0
8 6
80 10 0
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60 40
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4
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5 6 Noise Figure (dB)
7
Fig. 1. Transmitted Q-value fluctuates with the input power and noise figure of EDFA in (a) DCF-based and (b) CFBGbase DPSK system.
phase noise, DPSK system performance cannot be completely characterized by conventional Q-value evaluated method applied in OOK system [8]. Various methods to evaluate the Q-value of DPSK signal have been studied [1–3]. Here we adopt the method referred in [1] to calculate Q-value of DPSK system. From the simulated results shown in Fig. 1, we found: (i) 1.95 mW input power is the optimum launched power in this DCF-based simulated system. At this launched power level, the total nonlinear phase shift produced by the signal power is DCF fNL ¼ gSNF P0 LSMF eff þ gDCF P0 expðaSMF LÞLeff
¼ 0:95 ðradÞ.
3. Impact of the phase noise from intrachannel nonlinearity
80
80 SMF
10 Input Power (mW)
the bandpass-filter and low nonlinear effect of CFBG. The higher power input, the greater OSNR of the signal will be gotten within the nonlinear effect acceptable scope in optical transmission system. (ii) Comparing Fig. 1(a) and (b) it can be seem that although the performance will be decreased with the increasing of the noise figure of EDFA employed in both systems. The input power around the optimum point in the CFBG-based system has great noise tolerance than that in DCF-based system, which means the transmission distance will be extended and more stabile transmission performance will be achieved.
60
4.5
443
ð5Þ
It is up to the conclusion in [4] that the minimum error rate was gotten when the signal power produces a total nonlinear phase shift is approximate to 1 rad. But in CFBG-based system the optimum launched power is almost 7.5 mW that will produce 3.2 rad nonlinear phase shift, and the high input power tolerance benefited from
When RZ pulses broaden by chromatic dispersion and overlap with each other, intrachannel nonlinear effect including IXPM and IFWM is more dominant than interchannel ones. As a constant pulse train in DPSK system, IFWM adds ghost pulses to each DPSK pulse to impose pulses different phase jitter, resulting in intrachannel nonlinearity phase noise as it is mentioned above. Along the fiber link, the pulse peak power difference between z ¼ L and 0 can be written as 2 Z z 2 pffiffiffi T T DPq;r ðzÞ ¼ 2P20 g 0 aðBÞ 0 FðzÞ 0 FðBÞ " # 2 2 T 0 T Bit 2 2 exp ðq þ r Þ FðBÞ 2 ! GðzÞT 2Bit sin ð6Þ qr DCq;r dx, FðBÞ 2 where the GðzÞ ¼ b2 z is used to denote the dispersion distribution map, and the other parameters in this equation is described below: FðzÞ ¼ T 20 iGðzÞ, aðzÞ ¼ expð2azÞ. Here T0 is the temporal pulsewidth. Supposing the transmitted data is pseudo random binary serial (PRBS) and the noise derived from EDFA accumulating along the link is Gauss distribution, the mean of the nonlinear phase noise hdsNL i ¼ 0. The variance of the phase fluctuations can be expressed as hdsNL i2 ¼ 14ðgLeff DPq;r Þ2 .
(7)
Taking Eq. (7) into Eq. (3) phase noise induced by intrachannel nonlinearity can be calculated simply. Fig. 2 shows the simulated result of the transmission performance fluctuates with the input power and dispersion compensation shift in DCF-based and CFBG-base DPSK system, respectively. And intrachannel nonlinear effect was taken into account here. Most of the parameters for simulation in this section are the same with those in previous section but the dispersion map along the link is symmetric managed here. According to
ARTICLE IN PRESS 444
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considered in these theoretical researches could not be ignored in practical fiber link. In Fig. 2(a) it is seen clearly that the best system performance is achieved at the DCS deviating from 0.5 in both systems. But in CFBG-based system the best performance will be gotten in more wide scope when the DCS is around 0.5. Secondly, the input power tolerance is greater in CFBGbased system than in DCF-based system, and more OSNR will be expected to get in CFBG employed system. Thirdly, the discrepant stability in two systems was shown in Fig. 2. The Q-value of the system in DCFbased system fluctuates continually with the change of the input power and DCS, which was shown in Fig. 2(a) clearly. But in Fig. 2(b), the gotten Q-value will maintain stabilization in spite of the input power or DCS fluctuating within a certain scope.
4. Conclusion
Fig. 2. Transmission performance fluctuates with the input power and dispersion compensation shift in (a) DCF-based and (b) CFBG-base DPSK system when intrachannel nonlinear effect was taken into account.
Eq. (6), the sign of b2 determines the fluctuation of the peak power, i.e., if the accumulated GVD is inverse periodically energy transfer for each pulse will be reverse accordingly. That is, the variation of amplitude shift of a pulse can be eliminated in the subsequent link sections with alternated accumulated GVD. Here we define the concept of dispersion compensation shift (DCS). Let the length of the first span SMF be L1 and the length of the immediate DCF be L2, so the DCS is denoted as DCS ¼
DSMF L1 . DDCF L2
(8)
From the simulation result shown in Fig. 2 we will find some valuable results. Firstly, in the DCF-based system 50% precompensation of dispersion increases instead of reducing IFWM induced phase noise, which is consistent with the conclusion put forward in Ref. [2]. This result is different from many theoretical researches, and the reason for it is that the loss of the fiber that was not
We compared the performance of RZ-DPSK formats for long haul transmission over SMF with DCF and CFBG compensation by numerical simulations, respectively. CFBG is propitious to the linear phase and nonlinear phase noise suppressing, and better tolerance to the phase noise caused by intrachannel nonlinear effects. But in practical phase modulated systems, few work was implemented by CFBG, and the most obstacle for it is the impact of group-delay ripple of the grating originating from its nonideal fabricated technique which was analyzed in some papers [9]. The rule for the impact on nonideal characters of the grating in the phase modulated system is difficult to draw in theory. In conclusions, CFBG dispersion compensation is an attractive technique for long haul high-speed phasemodulated transmission, and more work will be done to find out the rule of dispersion compensation by CFBG in practical phase-modulated transmission so as to progress it.
Acknowledgements This work was supported by the National Natural science Foundation of China (nos. 60337010 and 60437010).
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