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Performance evaluation of a multi-wavelength gigahertz optical source for wavelength division multiplexed transmission
Optics Communications 235 (2004) 89–98 www.elsevier.com/locate/optcom
Performance evaluation of a multi-wavelength gigahertz optical source for wavelength division multiplexed transmission Nimish Dixit, R. Vijaya
*
Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India Received 2 October 2003; received in revised form 4 February 2004; accepted 3 March 2004
Abstract The performance of a multi-channel pulsed optical source derived from a broadband spectrum has been numerically studied in a wavelength division multiplexed (WDM) transmission system. Eye-opening penalty is calculated as a measure of the system performance. The possibility to vary the duty cycle of the pulses, other conditions being identical, leads to conclusive results for the physical mechanism of eye-degradation of these pulses in WDM transmission. Ó 2004 Elsevier B.V. All rights reserved. PACS: 42.79.Sz; 42.81.Dp Keywords: Optical fiber communication; Dispersion compensation; Wavelength division multiplexing; WDM source
1. Introduction The advent of optical fibers has completely revolutionized the field of information transfer due to the availability of enormous bandwidth associated with them. The large low loss transmission window of an optical fiber can be utilized through dense wavelength division multiplexing (DWDM) scheme. In DWDM, several closely spaced channels are multiplexed in the wavelength domain to
*
Corresponding author. Tel.: +912225767577; +912225723480. E-mail address: [email protected] (R. Vijaya).
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increase the system throughput [1]. A lot of effort has been devoted in the past to the study of WDM systems [2–9]. Since the chromatic dispersion and the optical nonlinear effects in fibers are the main limiting factors for realizing a WDM system, it is important to choose an optimal dispersion compensation scheme and a suitable modulation format [2,4–6]. Two commonly used modulation formats are return-to-zero (RZ) and nonreturn-to-zero (NRZ). An improved understanding of the WDM system design has been attained by the comparison between these two modulation formats under different conditions [2,4]. An alternate-chirped nonreturn-to-zero (AC-NRZ) format has been
0030-4018/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.03.008
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suggested by Hodzic et al. for improving the performance of 40 Gb/s/channel WDM system [6]. A variation of RZ modulation format known as carrier-suppressed return-to-zero (CS-RZ) has also been suggested [9]. Commonly, the source in a WDM network consists of separate laser diodes for each wavelength channel. However, in DWDM systems, where several closely spaced channels are simultaneously propagated through the same fiber, the wavelength stability of the source becomes an issue of prime importance. This has been achieved by spectrally slicing the output of a single broadband source to get multi-wavelength GHz output [10– 13]. Mode-locked lasers are used to generate a broadband spectrum, which is subsequently sliced in the spectral domain to get multiple channels [10–12]. Another alternative is to compress an optical beat signal in the time domain and enrich its spectral content through propagation in lowdispersion fibers. In our earlier work, we have studied the generation of picosecond pulse train of 10 GHz frequency at 16 different wavelengths suitable for WDM transmission beginning with a beat signal [13,14]. The double-side band, suppressed carrier beat signal, has the advantage that adjacent pulses have p-phase difference between them, thus maintaining an ultra-stable mark-tospace ratio [15,16]. In the present work, we numerically study the performance of the multi-wavelength source proposed by us earlier [13] in a practical WDM transmission system. Here, we consider the propagation of eight channels at 10 GHz repetition rate with an inter-channel separation of 100 GHz. For ease of interpretation of results, the number of channels has been kept low. It is possible to analyze more number of channels and at faster data rates of 40 Gb/s since the design can support these possibilities [14]. The duty cycle of the pulses used in WDM propagation can be varied in this design. A simple dispersion compensated fiber link, where the accumulated dispersion of the conventional single mode fiber (SMF) is exactly compensated with the help of a dispersion compensating fiber (DCF), is studied. A fiber amplifier compensates for the total loss suffered by the pulses in one span.
Eye-opening penalty (EOP) is used as a measure of the performance of the system. After elaborating on the theoretical background, the numerical tool used for studying the system performance is discussed in detail. This is followed by a brief description of the characteristics of the multi-wavelength source used for this study. Lastly, the variation of EOP as a function of span length and input power for different duty cycles is analyzed and the physical characteristics underlying the performance are deduced.
2. System description Pulse propagation in an optical fiber is governed by the nonlinear Schr€ oedinger equation (NLSE) given by [17] oA a b o2 A b3 o3 A ¼ Ai 2 þ oz 2" 2 oT 2 6 oT# 3 2 ojAj þ ic jAj2 A TR A ; oT
ð1Þ
where A denotes the complex amplitude of the slowly varying optical field and T is the time measured in the frame of reference which is moving with the pulse. The first term on the right-hand side of the above equation is the loss term, the second term governs the effect of second-order dispersion, the third term accounts for the thirdorder dispersion effects and fourth term takes in to account the effect of self-phase modulation (SPM), where c ð¼ 2pn2 =kAeff Þ is the nonlinear parameter (n2 is the intensity dependent refractive index and Aeff is the effective core area of the fiber). The last term in the above equation has its origin in the delayed Raman response and gives rise to Raman self-frequency shift due to the intrapulse Raman scattering. TR can be related to the slope of the Raman gain spectrum. This term becomes important and should be included for short pulses with a broad spectrum. In such a case, lower frequency components of the pulse get amplified at the expense of the higher frequency components of the same pulse due to the energy transfer from higher frequency components to the lower frequency components of the same pulse.
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There are two methods by which a WDM system can be modeled. In one method, the total optical field is split into, say, M-components to obtain a set of coupled NLSE, which include the important dispersive and nonlinear terms [18], where M is the total number of channels. This approach becomes too cumbersome when the number of channels is large. The other method that is comparatively simpler is the total field approach. In this technique, the NLSE is solved with the input field of the form [18], " # M pffiffiffiffiffi X K X Að0; T Þ ¼ Pm bk Um ðT kTB Þ m¼1
k¼1
exp½iðxm x0 ÞT ;
ð2Þ
where Pm is the power, Um is the pulse shape of the mth channel, TB is the bit slot at the bit rate B, K represents the number of bits included in the numerical model and bk ¼ 0 or 1 depending on whether kth time slot contains a 0 or 1 bit. This technique automatically includes the effects of SPM, XPM, FWM and Raman crosstalk. The NLSE is solved numerically using the wellknown split step Fourier transform algorithm [17]. Simulations are done for a random bit sequence consisting of 128-bits. The amplifier noise with a chosen noise figure of 6 dB is modeled as a white noise created by a gaussian random number generator and added to the optical field at the output of each amplifier [5,19,20]. At the output end, each of the channels are filtered using a specially designed optical filter with an amplitude transfer function [7,8], " 2n 2 # m mm m mm f ðmÞ ¼ exp ; ð3Þ dms dmg which is a combination of Gaussian and superGaussian filters. Here, m is the optical frequency, mm is the central frequency of the mth channel and n is the order of the superGaussian, which controls the degree of edge sharpness. dms and dmg are the bandwidths of the superGaussian and Gaussian respectively. This kind of filter performs two operations simultaneously: the first part gives a sharp cut-off so that the adjacent WDM channels are well separated and the second part ensures the
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guiding top [7,8]. For the filtering operation, the value of n ¼ 7, dmg ¼ 150 GHz and the ratio of dms and dmg to be 0.65 are considered. The combination of Gaussian and superGaussian functions in the filter leads to an effective 3-dB bandwidth of nearly 100 GHz. These optimized values were obtained after performing a number of trials on filtering of the input and output WDM channels. The performance of the different wavelength channels used in a WDM system is evaluated in terms of the eye-opening penalty (EOP) suffered by them, defined as [21], minð‘1’btb Þ maxð‘0’btb Þ EOP ¼ 10 log10 ; ð4Þ minð‘1’R Þ maxð‘0’R Þ where ‘1’btb and ‘0’btb are the amplitudes of ‘ones’ and ‘zeros’ in back-to-back (i.e., without any transmission line), and ‘1’R and ‘0’R are the amplitudes of the received marks and spaces. EOP predicts the qualitative behavior of the signal at the output of the link. Generally, a good system performance is obtained for an EOP less than 1 dB [21]. But even a higher EOP of 3 dB can give bit error rates lower than 109 [22], thus being within acceptable limits.
3. Generation of 10 GHz multi-wavelength optical pulse train The block diagram of the source for the generation of multi-wavelength 10 GHz output is shown in Fig. 1(a). This is essentially the same as proposed in our earlier work [13]. Fig. 1(b) shows the schematic system set-up for modeling the WDM transmission system using this source. The values of the fiber parameters used are given in Table 1. The beat signal at 10 GHz frequency can be generated by combining the outputs of two narrow line-width DFB laser diodes. The beat signal has an average power of a few milliwatts at the central wavelength of 1549.72 nm. This wavelength has been chosen such that after slicing, the wavelengths of the channels of the WDM source exactly fall on the ITU-T DWDM grid. This beat signal may be amplified to an average power of around 250 mW using high power Er3þ -doped fiber amplifier (EDFA) [23]. An additional
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λ1
BPF
EDFA
NOLM consisting of SMF for pulse shaping & noise reduction
Beat signal generation at 10 GHz
DFF 8 km for spectral broadening
DEMUX with bandwidth 40, 25 or 16 GHz
(a)
λ8
SMF-1 λ1 λ2
DCF-1
M
F I L T E R
EDFA 50km
10 km
U λ8
X
(b)
λ1 λ2
λ8
Repeated N times
Fig. 1. Schematic diagram of: (a) set-up for the generation of multi-channel optical source; BPF indicates a band pass filter; (b) set-up for the simulated WDM transmission.
Table 1 Fiber parameters used in the calculations Parameters
SMF
DFF
SMF-1
DCF-1
b2 (ps2 /km) b3 (ps3 /km) n2 (m2 /W) a (dB/km) Aeff (lm2 ) TR (fs)
)27.9 +0.13 3.2 1020 0.2 50 3
+0.55 0 3.2 1020 0.2 50 3
)20.4 +0.16 1.624 1020 0.2 50 3
+102 )0.51 4.33 1020 0.5 50 3
component of band pass filter (BPF) in Fig. 1(a) helps to suppress the broadband amplified spontaneous emission noise from the EDFA. When this beat signal with a peak power of 0.5 W is passed through a nonlinear optical loop mirror (NOLM) consisting of 6 km SMF, we obtain a pulse train of peak power 2.3 W having an FWHM of 4 ps. Here, the function of the NOLM is to shape the pulse with a simultaneous increase in the peak power [14]. In addition, it also suppresses the pedestals associated with the output pulse due to its intensity-dependent transmission. When this pulse train is subsequently passed through 9 km dispersion flattened fiber (DFF), the
3-dB bandwidth of the spectrum is enhanced to 1600 GHz. The output spectrum is then sliced using a 1 8 WDM DEMUX having a Gaussian profile with bandwidths of 40, 25 or 16 GHz and the central wavelengths separated by 100 GHz. The power variation and the pulse width variation for the eight channels for the filter bandwidths mentioned above are shown in Fig. 2(a) and (b), respectively. The filter bandwidths of 40, 25 and 16 GHz result in pulse trains with an average FWHM of 15, 27 and 37 ps, which correspond to duty ratios of 15%, 27% and 37%, respectively. A power variation of 5.2, 2.7 and 1.5 mW is observed across the channels in the case of 40, 25 and 16 GHz
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maximum peak power that we have chosen in our calculations. Generally, nonlinear phase shifts of 1 mrad/step are used [4,24]. 4.1. Propagation of pulses with 15% duty ratio
Fig. 2. (a) Peak power and (b) pulse width variation across the sliced channels in Fig. 1(a) for the filter bandwidths BW ¼ 40, 25 or 16 GHz.
bandwidths, respectively. The wavelengths of the eight sliced channels numbered 1–8 can be identified as 1546.92, 1547.72, 1548.52, 1549.32, 1550.12, 1550.92, 1551.72 and 1552.53 nm.
4. Multi-channel propagation Schematic diagram of the system proposed for studying the WDM propagation source is shown in Fig. 1(b). In the last section, we have mentioned that there is a power variation among the channels. The power of all the eight channels is equalized before propagation. The system set-up is composed of a 50 km SMF-1 and 10 km DCF-1. The DCF-1 length is chosen such that it compensates for the total dispersion of SMF-1 at the central wavelength. Then an EDFA compensates for the total loss suffered by the pulses during their propagation in one span (SMF-1 + DCF-1). Each channel is modulated with a 128-bit random sequence. The number of Fourier points in the spectral window is chosen to be 32,768 in order to meet the bandwidth requirements of the system simulations. The step size is 50 m, which gives a nonlinear phase shift of 1.1 mrad even for the
A data stream of 10 Gb/s rate is modulated on the pulse train with 15% duty cycle. Input peak power of each channel is fixed at 0 dBm. The EOP (in dB) is calculated and plotted as a function of number of spans in Fig. 3. The EOP increases with the increase in the number of spans, as expected. The EOP of the channels 1 and 8, 2 and 7, 3 and 6, and 4 and 5 are nearly equal even for 25 spans. The central two channels have the smallest value of EOP and it increases as we move towards the outer channels. This is due to the fact that residual dispersion for the central two channels will be the least among all the channels. The residual dispersion experienced by the pair of channels 1 and 8, 2 and 7, 3 and 6, and 4 and 5 will be the same in magnitude. But it is important to note that channels 1–4 experience normal residual dispersion and channels 5–8 experience anomalous residual dispersion. One interesting point here is that even for the larger number of spans up to 25 spans, the EOP of the symmetrically placed channels 1 and 8, 2 and 7, 3 and 6, and 4 and 5 remains the same. In the presence of optical nonlinearity of the fiber,
Fig. 3. EOP as a function of number of spans for the pulses with 15% duty ratio without including ASE noise.
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channels on one side should behave in a different manner as compared to the channels on the other side of the central wavelength. Normal and anomalous residual dispersion should give qualitatively different results in the presence of optical nonlinearity. But the trend in the present results leads to the conclusion that dispersion is playing a relatively more important role as compared to the nonlinearity. We will verify this point further in the next set of calculations. The ASE noise coming out of the EDFA was not included in this part of the study. We can see from Fig. 3 that, for an input power of 0 dBm, the EOP up to 10 spans (500 km of SMF) is less than 1 dB, which is an indication of good system performance [21]. So in the next part, the number of spans is fixed at 10 and the input power/channel is varied. The ASE noise of the EDFA is neglected. Fig. 4 shows the plot of EOP versus input power/channel in dBm. The EOP is initially constant and then increases with the increase in the power. The EOP of the channels 1 and 8, 2 and 7, 3 and 6, and 4 and 5 are the same even for input powers exceeding 5 dBm although the sign of the residual dispersion on either side of the central wavelength is opposite. This suggests that, although nonlinear effects will play a significant role in the eye-degradation at increased powers, dispersion is dominant since the duty ratio of the pulses is only 15%.
Fig. 5 depicts the variation of EOP with input power after including the ASE noise from EDFA. The average power of the ASE noise after each span is )17 dBm, calculated by the method suggested in [19,20]. If we compare Figs. 4 and 5, there is no appreciable difference between the EOP with and without the inclusion of the noise. This is mainly due to the limited number of spans considered here. The effect of noise will be more important when the SNR degrades for a larger number of spans. Moreover, the effect of noise is not significant even for signal powers as small as )16 dBm. If the effect of noise had shown up, the EOP for the lower powers would have been slightly larger. In an earlier work [4], RZ pulses with 50% duty ratio were found to be ASE noiselimited at lower powers, and at larger powers, either dispersion or nonlinearity-limited depending on the chosen bit rate. For our source design, the effect of ASE noise is not significant even at the lower powers and at larger powers, performance is limited more by dispersion than by nonlinearity. In Fig. 6, the output eye-diagrams are shown for channels 1, 4, 5 and 8 for an input power of 0 dBm after propagation in 10 spans. Eye-degradation for channels 4 and 5 is smaller as compared to channels 1 and 8. The larger eye-degradation in channels 1 and 8 is due to the decrease in the peak power, which is attributed to the presence of a larger residual dispersion. This is another indica-
Fig. 4. EOP as a function of input power per channel for the pulses with 15% duty ratio without including ASE noise.
Fig. 5. EOP as a function of input power per channel for the pulses with 15% duty ratio after including ASE noise.
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spans is fixed at 10 and the variation of EOP with the input power/channel in dBm is plotted in Figs. 7 and 8. These results lead us to the following conclusions: (i) If we compare the results obtained in Fig. 4 for 15% duty cycle with that obtained in Fig. 7 for 27% duty cycle, we see that, for lower power levels up to 4 dBm, the EOP in the case of 27% duty cycle is less than the EOP in the case of 15% duty cycle with the exception of central
Fig. 6. Two bit-wide output eye-diagrams for channels 1, 4, 5 and 8 (a–d) for an input peak power of 0 dBm after 10 spans of propagation.
tion of dominance of dispersion for these pulses. One more noteworthy feature is that there is no appreciable timing-jitter in the output eyediagram. Since these pulses have been derived from a beat signal, the adjacent pulses have a phase difference of p, thus reducing the interaction among the pulses and hence the reduced timingjitter. Walk-off among the channels, due to the presence of residual dispersion, is, however, present as observed from the eye-diagrams. A lesser walk-off is observed for channels 4 and 5 since they encounter smaller residual dispersion as compared to the channels 1 and 8. The effect of changing the duty cycle of the pulses on the system performance and elucidation of the physical mechanism for EOP degradation is carried out in the following section.
Fig. 7. EOP as a function of input power per channel for the pulses with 27% duty ratio after the inclusion of ASE noise.
4.2. Propagation of pulses with higher duty ratio As mentioned in an earlier section, the pulse train with 27% and 37% duty ratio can be generated by using a filter of suitable bandwidth to slice the channels from the broadband spectrum. Every channel is modulated with a 10 Gb/s, 128-bit data stream as in the previous case. The number of
Fig. 8. EOP as a function of input power per channel for the pulses with 37% duty ratio after the inclusion of ASE noise.
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two channels. Since the pulse power considered in both the cases is the same, we may infer that the larger dispersion felt by the shorter duration pulses of 15% duty cycle is the major cause for eye-degradation. (ii) On the other hand, as the power is increased to 8 dBm, EOP in the case of 27% duty cycle pulses becomes more than that with 15% duty cycle. This degradation in the eyeopening may be attributed to the increase in the nonlinear contribution for the larger powers. (iii) The difference of EOP among all the eight channels is less in the case of 27% duty cycle as compared to the case with 15% duty cycle. This is due to the larger interplay between the dispersion and nonlinearity for increased pulse widths. (iv) In Fig. 7, for lower powers, EOP of the channels 1 and 8, 2 and 7, 3 and 6, and 4 and 5 are equal, but as the power increases, there is a variation given by EOPchannel1 > EOPchannel8 , EOPchannel2 > EOPchannel7 , EOPchannel3 > EOPchannel6 and EOPchannel4 > EOPchannel5 , and this difference in EOP for similar channels keeps on increasing with the power. The residual dispersion in the case of channels 1–4 being normal, there is further broadening of the spectrum thus resulting in larger EOP in the presence of nonlinearity. In contrast, channels 5–8 experience anomalous residual dispersion; their interplay with the nonlinearity may increase the peak power thus resulting in lesser EOP. This behavior was not observed in the case of 15% where the dispersion was dominant. (v) From Fig. 8, it can be seen that at very low powers, such as )8 dBm, all the eight channels have almost the same EOP and this is somewhat less than that obtained in the case of 27% duty cycle. At the same time, the difference in the EOPs of the channels 1 and 8, 2 and 7, 3 and 6, and 4 and 5 increases and becomes more than that obtained in the case of 27% duty cycle. This trend further emphasizes a larger interplay between the optical nonlinearity and residual dispersion of the fiber for higher duty ratios similar to that indicated in (iii) earlier.
5. Discussion It has been suggested in an earlier work [4] that, at 10 and 20 Gb/s, WDM systems work better using RZ modulation format because they take advantage of soliton-like pulse compression in the SMF. For 40 Gb/s, systems perform better with the RZ modulation format if the number of channels is small but requires NRZ as the number of channels increase. NRZ format has an advantage over the RZ modulation format since it has a higher spectral efficiency because of lesser spectral bandwidth. In our case, the RZ modulation format considered has p-phase difference between the adjacent pulses since it has been derived from a double-side band, suppressed carrier signal, thus reducing the nonlinear interaction and hence the timing jitter. In addition, it gives more input power tolerance. In the case of RZ modulation format, the choice of duty ratio becomes very important. If the duty ratio of the pulse is small, the system performance is largely affected by the dispersion as we noticed in the case of 15% duty ratio pulses. This has the advantage that the system performance is more stable against the input power fluctuations. As the duty ratio is increased, the contribution of nonlinearity in deciding the system performance also increases. This leads to some interesting implications as we have observed in the case of 27% and 37% duty ratio pulses. At low powers, EOP of all the eight channels is nearly equal and difference in EOPs for the channels equispaced from the central wavelength increases with the increase in the power. One more noteworthy feature is that the spectral efficiency can be improved in going from 15% duty ratio pulses to 37% duty ratio pulses. If the dispersion dominates, it will lead to a reduction in the peak power of the pulse, resulting in a larger EOP and there will be a walk-off among the various channels. If the nonlinearity is dominant, this may lead to peak power fluctuations and timing jitter because of the nonlinear interaction among the adjacent pulses and neighboring channels. A judicious choice will result in the best system performance. For ease in the interpretation of the system performance, an eight-channel WDM transmis-
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sion system has been considered in this work. However, there is a possibility of slicing 16 channels from the same source as mentioned in [13]. While studying the performance of such a 16channel system, for lower duty ratio pulses, the effect of residual dispersion will be even more for the extreme channels as compared to the eightchannel system resulting in a larger EOP. In this case it would be better to use the pulses with higher duty ratio so as to counter the dispersion with the nonlinearity. But for a larger duty ratio, the difference in EOPs of the extreme channels 1 and 16 will be even larger than in an eight-channel system. For channel 1, interplay between normal residual dispersion and optical nonlinearity will lead to a larger EOP but channel 16 will have a lower EOP because the anomalous dispersion will get compensated by the optical nonlinearity. Thus, as the number of channels increases, it becomes very important to compensate the dispersion slope, i.e., third-order dispersion effects. It is possible to slice 16-channels at an inter-channel spacing of 50 GHz to overcome some of these difficulties. In our source design, there is a possibility of scaling the repetition rate of the pulses to higher values of 20 or 40 GHz by changing the wavelength difference between the two lasers used to generate the beat signal. By choosing a suitable system hardware, the spectral width of this beat signal can be enhanced in the same way as seen in the case of 10 GHz beat signal [13]. This broad spectrum can be sliced to obtain multi-wavelength carriers at 40 Gb/s repetition rate. Thus, the source design is capable of delivering pulses at 40 GHz repetition rate. For propagation of these pulses in a WDM transmission system, the choice of the duty ratio of the pulses will significantly affect the system performance. In the case of lower duty ratio pulses, the effect of dispersion will be more deteriorating as compared to 10 GHz pulses with the same duty ratio. Quantitatively, 15% duty ratio leads to pulse widths of 15 and 3.8 ps in the case of 10 and 40 GHz pulse train, respectively. In our point of view the duty ratio of the pulse should be as large as possible. The other factor determined by the duty ratio is the spectral efficiency, which can be made higher for the larger duty ratio pulses, thus giving a better system performance.
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6. Conclusion In conclusion, we have studied the performance of a multi-channel optical source for its utility in a realistic WDM transmission system. We have considered the propagation of eight channels of 10 Gb/s at different duty ratios for the pulses. At lower duty cycles, the main cause for eye-degradation is the chromatic dispersion because of the smaller pulse widths indicating a larger tolerance to input power fluctuations. In this case, it is observed that for the channels equi-spaced with the central wavelength, the EOP is equal. But as the duty ratio is increased, the difference of EOP among the channels at lower power levels is small, but gets unequal for similar channels at higher powers. This is due to the fact that the channels experience different signs of residual dispersion on either side of the central wavelength. The performance is not much limited by ASE noise even at very low signal powers but gets limited by a combined dispersion and nonlinearity effect at larger powers as the duty ratio is increased. The best system performance is therefore possible with a judicious choice for the duty cycle of the pulse train, sliced from the broadband source, for appropriate transmission conditions.
Acknowledgements The authors acknowledge Ninad V. Pimparkar for his help in the coding of the program for the WDM transmission.
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Performance evaluation of a multi-wavelength gigahertz optical source for wavelength division multiplexed transmission Nimish Dixit, R. Vijaya
*
Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India Received 2 October 2003; received in revised form 4 February 2004; accepted 3 March 2004
Abstract The performance of a multi-channel pulsed optical source derived from a broadband spectrum has been numerically studied in a wavelength division multiplexed (WDM) transmission system. Eye-opening penalty is calculated as a measure of the system performance. The possibility to vary the duty cycle of the pulses, other conditions being identical, leads to conclusive results for the physical mechanism of eye-degradation of these pulses in WDM transmission. Ó 2004 Elsevier B.V. All rights reserved. PACS: 42.79.Sz; 42.81.Dp Keywords: Optical fiber communication; Dispersion compensation; Wavelength division multiplexing; WDM source
1. Introduction The advent of optical fibers has completely revolutionized the field of information transfer due to the availability of enormous bandwidth associated with them. The large low loss transmission window of an optical fiber can be utilized through dense wavelength division multiplexing (DWDM) scheme. In DWDM, several closely spaced channels are multiplexed in the wavelength domain to
*
Corresponding author. Tel.: +912225767577; +912225723480. E-mail address: [email protected] (R. Vijaya).
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increase the system throughput [1]. A lot of effort has been devoted in the past to the study of WDM systems [2–9]. Since the chromatic dispersion and the optical nonlinear effects in fibers are the main limiting factors for realizing a WDM system, it is important to choose an optimal dispersion compensation scheme and a suitable modulation format [2,4–6]. Two commonly used modulation formats are return-to-zero (RZ) and nonreturn-to-zero (NRZ). An improved understanding of the WDM system design has been attained by the comparison between these two modulation formats under different conditions [2,4]. An alternate-chirped nonreturn-to-zero (AC-NRZ) format has been
0030-4018/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.03.008
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suggested by Hodzic et al. for improving the performance of 40 Gb/s/channel WDM system [6]. A variation of RZ modulation format known as carrier-suppressed return-to-zero (CS-RZ) has also been suggested [9]. Commonly, the source in a WDM network consists of separate laser diodes for each wavelength channel. However, in DWDM systems, where several closely spaced channels are simultaneously propagated through the same fiber, the wavelength stability of the source becomes an issue of prime importance. This has been achieved by spectrally slicing the output of a single broadband source to get multi-wavelength GHz output [10– 13]. Mode-locked lasers are used to generate a broadband spectrum, which is subsequently sliced in the spectral domain to get multiple channels [10–12]. Another alternative is to compress an optical beat signal in the time domain and enrich its spectral content through propagation in lowdispersion fibers. In our earlier work, we have studied the generation of picosecond pulse train of 10 GHz frequency at 16 different wavelengths suitable for WDM transmission beginning with a beat signal [13,14]. The double-side band, suppressed carrier beat signal, has the advantage that adjacent pulses have p-phase difference between them, thus maintaining an ultra-stable mark-tospace ratio [15,16]. In the present work, we numerically study the performance of the multi-wavelength source proposed by us earlier [13] in a practical WDM transmission system. Here, we consider the propagation of eight channels at 10 GHz repetition rate with an inter-channel separation of 100 GHz. For ease of interpretation of results, the number of channels has been kept low. It is possible to analyze more number of channels and at faster data rates of 40 Gb/s since the design can support these possibilities [14]. The duty cycle of the pulses used in WDM propagation can be varied in this design. A simple dispersion compensated fiber link, where the accumulated dispersion of the conventional single mode fiber (SMF) is exactly compensated with the help of a dispersion compensating fiber (DCF), is studied. A fiber amplifier compensates for the total loss suffered by the pulses in one span.
Eye-opening penalty (EOP) is used as a measure of the performance of the system. After elaborating on the theoretical background, the numerical tool used for studying the system performance is discussed in detail. This is followed by a brief description of the characteristics of the multi-wavelength source used for this study. Lastly, the variation of EOP as a function of span length and input power for different duty cycles is analyzed and the physical characteristics underlying the performance are deduced.
2. System description Pulse propagation in an optical fiber is governed by the nonlinear Schr€ oedinger equation (NLSE) given by [17] oA a b o2 A b3 o3 A ¼ Ai 2 þ oz 2" 2 oT 2 6 oT# 3 2 ojAj þ ic jAj2 A TR A ; oT
ð1Þ
where A denotes the complex amplitude of the slowly varying optical field and T is the time measured in the frame of reference which is moving with the pulse. The first term on the right-hand side of the above equation is the loss term, the second term governs the effect of second-order dispersion, the third term accounts for the thirdorder dispersion effects and fourth term takes in to account the effect of self-phase modulation (SPM), where c ð¼ 2pn2 =kAeff Þ is the nonlinear parameter (n2 is the intensity dependent refractive index and Aeff is the effective core area of the fiber). The last term in the above equation has its origin in the delayed Raman response and gives rise to Raman self-frequency shift due to the intrapulse Raman scattering. TR can be related to the slope of the Raman gain spectrum. This term becomes important and should be included for short pulses with a broad spectrum. In such a case, lower frequency components of the pulse get amplified at the expense of the higher frequency components of the same pulse due to the energy transfer from higher frequency components to the lower frequency components of the same pulse.
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There are two methods by which a WDM system can be modeled. In one method, the total optical field is split into, say, M-components to obtain a set of coupled NLSE, which include the important dispersive and nonlinear terms [18], where M is the total number of channels. This approach becomes too cumbersome when the number of channels is large. The other method that is comparatively simpler is the total field approach. In this technique, the NLSE is solved with the input field of the form [18], " # M pffiffiffiffiffi X K X Að0; T Þ ¼ Pm bk Um ðT kTB Þ m¼1
k¼1
exp½iðxm x0 ÞT ;
ð2Þ
where Pm is the power, Um is the pulse shape of the mth channel, TB is the bit slot at the bit rate B, K represents the number of bits included in the numerical model and bk ¼ 0 or 1 depending on whether kth time slot contains a 0 or 1 bit. This technique automatically includes the effects of SPM, XPM, FWM and Raman crosstalk. The NLSE is solved numerically using the wellknown split step Fourier transform algorithm [17]. Simulations are done for a random bit sequence consisting of 128-bits. The amplifier noise with a chosen noise figure of 6 dB is modeled as a white noise created by a gaussian random number generator and added to the optical field at the output of each amplifier [5,19,20]. At the output end, each of the channels are filtered using a specially designed optical filter with an amplitude transfer function [7,8], " 2n 2 # m mm m mm f ðmÞ ¼ exp ; ð3Þ dms dmg which is a combination of Gaussian and superGaussian filters. Here, m is the optical frequency, mm is the central frequency of the mth channel and n is the order of the superGaussian, which controls the degree of edge sharpness. dms and dmg are the bandwidths of the superGaussian and Gaussian respectively. This kind of filter performs two operations simultaneously: the first part gives a sharp cut-off so that the adjacent WDM channels are well separated and the second part ensures the
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guiding top [7,8]. For the filtering operation, the value of n ¼ 7, dmg ¼ 150 GHz and the ratio of dms and dmg to be 0.65 are considered. The combination of Gaussian and superGaussian functions in the filter leads to an effective 3-dB bandwidth of nearly 100 GHz. These optimized values were obtained after performing a number of trials on filtering of the input and output WDM channels. The performance of the different wavelength channels used in a WDM system is evaluated in terms of the eye-opening penalty (EOP) suffered by them, defined as [21], minð‘1’btb Þ maxð‘0’btb Þ EOP ¼ 10 log10 ; ð4Þ minð‘1’R Þ maxð‘0’R Þ where ‘1’btb and ‘0’btb are the amplitudes of ‘ones’ and ‘zeros’ in back-to-back (i.e., without any transmission line), and ‘1’R and ‘0’R are the amplitudes of the received marks and spaces. EOP predicts the qualitative behavior of the signal at the output of the link. Generally, a good system performance is obtained for an EOP less than 1 dB [21]. But even a higher EOP of 3 dB can give bit error rates lower than 109 [22], thus being within acceptable limits.
3. Generation of 10 GHz multi-wavelength optical pulse train The block diagram of the source for the generation of multi-wavelength 10 GHz output is shown in Fig. 1(a). This is essentially the same as proposed in our earlier work [13]. Fig. 1(b) shows the schematic system set-up for modeling the WDM transmission system using this source. The values of the fiber parameters used are given in Table 1. The beat signal at 10 GHz frequency can be generated by combining the outputs of two narrow line-width DFB laser diodes. The beat signal has an average power of a few milliwatts at the central wavelength of 1549.72 nm. This wavelength has been chosen such that after slicing, the wavelengths of the channels of the WDM source exactly fall on the ITU-T DWDM grid. This beat signal may be amplified to an average power of around 250 mW using high power Er3þ -doped fiber amplifier (EDFA) [23]. An additional
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λ1
BPF
EDFA
NOLM consisting of SMF for pulse shaping & noise reduction
Beat signal generation at 10 GHz
DFF 8 km for spectral broadening
DEMUX with bandwidth 40, 25 or 16 GHz
(a)
λ8
SMF-1 λ1 λ2
DCF-1
M
F I L T E R
EDFA 50km
10 km
U λ8
X
(b)
λ1 λ2
λ8
Repeated N times
Fig. 1. Schematic diagram of: (a) set-up for the generation of multi-channel optical source; BPF indicates a band pass filter; (b) set-up for the simulated WDM transmission.
Table 1 Fiber parameters used in the calculations Parameters
SMF
DFF
SMF-1
DCF-1
b2 (ps2 /km) b3 (ps3 /km) n2 (m2 /W) a (dB/km) Aeff (lm2 ) TR (fs)
)27.9 +0.13 3.2 1020 0.2 50 3
+0.55 0 3.2 1020 0.2 50 3
)20.4 +0.16 1.624 1020 0.2 50 3
+102 )0.51 4.33 1020 0.5 50 3
component of band pass filter (BPF) in Fig. 1(a) helps to suppress the broadband amplified spontaneous emission noise from the EDFA. When this beat signal with a peak power of 0.5 W is passed through a nonlinear optical loop mirror (NOLM) consisting of 6 km SMF, we obtain a pulse train of peak power 2.3 W having an FWHM of 4 ps. Here, the function of the NOLM is to shape the pulse with a simultaneous increase in the peak power [14]. In addition, it also suppresses the pedestals associated with the output pulse due to its intensity-dependent transmission. When this pulse train is subsequently passed through 9 km dispersion flattened fiber (DFF), the
3-dB bandwidth of the spectrum is enhanced to 1600 GHz. The output spectrum is then sliced using a 1 8 WDM DEMUX having a Gaussian profile with bandwidths of 40, 25 or 16 GHz and the central wavelengths separated by 100 GHz. The power variation and the pulse width variation for the eight channels for the filter bandwidths mentioned above are shown in Fig. 2(a) and (b), respectively. The filter bandwidths of 40, 25 and 16 GHz result in pulse trains with an average FWHM of 15, 27 and 37 ps, which correspond to duty ratios of 15%, 27% and 37%, respectively. A power variation of 5.2, 2.7 and 1.5 mW is observed across the channels in the case of 40, 25 and 16 GHz
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maximum peak power that we have chosen in our calculations. Generally, nonlinear phase shifts of 1 mrad/step are used [4,24]. 4.1. Propagation of pulses with 15% duty ratio
Fig. 2. (a) Peak power and (b) pulse width variation across the sliced channels in Fig. 1(a) for the filter bandwidths BW ¼ 40, 25 or 16 GHz.
bandwidths, respectively. The wavelengths of the eight sliced channels numbered 1–8 can be identified as 1546.92, 1547.72, 1548.52, 1549.32, 1550.12, 1550.92, 1551.72 and 1552.53 nm.
4. Multi-channel propagation Schematic diagram of the system proposed for studying the WDM propagation source is shown in Fig. 1(b). In the last section, we have mentioned that there is a power variation among the channels. The power of all the eight channels is equalized before propagation. The system set-up is composed of a 50 km SMF-1 and 10 km DCF-1. The DCF-1 length is chosen such that it compensates for the total dispersion of SMF-1 at the central wavelength. Then an EDFA compensates for the total loss suffered by the pulses during their propagation in one span (SMF-1 + DCF-1). Each channel is modulated with a 128-bit random sequence. The number of Fourier points in the spectral window is chosen to be 32,768 in order to meet the bandwidth requirements of the system simulations. The step size is 50 m, which gives a nonlinear phase shift of 1.1 mrad even for the
A data stream of 10 Gb/s rate is modulated on the pulse train with 15% duty cycle. Input peak power of each channel is fixed at 0 dBm. The EOP (in dB) is calculated and plotted as a function of number of spans in Fig. 3. The EOP increases with the increase in the number of spans, as expected. The EOP of the channels 1 and 8, 2 and 7, 3 and 6, and 4 and 5 are nearly equal even for 25 spans. The central two channels have the smallest value of EOP and it increases as we move towards the outer channels. This is due to the fact that residual dispersion for the central two channels will be the least among all the channels. The residual dispersion experienced by the pair of channels 1 and 8, 2 and 7, 3 and 6, and 4 and 5 will be the same in magnitude. But it is important to note that channels 1–4 experience normal residual dispersion and channels 5–8 experience anomalous residual dispersion. One interesting point here is that even for the larger number of spans up to 25 spans, the EOP of the symmetrically placed channels 1 and 8, 2 and 7, 3 and 6, and 4 and 5 remains the same. In the presence of optical nonlinearity of the fiber,
Fig. 3. EOP as a function of number of spans for the pulses with 15% duty ratio without including ASE noise.
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channels on one side should behave in a different manner as compared to the channels on the other side of the central wavelength. Normal and anomalous residual dispersion should give qualitatively different results in the presence of optical nonlinearity. But the trend in the present results leads to the conclusion that dispersion is playing a relatively more important role as compared to the nonlinearity. We will verify this point further in the next set of calculations. The ASE noise coming out of the EDFA was not included in this part of the study. We can see from Fig. 3 that, for an input power of 0 dBm, the EOP up to 10 spans (500 km of SMF) is less than 1 dB, which is an indication of good system performance [21]. So in the next part, the number of spans is fixed at 10 and the input power/channel is varied. The ASE noise of the EDFA is neglected. Fig. 4 shows the plot of EOP versus input power/channel in dBm. The EOP is initially constant and then increases with the increase in the power. The EOP of the channels 1 and 8, 2 and 7, 3 and 6, and 4 and 5 are the same even for input powers exceeding 5 dBm although the sign of the residual dispersion on either side of the central wavelength is opposite. This suggests that, although nonlinear effects will play a significant role in the eye-degradation at increased powers, dispersion is dominant since the duty ratio of the pulses is only 15%.
Fig. 5 depicts the variation of EOP with input power after including the ASE noise from EDFA. The average power of the ASE noise after each span is )17 dBm, calculated by the method suggested in [19,20]. If we compare Figs. 4 and 5, there is no appreciable difference between the EOP with and without the inclusion of the noise. This is mainly due to the limited number of spans considered here. The effect of noise will be more important when the SNR degrades for a larger number of spans. Moreover, the effect of noise is not significant even for signal powers as small as )16 dBm. If the effect of noise had shown up, the EOP for the lower powers would have been slightly larger. In an earlier work [4], RZ pulses with 50% duty ratio were found to be ASE noiselimited at lower powers, and at larger powers, either dispersion or nonlinearity-limited depending on the chosen bit rate. For our source design, the effect of ASE noise is not significant even at the lower powers and at larger powers, performance is limited more by dispersion than by nonlinearity. In Fig. 6, the output eye-diagrams are shown for channels 1, 4, 5 and 8 for an input power of 0 dBm after propagation in 10 spans. Eye-degradation for channels 4 and 5 is smaller as compared to channels 1 and 8. The larger eye-degradation in channels 1 and 8 is due to the decrease in the peak power, which is attributed to the presence of a larger residual dispersion. This is another indica-
Fig. 4. EOP as a function of input power per channel for the pulses with 15% duty ratio without including ASE noise.
Fig. 5. EOP as a function of input power per channel for the pulses with 15% duty ratio after including ASE noise.
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spans is fixed at 10 and the variation of EOP with the input power/channel in dBm is plotted in Figs. 7 and 8. These results lead us to the following conclusions: (i) If we compare the results obtained in Fig. 4 for 15% duty cycle with that obtained in Fig. 7 for 27% duty cycle, we see that, for lower power levels up to 4 dBm, the EOP in the case of 27% duty cycle is less than the EOP in the case of 15% duty cycle with the exception of central
Fig. 6. Two bit-wide output eye-diagrams for channels 1, 4, 5 and 8 (a–d) for an input peak power of 0 dBm after 10 spans of propagation.
tion of dominance of dispersion for these pulses. One more noteworthy feature is that there is no appreciable timing-jitter in the output eyediagram. Since these pulses have been derived from a beat signal, the adjacent pulses have a phase difference of p, thus reducing the interaction among the pulses and hence the reduced timingjitter. Walk-off among the channels, due to the presence of residual dispersion, is, however, present as observed from the eye-diagrams. A lesser walk-off is observed for channels 4 and 5 since they encounter smaller residual dispersion as compared to the channels 1 and 8. The effect of changing the duty cycle of the pulses on the system performance and elucidation of the physical mechanism for EOP degradation is carried out in the following section.
Fig. 7. EOP as a function of input power per channel for the pulses with 27% duty ratio after the inclusion of ASE noise.
4.2. Propagation of pulses with higher duty ratio As mentioned in an earlier section, the pulse train with 27% and 37% duty ratio can be generated by using a filter of suitable bandwidth to slice the channels from the broadband spectrum. Every channel is modulated with a 10 Gb/s, 128-bit data stream as in the previous case. The number of
Fig. 8. EOP as a function of input power per channel for the pulses with 37% duty ratio after the inclusion of ASE noise.
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two channels. Since the pulse power considered in both the cases is the same, we may infer that the larger dispersion felt by the shorter duration pulses of 15% duty cycle is the major cause for eye-degradation. (ii) On the other hand, as the power is increased to 8 dBm, EOP in the case of 27% duty cycle pulses becomes more than that with 15% duty cycle. This degradation in the eyeopening may be attributed to the increase in the nonlinear contribution for the larger powers. (iii) The difference of EOP among all the eight channels is less in the case of 27% duty cycle as compared to the case with 15% duty cycle. This is due to the larger interplay between the dispersion and nonlinearity for increased pulse widths. (iv) In Fig. 7, for lower powers, EOP of the channels 1 and 8, 2 and 7, 3 and 6, and 4 and 5 are equal, but as the power increases, there is a variation given by EOPchannel1 > EOPchannel8 , EOPchannel2 > EOPchannel7 , EOPchannel3 > EOPchannel6 and EOPchannel4 > EOPchannel5 , and this difference in EOP for similar channels keeps on increasing with the power. The residual dispersion in the case of channels 1–4 being normal, there is further broadening of the spectrum thus resulting in larger EOP in the presence of nonlinearity. In contrast, channels 5–8 experience anomalous residual dispersion; their interplay with the nonlinearity may increase the peak power thus resulting in lesser EOP. This behavior was not observed in the case of 15% where the dispersion was dominant. (v) From Fig. 8, it can be seen that at very low powers, such as )8 dBm, all the eight channels have almost the same EOP and this is somewhat less than that obtained in the case of 27% duty cycle. At the same time, the difference in the EOPs of the channels 1 and 8, 2 and 7, 3 and 6, and 4 and 5 increases and becomes more than that obtained in the case of 27% duty cycle. This trend further emphasizes a larger interplay between the optical nonlinearity and residual dispersion of the fiber for higher duty ratios similar to that indicated in (iii) earlier.
5. Discussion It has been suggested in an earlier work [4] that, at 10 and 20 Gb/s, WDM systems work better using RZ modulation format because they take advantage of soliton-like pulse compression in the SMF. For 40 Gb/s, systems perform better with the RZ modulation format if the number of channels is small but requires NRZ as the number of channels increase. NRZ format has an advantage over the RZ modulation format since it has a higher spectral efficiency because of lesser spectral bandwidth. In our case, the RZ modulation format considered has p-phase difference between the adjacent pulses since it has been derived from a double-side band, suppressed carrier signal, thus reducing the nonlinear interaction and hence the timing jitter. In addition, it gives more input power tolerance. In the case of RZ modulation format, the choice of duty ratio becomes very important. If the duty ratio of the pulse is small, the system performance is largely affected by the dispersion as we noticed in the case of 15% duty ratio pulses. This has the advantage that the system performance is more stable against the input power fluctuations. As the duty ratio is increased, the contribution of nonlinearity in deciding the system performance also increases. This leads to some interesting implications as we have observed in the case of 27% and 37% duty ratio pulses. At low powers, EOP of all the eight channels is nearly equal and difference in EOPs for the channels equispaced from the central wavelength increases with the increase in the power. One more noteworthy feature is that the spectral efficiency can be improved in going from 15% duty ratio pulses to 37% duty ratio pulses. If the dispersion dominates, it will lead to a reduction in the peak power of the pulse, resulting in a larger EOP and there will be a walk-off among the various channels. If the nonlinearity is dominant, this may lead to peak power fluctuations and timing jitter because of the nonlinear interaction among the adjacent pulses and neighboring channels. A judicious choice will result in the best system performance. For ease in the interpretation of the system performance, an eight-channel WDM transmis-
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sion system has been considered in this work. However, there is a possibility of slicing 16 channels from the same source as mentioned in [13]. While studying the performance of such a 16channel system, for lower duty ratio pulses, the effect of residual dispersion will be even more for the extreme channels as compared to the eightchannel system resulting in a larger EOP. In this case it would be better to use the pulses with higher duty ratio so as to counter the dispersion with the nonlinearity. But for a larger duty ratio, the difference in EOPs of the extreme channels 1 and 16 will be even larger than in an eight-channel system. For channel 1, interplay between normal residual dispersion and optical nonlinearity will lead to a larger EOP but channel 16 will have a lower EOP because the anomalous dispersion will get compensated by the optical nonlinearity. Thus, as the number of channels increases, it becomes very important to compensate the dispersion slope, i.e., third-order dispersion effects. It is possible to slice 16-channels at an inter-channel spacing of 50 GHz to overcome some of these difficulties. In our source design, there is a possibility of scaling the repetition rate of the pulses to higher values of 20 or 40 GHz by changing the wavelength difference between the two lasers used to generate the beat signal. By choosing a suitable system hardware, the spectral width of this beat signal can be enhanced in the same way as seen in the case of 10 GHz beat signal [13]. This broad spectrum can be sliced to obtain multi-wavelength carriers at 40 Gb/s repetition rate. Thus, the source design is capable of delivering pulses at 40 GHz repetition rate. For propagation of these pulses in a WDM transmission system, the choice of the duty ratio of the pulses will significantly affect the system performance. In the case of lower duty ratio pulses, the effect of dispersion will be more deteriorating as compared to 10 GHz pulses with the same duty ratio. Quantitatively, 15% duty ratio leads to pulse widths of 15 and 3.8 ps in the case of 10 and 40 GHz pulse train, respectively. In our point of view the duty ratio of the pulse should be as large as possible. The other factor determined by the duty ratio is the spectral efficiency, which can be made higher for the larger duty ratio pulses, thus giving a better system performance.
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6. Conclusion In conclusion, we have studied the performance of a multi-channel optical source for its utility in a realistic WDM transmission system. We have considered the propagation of eight channels of 10 Gb/s at different duty ratios for the pulses. At lower duty cycles, the main cause for eye-degradation is the chromatic dispersion because of the smaller pulse widths indicating a larger tolerance to input power fluctuations. In this case, it is observed that for the channels equi-spaced with the central wavelength, the EOP is equal. But as the duty ratio is increased, the difference of EOP among the channels at lower power levels is small, but gets unequal for similar channels at higher powers. This is due to the fact that the channels experience different signs of residual dispersion on either side of the central wavelength. The performance is not much limited by ASE noise even at very low signal powers but gets limited by a combined dispersion and nonlinearity effect at larger powers as the duty ratio is increased. The best system performance is therefore possible with a judicious choice for the duty cycle of the pulse train, sliced from the broadband source, for appropriate transmission conditions.
Acknowledgements The authors acknowledge Ninad V. Pimparkar for his help in the coding of the program for the WDM transmission.
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