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A theoretical study focusing on the effect of zero-crossing points in the dispersion map for the long-haul return-to-zero differential phase shift keying (RZ-DPSK) transmission system had been conducted. Difference of the transmission performance was characterized with regard to number of zero-crossing points within the dispersion map. It was observed that increasing the number of zero-crossing points in the dispersion map combined with the self phase modulation (SPM) caused the performance degradation near the system zero dispersion wavelength.
©2008 Optical Society of America
1. Introduction
Return-to-zero differential phase shift keying (RZ-DPSK) modulation format is attractive for the long-haul transmission systems, because it can improve the transmission performance [1–3]. Recently, it was reported that the combination of the RZ-DPSK modulation and the block type dispersion map showed a performance dip near the system zero dispersion wavelength while it was not observed for the block less type dispersion map [4–6]. The authors had conducted a theoretical study, and confirmed that the self phase modulation (SPM) played a significant role on this performance dip [7]. Previous experimental study also showed that the SPM was the primary reason to limit the transmission performance of long-haul RZ-DPSK system [8].
One notable difference between the block type map and the block less map is number of zero-crossing points of the cumulative chromatic dispersion along the transmission distance. There are several zero-crossing points in the block type dispersion map because the cumulative dispersion is compensated periodically, while there is only one zero-crossing point in the block less dispersion map. Therefore, increasing the number of zero-crossing points in the dispersion map is suspected to enhance the performance dip near the system zero dispersion wavelength of the RZ-DPSK system.
In this paper, we have numerically studied the effect of the zero-crossing points in the chromatic dispersion map. At first, the system performance of the block type dispersion map was evaluated as a function of the transmission distance. Then, the system performances of several different dispersion maps were evaluated as a function of number of zero-crossing points within the map. The results showed that large number of zero-crossing points in the dispersion map and the SPM caused the performance dip of the long-haul RZ-DPSK system near the system zero dispersion wavelength.
2. Simulation method and model
The numerical simulator solved coupled nonlinear Schrödinger equations using the split-step Fourier method [9]. The equation used for the simulation is:
where β2j is the second order group velocity dispersion (GVD) coefficient, β3j is the third order GVD coefficient, αj is the fiber loss coefficient, γj is the nonlinear parameter of the fiber, and the suffix j and k are the channel number. The simulator was capable to ignore the SPM and the cross phase modulation (XPM) by setting coefficients a and b in Eq. (1) to zero. In addition, four wave mixing (FWM) was ignored, because the generated power through the FWM [10] was negligibly small owing to the dispersion map. The fiber step length for the calculation was set to non-uniform, and it was expanded exponentially from the initial length of 100 meter [11].
Figure 1 shows a schematic diagram of the simulation model. There were 32 optical transmitters (TX), and the signal wavelengths were ranged from 1543.8 nm to 1556.2 nm with 0.4 nm channel separation. The bit rate and the pattern were 10Gbit/s and 29 a De Brujin sequence, respectively. In this simulation, the PSK signal was assumed to be generated by a Mach-Zehnder modulator (MZM), and the waveform applied for the two arms of the MZM was a raised cosine with the non return-to-zero (NRZ) format. The RZ waveform was applied after the PSK modulation, and the waveform was also raised cosine. The pulse duty ratio was 50%, because the waveform was raised cosine. The multiplexer (MUX) did not have any wavelength selective function, and the modulated pattern of each transmitter was randomized at the output of the MUX. We conducted three different sets of the initial pattern at the output of the MUX in order to reduce the pattern dependent XPM impact [12], and the obtained results were averaged over these three sets.
The block type dispersion map used for the simulation comprised non-zero dispersion shifted fiber (NZDSF) and conventional single mode fiber (SMF). The parameters of the fibers were summarized in Table 1. Eight NZDSF spans and one SMF span composed one block, and the SMF span was placed in the center of the block (i.e., fifth span). Each NZDSF span comprised NZDSF1 and NZDSF2, and NZDSF1 had larger effective area, while NZDSF2 had smaller dispersion slope. The averaged zero dispersion wavelength of the transmission line was set to 1550nm. Figure 2 shows the cumulative dispersion at 1543.8nm, 1550nm, and 1556.2nm. There were seven blocks in the map, and the total transmission distance was 6300km.
Table 1. Parameters of the transmission fiber
The output power and the noise figure of the repeater were set to +11dBm and 4.5dB, respectively. The amplifier spontaneous emission (ASE) noise generated by the repeater had a random complex electrical field, and it was added to the complex electrical field of the optical signal. The repeater span length was 100km. The wavelength dependent gain of the repeater was ignored in the simulation.
The optical demultiplexer (DEMUX) had the Gaussian shape with 3dB bandwidth of 0.1nm. The cumulative chromatic dispersion for each channel was compensated at the receiving end, and the residual dispersion after dispersion equalization was set to 100ps/nm. For the signal demodulation, difference of the optical phase was directly calculated from the optical field [13,14]. The difference of the phase was defined as the phase difference between two sampling points separated by one bit period, and an eye-like diagram of the phase can be obtained within the phase range between -π/2 to 3π/2. The performance was evaluated by the Q-factor obtained from the rails of 0 phase and π phase explained in reference [13].
3. Results and discussions
At first, the system performance was evaluated as a function of the transmission distance. Figure 3 shows the results. The horizontal axes shows the channel number, and the vertical axes shows the relative Q-factor for each transmission distance. The relative Q-factor is defined as the difference from the value of channel 32. As seen in Fig. 3(a), the performance dip near the system zero dispersion wavelength becomes obvious when the transmission distance increases. On the other hand, there is no significant dip when the SPM effect is ignored as shown in Fig. 3(b). These results imply that number of the zero-crossing points within the dispersion map combined with the SPM degrades the performance of the RZ-DPSK signal near the system zero dispersion wavelength.
Then, the system performance of several different dispersion maps was evaluated. Figure 4 shows these maps. Number of zero-crossing points was changed by re-arranging the NZDSF spans and SMF spans within the dispersion map shown in Fig. 2 while all the fiber parameters were identical as before. Map 1 had one crossing point, and number of zero-crossing points was increased as map number increased. Map 6 was the same as Fig. 2. Figure 5 shows the results. As seen in Fig. 5(a), the performance dip becomes significant when number of zero-crossing points is increased, while there is no significant wavelength dependence when the SPM effect is ignored as shown in Fig. 5(b). These results clearly show that the performance of the RZ-DPSK system strongly depends on number of the zero-crossing points combined with the SPM.
In addition, single channel transmission simulations with map 1 and map 6 were conducted. In order to maintain the same signal power per channel, repeater output power was reduced to -4dBm for these simulations. Several signal wavelengths were selected, and they were channels 1, 2, 16, 17, 31, and 32. Their wavelengths were 1543.8nm, 1544.2nm, 1549.8nm, 1550.2nm, 1555.8nm, and 1556.2nm, respectively. Figure 6 shows the result. As seen in Fig. 6, single channel transmission showed the same tendency as WDM transmission. The performances of edge channels did not change so much while those of center channels showed significant difference between two maps. This result also shows that the performance dip near the system zero dispersion wavelength is caused by the combination of the SPM and the zero-crossing points in the dispersion map.
4. Conclusions
We have conducted a theoretical investigation of the transmission performance of the long-haul RZ-DPSK system, and found that large number of zero-crossing points in the dispersion map and the SPM caused the performance dip near the system zero dispersion wavelength. As the physical reason of this phenomenon is still not clear, it will require a further study.
Acknowledgments
This work is supported partially by National Science Council 96-2221-E-110-049-MY3, partially by key module technologies for ultra-broad bandwidth optical fiber communication project of Ministry of Economy, Taiwan, R.O.C., and partially by Aim for the Top University Plan of the National Sun Yat-Sen University and Ministry of Education, Taiwan, R.O.C.
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