Open Access
Add to BibSonomyAbstract
We study a whole compensation system for chromatic dispersion and polarization mode dispersion, including monitoring subsystems and compensation subsystems in optical communication systems with single channel speed 40Gbit/s and CSRZ format. We employed the spectral shift effect of a semiconductor optical amplifier for chromatic dispersion monitoring, and a non-linearly chirped fiber Bragg grating for chromatic dispersion compensation. The degree of polarization characterizes is used as feedback control signal of polarization mode dispersion monitoring, and a polarization controller and a polarization maintaining fiber are formed a polarization mode dispersion compensator. The transmission experiment demonstrates that the whole compensation system is effective. It is suit for chromatic dispersion management and polarization mode dispersion eliminating in optical communication systems with high single channel speed and CSRZ format.
©2007 Optical Society of America
1. Introduction
As the bit rate and distance of optical fiber transmission systems continue to increase, chromatic dispersion (CD) and polarization mode dispersion (PMD) have become two major sources of transmission degradation in high-speed long-distance optical communication systems [1–4]. They change with dynamic network reconfigurations and variations in environmental conditions such as temperature, thus there need careful CD management and PMD compensation [1, 2]. The CD tolerance is restricted ~50ps/nm and the average PMD tolerance is ~5ps in 40Gbit/s systems. In practice, the most popular dispersion map is positive (using SMF as the transmission fibers) periodically balanced by negative dispersion elements (using dispersion compensation fibers (DCFs)). But the residual CD can easily extend the CD tolerance for high speed systems, there need more precise and dynamical CD compensation methods [1, 3, 4] and there need effective and low-costly PMD compensation methods [3].
So far, several CD and PMD monitoring methods and compensation methods have been proposed. On the CD monitoring methods studies, there have measurement of the eye-opening penalty [4], bit-error-rate (BER)[5] or Q-factor[6], the phase modulation amplitude modulation conversion [7], clock power and so on [8–12]. PMD is considered the ultimate limiting factor for ultrahigh-bit-rate transmission, which can be introduced through manufacturing imperfections, cabling stresses, installation procedures, and environmental sensitivities of fiber and other in-line components [1]. Several online methods of PMD monitoring are proposed. They include using RF spectrum and power[13], using optical clock components [14] and other monitoring methods[15–17]. The popular method for PMD monitoring is the degree of polarization (DOP) characterizes [1,16–17] in practice.
On the CD and PMD compensation methods studies, the CD compensation techniques include DCFs [1], chirped fiber Bragg gratings [1, 18], virtually imaged phase array [19] and high negative CD microstructure fibers [20–22] etc. In high speed optical communication systems with re-configurable networks, the CD tolerance is very low, the residual CD can easily extend the tolerance, there need more precise and dynamical dispersion compensation methods [1].
Many methods, such as using low PMD fibers, alternative modulation formats[23], and many optical and electrical compensation techniques[1,24–25], have been proposed to mitigate or eliminate the infection of PMD. But as the speed increasing and the topology structure of the optical networks become more and more complex, the PMD tolerance is sharply decreasing. There is need more effective techniques to ensure that the PMD not exceeding the designed tolerance in those systems.
Therefore, variable and adaptive compensation for PMD and CD is needed to compensate the changing PMD and residual CD in the fiber communication systems. As previously mentioned, there are many papers on the PMD and CD monitoring [1, 3–14, 16–17], PMD and CD compensation [1, 15, 18–31] respectively. However, few of these papers introduce the whole compensation system which is very important and practical in high-speed optical communication systems. In this paper, we introduced a whole adaptive compensation design including monitor and compensation modules, and then gave our experimental results in 40Gbit/s carrier suppressed return to zero (CSRZ) format optical transmission system. An adaptive compensation system must include three modules: the compensation module, the feedback module, and the algorithm control module. We demonstrate them respectively in the following parts of this paper.
2. Chromatic dispersion and PMD monitoring
Our CD dynamical monitoring method is based on the spectral shift effect of SOA [26]. We will describe this new CD monitoring method and show the performance and effect in the following section. As optical signals transmit in optical fiber links with chromatic dispersion, the peaks power of the optical signal pulses are influenced due to the CD. Because the self phase modulation is relation to the peaks power of the input pulses, and then the peaks power, which decide the spectral shift effect resulted from self phase modulation. By monitoring the optical power of the corresponding shifted spectrum, one can obtain effective CD monitoring control signal for dynamical high speed CD compensation subsystems. The CD monitoring subsystem is shown in Fig. 1. Optical signal is drawn from optical communication systems and be sent into the monitoring subsystem. As shown in Fig. 1, the input optical signal is transmitted into a SOA after an optical isolator, the amplified signal from the SOA is split into two beams with same optical power after another optical isolator by a 3dB optical coupler. One beam is received by an optical detector and obtained optical power P 1, the other beam is received by an optical detector and obtained optical power P 2 after a circulator and an optical fiber grating which can filter the corresponding shifted spectrum to detect. We use the ratio between optical power P 2 and P 1 for online dynamical monitoring chromatic dispersion because it can get rid of the influence of power variety in the optical communication links.
Fig. 2. Back to back optical spectrum denoted by a) and amplified optical spectrum denoted by b) from the SOA of high speed optical communication system with single channel speed 40Gbit/s. The center wavelength is 1553.40nm. The shadow parts, marked by I, II and III, denote the pass-band of the three filters with different center wavelengths and with the same bandwidth 20GHz
Figure 2 shows the back to back optical spectrum (denoted by a)) and the amplified optical spectrum (denoted by b)) from the SOA of the single channel speed 40Gbit/s optical communication system with CSRZ format. A Q8384 optical spectrum analyzer from Advantest Ltd. is used. The shadow parts marked by I, II, and III in figure are denoted three classes of optical filters with different center wavelength, which can filter the shifted spectrum power to detect. The center wavelength of the spectrum is 1553.40nm, the optical carrier is suppressed, the frequency difference of the two 1st-order harmonic wave peaks is 40GHz, and the frequency difference is also 40GHz between the high (order>1) order harmonic waves and the neighboring lower order harmonic waves. The back-to-back spectrum has high symmetry, but the amplified spectrum is loss the symmetry, as shown in Fig. 1 (b). The power of long wavelength part is higher than that of short wavelength part. Due to the distribution of spectral shift result from SOA self phase modulation is spanned a wide frequency range, it need optimal scheme of the filter which can output the power of spectral shift components for dispersion monitoring. As shown in Fig. 2, the power of the each separate harmonic wave peak has higher than the shift power because of the frequency shift effect. So the separate harmonic wave peaks should be excluded out of the band of the band pass filter. We divide the spectrum of long wavelength side into three parts: part I, part II and Part III with frequency range 20~60GHz, 60~100GHz and 100~140GHz offset from center frequency of the optical signal spectrum respectively, as shown in the Fig. 2. In theory, the part III can be used to monitor CD and have very high monitoring precision, but it is ignored due to low optical power and noises sharply sensitive. Using the more narrow band filter, we can provide the more dispersion monitoring precision in our method, but the output power will too low to detect due to noise of photoelectric diodes and optical amplifiers. In our studies, an optical grating is used as the filter with 3dB reflective bandwidth 20GHz. To obtain preferable monitoring purpose, we use two filters with center wavelength 1553.72nm and 1554.04nm to analysis. The reflective band of the filter with center wavelength 1553.72nm is in part I and other is in part II, as shown in Fig. 2.
Figure 3 show the theoretical CD monitoring curves using the two filters mentioned above in high speed optical communication system with single channel speed 40Gbit/s and CSRZ format. Using the filter with center wavelength 1553.72nm, the monitoring range is ±120ps/nm and the monitoring precision is about 10ps/nm, as shown in Fig. 3(a). However using filter with center wavelength 1554.04nm, the monitoring range is ±60ps/nm and the monitoring precision is higher than 5ps/nm, as shown in Fig. 3(b). From discussion above, it is concluded that monitoring precision is higher when the filter with the longer center wavelength. In practice, we should choose an optimal filter by considering dispersion monitoring range and precision. In our system, we choose the filter with center wavelength 1554.04nm. This method can provide effective control signal for dynamical CD compensation subsystems.
Fig. 3. Dispersion monitoring curves with filters which center wavelength are 1553.72nm (denoted by a) in the figure) and 1554.04nm (denoted by b) in the figure respectively. The bandwidth of the two filter based optical gratings are 20GHz.
The concept of the DOP characterizes the average polarization state of light over a broad spectral range. Time dependent signals are also defined as an average over a specified time period. The definition of DOP is based on the Stokes parameters measured by a DOP monitor or other polarimeter-based instrument. The definition of DOP is
where S i, (i=0,1,2,3) denote the Stokes parameters, S 0 is the total intensity of the light, S 1, S 2 and S 3 refer to the vertical/horizontal polarizations, ±45° polarizations and right/left polarizations. We use the common method, DOP characterizes, to monitor DGD of the optical communication system. The DOP monitor is a high speed in-line polarimeter—PolaDetect from General Photonics Ltd. The responding time is 1.5 μs, the insert loss is 0.8dB and the testing error is about ±2.0%. If the optical links DGD is within tolerance of the optical communication system, the DOP is near to the maximal value 1.0. The DOP decreases when the optical links DGD increasing. That is to say, the algorithm control module of the PMD compensation subsystem maximizes the DOP of the optical communication systems. General, the optical communication systems need PMD compensation and the BER increase when the DOP<0.9[1,4]. In our experimental system, we use the DOP=0.9 as the adjudge condition for PMD compensation needing or not. The PMD monitoring subsystem uninterruptedly monitors the DOP. If the DOP<0.9, the PMD compensation subsystem operates till to the monitored DOP>0.9.
3. Chromatic dispersion and PMD compensation
In this section, we demonstrate the PMD compensation subsystem and CD compensation subsystem in our whole optical communication system. Figure 4 shows the PMD compensation subsystem and the CD compensation subsystem, where the PMD compensation subsystem, demonstrated in the left part of the figure, is consisted of an electrical tunable polarization control with four controlling voltage values and a high birefringence optical fiber, which can be replaced by other birefringence devices, such as high birefringence microstructure fibers [27–28]. When high birefringence microstructure fibers are used, the length of fiber is reduced due to the high birefringence of the microstructure fibers. By change the four input voltage values to change the polarization state and together with the high birefringence optical fiber we can compensate the PMD from the optical communication system links. The CD compensation subsystem, demonstrated in the right part of the Fig. 4, is form by an optical circulator and an optical fiber grating with nonlinear group delay. This nonlinear chirped fiber grating reflects different frequency components at different locations within the gratings. They can be used for dispersion compensation when the time delay for the gratings is the inverse of the delay caused by dispersion. The reflection spectrum and the group delay curves are shown in Fig. 5(a), where the solid line denotes the reflection spectrum curve and the dot line denotes the group delay curve respectively. The slope of the group delay is the chromatic dispersion. The center wavelength of the reflection spectrum is about 1553.0nm. We can conclude that different frequencies can pass different length in the fiber grating and have different group delay, thus the CD can be compensated using this characters.
Fig. 5. Reflection spectrum a) and group delay b) curves of FBG and shift of group delay curve at various voltages
Because that the reflection spectrum and group delay are all sensitive by grating structure, stress and temperature, our dispersion compensation system is based on a thermally tunable nonlinear chirped optical fiber grating [29]. The fiber grating is covered with uniform thin metal electric-conducting film which can add voltage to heat up. When the fiber grating is add voltage and has current in the electric-conducting film, the fiber grating is heated and the temperature is changed, so the reflection spectrum and group delay is changed. We can control the group delay at certain wavelength by control the voltage in the film-covered optical fiber grating.
In Fig. 5(b), we show three group delay curves with different voltages. The solid line denotes the voltage 1.20V, the dashed line denotes the voltage 3.82V and the dotted line denotes the voltage 5.08V respectively. From this figure, we can conclude that the reflective spectrum and group delay curves are shift toward long wavelength side and the form is unchanged during the voltage increasing. The CD for certain wavelength such as 1553.0nm becoming low during the voltage increasing. The measured CD can be varied from -60ps/nm to -260ps/nm for wavelength 1553.40nm. By controlling the voltage added to the FBG, tunable CD compensation can be achieved.
Experiment shows that the influence of CD to PMD monitoring using DOP characterizes method is very small and do not affect the PMD compensation. To get rid of the influence from PMD to CD monitoring, we firstly compensate the PMD and later compensate the CD, as shown in Fig. 4.
4. Experimental testing
The whole experimental setup is schematically shown in Fig. 6. The light with wavelength 1553.40nm from the tunable external cavity laser made by Photonetice Ltd., is sent into a pseudo random binary sequence (PRBS) system which can produce PRBS codes with speed 40Gbit/s CSRZ format. After the PRBS system, the output light is transmitted into a optical fiber links consisted with many kilometers single mode fibers (SMFs) and some microstructure fibers (MSFs) drawn by our research group which has high negative CD [20]. The negative CD MSFs can compensate some fixed CD of the optical fiber links. Microstructure fibers study is a new research hotspot and has been far and wide studied due to their many interesting characteristics [20–22]. And then, the light be sent into a PMD simulator after a polarization control (PC), the PMD simulator can simulate the PMD in practice optical fiber communication systems or make a certain difference group delay (DGD) for experimental testing. Output from the PMD simulator, the light transmitted into a PMD compensation subsystem and a CD compensation subsystem. The subsystems can used the control signals from PMD and CD monitoring subsystems to compensate the PMD and residual CD of the optical links. Because the MSFs can compensate some fixed CD, the CD compensation subsystem need only compensate the residual CD of the optical fiber links. Out from the CD compensation subsystem, the light is split into two beams by an optical coupler. One beam is sent into a digital sampling oscilloscope to test the eye diagrams. A TDS8200 digital sampling oscilloscope from Teltronix Ltd. is used. The other beam is transmitted into an erbium-doped optical fiber amplifier (EDFA) and an ASE filter. The power of the optical signal is too low to use for PMD and CD monitoring, so the EDFA is needed. The Ald-D02 EDFA from KAIFA Ltd. is used, the small signal gain is 25dB. And then the amplified light is be split into two beams with the same optical power be a 3dB optical coupler. One beam is sent into the CD monitoring subsystem to monitor residual CD of the optical links after a tunable attenuator and the other beam is sent into the PMD monitoring subsystem to monitor PMD of the optical links after a tunable attenuator too, as shown in Fig. 6.
Fig. 7. Eye diagrams tested by Tektronix TDS8200 digital sampling oscilloscope of without CD and PMD compensation (a), with PMD compensation and without CD compensation (b) and with CD and PMD compensation (c).
The monitoring signals from the PMD monitoring subsystem and CD monitoring subsystem are sent into a computer by A/D conversion circuits and a digital collect card through a serial port of the computer. The computer creates the digital control signals for PMD and CD subsystems by the appropriate algorithm control module [4, 30–31], and then the digital control signals are sent into the PMD and CD subsystems by D/A conversion circuits.
In our experiment, the SMFs with chromatic dispersion coefficient D =17 ps/(nm·km) and MSFs with high negative chromatic dispersion D=-220 ps/(nm·km) at 1553.5nm are used[20]. The length of SMFs and MSFs are 10km and 500m respectively, and the high birefringence fiber with fixed DGD 15ps is used.
To demonstrate the PMD and CD compensation performance, we shown the tested eye diagrams without PMD and CD compensation, with PMD compensation but without CD compensation, and with PMD and CD compensation respectively in Fig. 7. The eye diagrams tested by Tektronix TDS8200 digital sampling oscilloscope, where the Fig. 7(a) denotes eye diagram without PMD and CD compensation, the residual CD of the optical fiber link system is the 60ps/nm and the average DGD is 5ps, the signals are affected by CD and PMD from optical communication system. The Fig. 7(b) denotes eye diagram with PMD compensation but without CD compensation, the signals are suffering from CD, but have gotten rid of PMD affection from optical communication system. And the Fig. 7(c) denotes eye diagram with PMD and CD compensation, the optical communication system signals are avoided from PMD and CD influence.
The measured BER is shown in Fig. 8, while the power penalty after the adaptive compensation at a BER=10-10 is about 1.3dB. This power penalty may be caused by the small residual chromatic dispersion, polarization mode dispersion and group delay ripple of nonlinear chirped fiber Bragg grating. This ripple is difficult to avoid, but can be reduced. The peak-to-peak group delay ripple of the used nonlinear chirped fiber Bragg grating across the whole reflective band is about 10ps, and it can deteriorate optical communication system performance during the thermally tuning process of the fiber Bragg grating.
The experimental results demonstrate that the automatic compensation can mitigate the distortion of output signal effectively. However, the power penalty is a little high. Further work should been done to reduce the loss of the optical components, and the ripple of the nonlinear chirped fiber Bragg grating.
Summarized mentioned previously, we can conclude that our proposed dynamical CD and PMD monitoring and compensation system for optical communication system with single channel speed 40Gbit/s and CSRZ format is effective. The whole system can work synchronously and well. The methods and principles can directly be used in other high speed optical fiber communication systems or by minimized modification.
Fig. 8. BER curves of the CD and PMD monitoring and compensation system for 40Gbit/s CSRZ format high speed optical communication system
5. Conclusion
We introduced a whole adaptive compensation design including monitor and compensation modules, and then gave our experimental results in 40Gbit/s CSRZ format optical fiber transmission system. The CD monitoring method is based on the spectral shift resulted from SPM of SOA. We showed that the wavelength components range using for dispersion monitoring is longer, the monitoring precision of this method is high but the monitoring range is small. For high speed optical communication system with single channel speed 40Gbit/s and CSRZ format, we use the optical fiber grating with center wavelength and band width of the reflective band 1554.04nm and 20GHz respectively. The CD monitoring range is ±60ps/nm and the monitoring precision is higher than 5ps/nm. We used the DOP characterizes to monitor the PMD of the optical fiber communication system. An optical fiber grating, covered with uniform thin metal electric-conducting film and with nonlinear group delay curve, is used for CD compensation. The measured CD can be varied from -60ps/nm to -260ps/nm for wavelength 1553.40nm. By controlling the voltage added to the FBG, tunable CD compensation can be achieved. The PMD compensation subsystem is consisted of an electrical tunable polarization control with four controlling voltage values and a high birefringence optical fiber with fixed DGD 15ps. By change the four input voltage values to change the polarization state and together with the high birefringence optical fiber we can compensate the PMD from the optical communication system links.
Due to the influence of CD to PMD monitoring using DOP characterizes method is very small and do not affect the PMD compensation. To get rid of the influence from PMD to CD monitoring, we firstly compensate the PMD and compensate the CD later.
The power penalty after the adaptive compensation at a BER=10-10 is about 1.3dB. This power penalty may be caused by group delay ripple of the nonlinear chirped fiber Bragg grating, small residual chromatic dispersion and polarization mode dispersion.
Summarized the performances of the CD and PMD monitoring and compensation subsystems, our system can be used for CD and PMD monitoring and compensation in high speed optical fiber communication system with 40Gbit/s single channel speed CSRZ format. Experiments show that the whole system can work synchronously and perfectly. The methods and principles can directly be used in other high speed optical fiber communication systems or can be used by minimized modification.
Acknowledgments
The authors thank the National Basic Research Program of China (973 Program) under Contract 2003CB314907, the China Postdoctoral Science Foundation of under Contract 20060400059, the National Science Foundation Council of China under Contract 90604026 and 60310174, and the Basic Research Foundation of Tsinghua National Laboratory for Information Science and Technology (TNList) for their supports. The authors would like to thank the reviewers for their important comments and consideration. Ming Chen’s e-mail addresses are m_chen@126.com and mchen2006@tsinghua.edu.cn.
References and links
1. I. P. Kaminow and T. Li, Optical Telecommunications IV B Systems and Impairments (Academic, 2002)
2. B. Fu and R. Hui, “Fiber chromatic dispersion and polarization-mode dispersion monitoring using coherent detection,” IEEE Photon. Technol. Lett. 17, 1561–1563 (2005). [CrossRef]
3. A. S. Lenihan, W. A. Babson, H. Jiao J. Sobieski, and G. M. Carter, “An experimental demonstration of a soft-failure approach to PMD mitigation in an installed optical link,” Opt. Express 15, 24–32 (2007). [CrossRef] [PubMed]
4. S. M. R. M. Nezam, “Chromatic and polarization mode dispersion monitoring for equalization in optical fiber communications,” Dissertation of University of Southern California for PhD (2004).
5. R. Wiesmann, O. Beck, and H. Heppner, “Cost effective performance monitoring in WDM systems,” in Optical Fiber Communication Conference, 2000 OSA Technical Digest Series (Optical Society of America, 2000), 171–173.
6. I. Shake, H. Takara, K. Uchiyama, and Y. Yamabayashi, “Quality monitoring of optical signals influence by chromatic dispersion in a transmission fiber using averaged Q-factor evaluation,” IEEE Photonics Technology Letters 13, 385–387 (2001). [CrossRef]
7. M. Tomizawa, Y. Yamabayashi, Y. Sato, and T. Kataoka, “Nonlinear influence on PM-AM conversion measurement of group velocity dispersion in optical fibers,” Electron. Lett. 30, 1434–1435 (1994). [CrossRef]
8. X. Yi, F. Buchali, W. Chen, and W. Shieh, “Chromatic dispersion monitoring in electronic dispersion equalizers using tapped delay lines,” Opt. Express 15, 312–315 (2007). [CrossRef] [PubMed]
9. N. Liu, W. D. Zhong, Y. J. Wen, and Z. Li, “New transmitter configuration for subcarrier multiplexed DPSK systems and its applications to chromatic dispersion monitoring,” Opt.s Express 15, 839–844 (2007). [CrossRef]
10. G. Ning, P. Shum, S. Aditya, N. Liu, and Y. D. Gong, “On-line simultaneous monitoring of polarization and chromatic dispersion,” Appl. Opt. 45, 2781–2785 (2006). [CrossRef] [PubMed]
11. G. Ning, S. Aditya, P. Shum, H. Dong, C. Q. Wu, and Y. D. Gong, “New approach to determine the effects of polarization mode dispersion and chromatic dispersion on pulse and RF signals, ” J. Opt. Soc. Am. A 23, 117–123 (2006). [CrossRef]
12. A. Liu, G. J. Pendock, and R. S. Tucker, “Improved chromatic dispersion monitoring using single RF monitoring tone,” Optics Express 14, 4611–4616 (2006). [CrossRef] [PubMed]
13. T. Luo, Z. Pan, S. M. R. M. Nezam, L. S. Yan, A. B. Sahin, and A. E. Willner, “PMD monitoring by tracking the chromatic-dispersion-insensitive RF power of the vestigial sideband,” IEEE Photon. Technol. Lett. 16, 2177–2179 (2004). [CrossRef]
14. F. Buchali, W. Baumert, H. Bulow, and J. Poirrier, “A 40Gbit/s eye monitor and its application to adaptive PMD compensation,” in Optical Fiber Communication Conference, Vol. 1 of 2002 OSA Technical Digest Series (Optical Society of America, 2002) 202–203.
15. B. W. Hakki, “Polarization mode dispersion compensation by phase diversity detection,” IEEE Photon. Technol. Lett. 9, 121–123 (1997). [CrossRef]
16. L. Möller and L. Buhl, “Method for PMD vector monitoring in picosecond pulse transmission systems,” IEEE J. Lightwave Technol. 19, 1125–1129 (2001). [CrossRef]
17. N. Kikuchi, “Analysis of signal degree of polarization degradation used as control signal for optical polarization mode dispersion compensation,” IEEE J. Lightwave Technol. 19, 480–486 (2001). [CrossRef]
18. K. Ennser, M. N. Zervas, and R. L. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron. 34, 770–778(1998). [CrossRef]
19. M. Shirasaki, “Chromatic dispersion compensator using virtually imaged phase array,” IEEE Photon. Technol. Lett. 12, 1598–1600 (1997). [CrossRef]
20. S. Yang, Y. Zhang, X. Peng, Y. Lu, S. Xie, J. Li, W. Chen, Z. Jiang, J. Peng, and H. Li, “Theoretical study and experimental fabrication of high negative dispersion photonic crystal fiber with large area mode field,” Opt. Express 14, 3015–3023 (2006). [CrossRef] [PubMed]
21. T. Fujisawa, K. Saitoh, K. Wada, and M. Koshiba, “Chromatic dispersion profile optimization of dual concentric core photonic crystal fibers for broadband dispersion compensation,” Opt. Express 14, 893–900 (2006). [CrossRef] [PubMed]
22. F. Gérôme, J. L. Auguste, J. Maury, J. M. Blondy, and J. Marcou, “Theretical and experimental analysis of chromatic dispersion compensating module using dual concentric core fiber,” IEEE J. Lightwave Technol. 24, 442–448 (2006). [CrossRef]
23. P. J. Winzer and R. J. Essiambre, “Advanced optical modulation formats,” Proceeding of the IEEE 94, 952–985 (2006). [CrossRef]
24. G. Katz and D. Sadot, “Minimum BER criterion for electrical equalizer in optical communication system,” IEEE J. Lightwave Technol. 24, 2844–2850 (2006). [CrossRef]
25. O. E. Agazzi, M. R. Hueda, H. S. Carrer, and D. E. Crivelli, “Maximum-likelihood sequence estimation in dispersive optical channels,” IEEE J. Lightwave Technol. 23, 749–763 (2005). [CrossRef]
26. G. P. Agrawal and N. A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 25, 2297–2306 (1989). [CrossRef]
27. L. He, Y. Zhang, S. Yang, X. Chen, and S. Xie, “Study of properties of highly birefringent microstructure fibers,” Microwave Opt. Technol. Lett. 48, 940–944 (2006). [CrossRef]
28. A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic crystal fibres (Kluwer Academic Publishers, 2003). [CrossRef]
29. J. Sun, Y. Dai, X. Chen, Y. Zhang, and S. Xie, “Thermally tunable dispersion compensator in 40Gb/s system using FBG fabricated with linearly chirped phase mask, ” Opt. Express 14, 44–49 (2006). [CrossRef] [PubMed]
30. D. Aizetta and M. Matsumoto, “Location optimization and distribution of polarization mode dispersion compensators using polarizers,” J. Lightwave Technol. 22, 1014–1022 (2004). [CrossRef]
31. Z. Q. Pan, “Overcoming fiber dispersion effects in high-speed reconfigurable wavelength division multiplexing optical communication systems and networks,” Dissertation of University of Southern California for PhD (2003)
