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A Review on Non linearity in optical fiber due to Self-phase modulation Shafaq Mehmood, Ashiq Hussain University College Of Engineering And Technology Islamia University Bahawalpur, Pakistan [email protected] Abstract: Nonlinear effects are just a consequence of increasing need for high data rates, number of wavelengths, transmission lengths and optical power levels. Nonlinear effects can be minimized using suitable optical fiber although there are many techniques mention in this paper which are using now a days. Highly Accurate Compensation Technique for 10-GHz Pulse Intensity Fluctuation is one of the best techniques. Keywords: Kerr effect, Nonlinear effects, Nonlinear photonics, Optical telecommunication Introduction: Self-phase modulation (SPM) is a nonlinear optical effect of light-matter interaction. Due to the optical Kerr effect an ultra-short pulse of light when travelling in the optical fiber will induce a changing refractive index of the medium. Due to this variation in refractive index will yield a phase shift in the pulse, leading to a change of the pulse's frequency spectrum [1]. In long-haul light wave transmission systems with the increased demand for capacity, the selection of a suitable optical modulation format is a key issue to confirm the optimum system performance. Self-phase modulation (SPM) is one of the main nonlinear degradation effects in optical amplified systems, specifically when the per-channel data rate is higher than 10 Gb/s.[2] SPM-induced phase modulation is proportional to the Kerr-effect nonlinearity in the fiber and through accumulated chromatic dispersion this phase modulation is changed into intensity modulation. By decreasing the efficiency of PM/AM conversion dispersion compensation may decrease the impact of SPM, but it cannot be remove completely [3]. If the amplitude of a phase-modulated optical signal is constant before transmission, chromatic dispersion is caused by fiber amplitude modulation. Due to which self-phase modulation (SPM) is induced. In optical heterodyne detection, SPM cannot be compensated by the delay equalizer (electrical domain) used to compensate fiber chromatic dispersion. However, in the presence of SPM the transmission distance restriction of multirepeated coherent transmission systems has not been examined. When a phase/frequency modulated optical signal at the wavelength of 1.55 pm is transferred through a conventional single-mode (SM) fiber, changes in the phase and frequency are converted to adjustment of the signals' amplitude, which then modulates the refractive index of the fiber. This self-phase modulation (SPM) lowers the receiver sensitivity. This mechanism severely degrades system performance irrespective of the number of optical amplifiers At high bit rates exceeding 10 Gb/s.[4] 1 Nonlinearity & SPM due to high data rate: For error free detection at high data rate systems however require larger received power. As peak powers of input approach 10 mw and data rates beat 10 Gb/s, self-phase modulation (SPM), which is caused by the nonlinear dependence of the refractive index on intensity. At 50 Gb/s data rates the modulation bandwidth is so large, that even for an ideal source without phase noise, fiber dispersion broadens the optical pulses and limits transmission. The deadly influence of linear fiber dispersion may be minimized by operating at the minimum group velocity dispersion (GVD) wavelength dispersion is not eliminated completely. As the fiberinput power amplified beyond approximately 5mW for very high-bit rate systems, the fiber cannot be assumed to behave as a linear transmission medium. The nonlinear Kerr effect also needs to be included in a more accurate model [5]. It can be defined by the nonlinear dependence of the effective fiber refractive index n on intensity I as π(π€, πΌ) = ππ(π€) + π2 πΌ-------(1) Where no(w) is the linear index of refraction, and n2 is the Kerr coefficient which is approximately 3.2 X10β16 cm/W in silica fibers.[6] The propagation constant Ξ² (π, I ) depends on n (π, I ) as ππ(π,πΌ) π½(π, πΌ) = π ------------------(2) The propagation constant changes in time when the intensity I ( t ) is modulated. The βinstantaneousβ optical frequency dw/dt is related to the propagation constantβs time derivative thus new frequency components are caused due to the intensity variation of the pulse. The interaction of nonlinear SPM and linear GVD, depending on the sign of the dispersion produces different things on the temporal pulse profile. In the positive dispersion region (i.e., X < Xo), a pulse develops a linear frequency chirp, and the pulse broadens temporally. The pulse broadening can be compensated by a negative dispersive delay line, such as a grating pair [7]. The positive chirp of the SPM and the negative dispersion cancel in the negative dispersion wavelength region (i.e., A>Xo). They can be made to compensate exactly if the input power is accurately adjusted to the pulse width and to the fiber dispersion. Performance improvement using SPM: The use of dispersion compensating fibers (DCFβs) has now appeared as the most practical technique to compensate for the chromatic dispersion in the long-haul, optically amplified standard fiber transmission systems. [8] The fiber nonlinearities and dispersion has become the main problem in extending the high-speed transmission distance, long haul standard fiber transmission systems. Among the many methods reported [9]-[13],to compensate chromatic dispersion the use of DCFβs has been emerging as the most practical technique due to its constancy over temperature and wide-band dispersion compensating characteristics. So far, it has been believed that the SPM in the DCF degrades the system performance although the SPM in the standard fiber enhances the performance by compressing the pulse. For this reason, the importance of launching a short power into the DCF in order to reduce the SPM effect in the DCF and to operate the DCF in the linear regime [14]-[21]. The system configuration that we considered is a 120-km standard fiber transmission system with a DCF at the receiver. The total 2 dispersion of the standard fiber was D ~ M =F +2131 ps/nm at the 1557 nm wavelength. The transmitter was a DFBlaser externally modulated by a zero-chirp LiNb03 modulator with NRZ (non-return to zero), 223- 1 PRBS data. To conquer stimulated Brillouin scattering (SBS) the DFB-laser was dithered [ 22]. The power booster was a two-stage EDFA pumped with two 1480-nm pump lasers. The amplifiers at the receiver were 980-nm double pumped dual stage EDFAβs with a noise figure of 4 dB. The receiver/regenerator consisted of a PIN-HEMT front end and an AGC with a total bandwidth of 8.5 GHz, clock and data recovery circuitry and a decision circuit. We first calculated the signal spectrum at the transmitter, standard fiber at the output of the 120 km and after the DCF to show the spectral broadening by the SPM in the standard fiber and the subsequent spectral compression due to the SPM in the DCF. SPM based reshaping in receiver: Dispersion tolerance improvement through self-phase modulation-based all-optical reshaping in receiver was experimentally explored using 10-Gb/s return-to-zero signal. This scheme is quite effective to return the optical signal deformed due to chromatic dispersion. [23] For high bit rate optical communication systems all optical reshaping is an attractive technology, where the signal waveform is easily damaged by unavoidable dispersion and nonlinearity of the transmission fiber. Among these schemes, a technique based on self-phase modulation (SPM) in a nonlinear medium with optical band pass filtering [24] is one of the simplest ways to provide such functionality. Furthermore, this method has benefits of polarization insensitivity and bitrate transparency. However, the effectiveness of this method to the signal the waveform, which is damaged due to chromatic dispersion, has not yet been investigated, although the dispersion tolerance is very tight in such high bit rate wavelength-division-multiplexing (WDM) transmission systems [25]. Fig.1 experimental setup.[26] In the transmitter, the light from a continuous-wave (CW) distributed feedback laser diode (DFB-LD) oscillating at 1554.5 nm was fed into two LiNbO MachβZehnder modulators connected in cascade for RZformatting and data coding with a 9.953Gb/s, pseudorandom binary sequence. To simulate the signal degradation due to dispersion compensation error, the chromatic dispersion fluctuating from 50 to 200ps/nm was applied to the signal using several lengths of dispersion compensating fiber (DCF) at the output of the transmitter. In the reshaping part, SAOR in a 5-km-long high-nonlinear dispersion-shifted fiber (HNL-DSF) was used. The zero dispersion wavelength and dispersion slope of the HNL-DSF were 1554.5 nm and 0.04 ps/nm2 /km, respectively. With a high-power erbium-doped fiber amplifier (EDFA), the input power to the HNL-DSF was boosted to 20~ 24 dBm, which was optimized in order to obtain the best performance for various applied dispersion. An optical band pass filter (OBPF) with a 3-dB bandwidth of 0.28 nm was placed at the output of the HNL- 3 DSF to slice the signal spectrum broadened due to the SPM effect in the HNL-DSF. Optical phase conjugation technique: In optical fiber communications optical phase conjugation (OPC) is a promising technique to compensate the nonlinear damage [27]. Compensation for nonlinearity by OPC is limited by the asymmetry of the strength of the Kerr effect along the fiber with respect to the OPC position [28],[29]. In order to defeat the nonlinearity impairments to a large extent, the system parameters of an OPC link, need be optimized. When proposing a novel design of OPC link it is necessary to predict the nonlinearity-compensation efficiency of the new link. Generally, optimization of an OPC link or evaluation of nonlinear impairment depends on numerical simulation, which is time consuming and shortages physical insight. Thus, fast approaches for first-order system design are required. Minzioni et al. presented two simple techniques to design OPC systems [30]β[32]. The two methods are powerful for designing intra channel cross-phase modulation/four wave mixing (IXPM/IFWM) compensation systems; however they have certain restriction for the design of self-phase-modulation (SPM)limited systems. This is due to the superior character of SPM, i.e., the SPM-induced chirp can compress signal pulse combined with chromatic dispersion [33]. Thus, SPM can assist signal transmission in some cases. It was found that, for SPM-limited systems, net residual dispersion (NRD) can improve the system presentation significantly[34].An equivalent principle is suggested, through which almost all the analytical models of conventional transmission systems proposed in the literature can be extended to OPC systems. This analytical method raises system performance taking advantage of the fiber nonlinearity while the method [29]β [30] is studied to compensate nonlinearities. This is the main difference between the optimization methods for SPM-limited systems and those for IXPM/IFWM-limited systems. Considering an electric field transmission along a fiber with attenuation or gain Ξ±(z), group velocity dispersion (GVD) Ξ²2(z), and nonlinear coefficient Ξ³(z) , the propagation of the amplitude envelope A(z, t) follows the nonlinear Schrödinger equation[31]. ππΌ(π§) π½π§ (π§)π22 [πππ§ = 2 β 2 π‘ + πΎ(π§)π΄|2 ]A=0---(3) Taking the complex conjugate of (3) yields [πππ§ + ππΌ(π§) 2 β (βπ½π§ (π§))ππ‘22 2 +(-Ξ³(z))|A*|2]A*=0---(4) Comparing (3) and (4) shows that the transmission of along a fiber with Ξ±(z),Ξ²(z), and Ξ³(z) is equivalent to the propagation of its complex conjugate A* (z,t)along a hypothetic fiber with Ξ±(z),-Ξ²(z) and - Ξ³(z). Therefore, in OPC links, the phase conjugated signal transmitting along the fiber link after OPC is equivalent to the original signal propagating along a fiber link with the same attenuation/gain, negative GVD and negative nonlinear coefficient, and then taking the conjugate of the output. In the following text, that is called βequivalent principle.β The analytical model to optimize the dispersion of SPM-limited dispersion managed systems. Fig. 2 (a) system setup for general OPC link and (b) the corresponding dispersion map.[35] 4 Combining this model with the equivalent principle one can obtain the single-pulse π broadening factor π for OPC systems, where π πand ππ are the rms widths of the output and input pulse, respectively. π ππ β©π2 βͺ 1β 2 =(π ) 0 --------------------(5) Where β©π 2 βͺ = ππ β π2 ππ β© + 2 π11 (2|πππ2 β© β 0.5ππ β© ) + 3π42 ππ3 β© + ππ + ππ 2 -------(6) R=β«π ππ . π½2 (π§)βππ2 ππ§ the amount of NRD-----(7) c=π2 πβ© + π41 πβ©|ππ2 β© β 4π41 |πππ β© β 5π42 |ππ2 β© (8) d=π2 + 0.5π42 |πβ©2 + 2π42 ππ β©----------------------(9) π πΏπ π π 2 |ππ π β© = β« π(π§) [β« π(π₯)ππ₯ ] π 0 2 π × [β« πΊ(π₯)ππ₯ ] π, π = 0~3 0 N(z)=πΎ(π§)ππ π βπΌ(π§) , -------------------------(10) G(x)=π½2 (π₯)βππ2 , Lo is the length of whole link Po and To are the peak power and width of input pulse, respectively. bo,b2, a0, a41 and a42 are coefficients only depending on the input signal pulse. [27] Optical Signal Processing by Phase Modulation: Optical signal processing based on optical phase modulation and subsequent optical filtering, which is appropriate to 160-Gb/s optical time-division multiplexed (OTDM) subsystems. When an optical pulse passes over a nonlinear optical fiber ultrafast phase modulation of an optical signal is done by self-phase modulation (SPM) and crossphase modulation (XPM). Such phase modulation brings the spectral shift of the signal in optical fiber. Many types of optical signal processing are realized simply by filtering out the spectral-shifted component. Using SPM-based pulse reshaping in a 500m-long silica-based highly nonlinear fiber (HNLF).[36] An incoming optical signal is phase modulated the spectral component frequency shifted by such phase modulation is filtered out with a band pass filter (BPF). The phase modulation in optical signal can be done through the following procedures: 1) SPM, which is the phase shift dependent on the strength of the incoming optical signal itself; 2) XPM, which is the phase shift caused by the power of another optical signal; and 3) electro optic modulation (EOM), which is the phase shift induced by the electrical RF signal. In the SPM-based scheme, an RZ data signal is phase modulated by its own strength waveform, while the signal transmits through a nonlinear fiber. The temporal phase variation induces the instantaneous frequency shift; the intensity slope point of the incoming signal is spectrally shifted and broadening the signal spectrum. If we remove the spectral-shifted components by BPF, the intensity slope point of the original signal is selected. Such SPM-based signal processing provides us with the pulse reshaping function [37]β[39]. When the input signal with a base is incident on the nonlinear fiber, the pedestal component does not induce the spectral shift the main pulse component is frequency shifted. Therefore, as far as we filter out the broadened spectrum at off-center wavelengths, we can remove the pedestal component. There are some requirements for the frequency shift 1 πππ > (1 + π)βπππ -----------------(11) Where βπππ = 160 πΊπ»π§ in the 160-Gb/s system, we require πππ > 320πΊπ»π§ when N=1. In the case of SPM, we can express the frequency shift πππ induced by the maximum slope of the temporal phase variation as 3.45 πππ = 2π πΎππ πΏβπππ ---------------------(12) Where Po is peak power L and πΎ are the length and the nonlinear coefficient of the optical fiber, respectively. Using eq. 11 & 5 12we obtain the requirement for Po , πΎ and L as 4π πΎπΏππ = 3.45 --------------------------(13) Where we assume N = 1 since the bit rate of the processed signal is usually the same as that of the incoming signal in the SPMbased signal processing. Dispersion compensation of SPM impairment in optical channel: In high power optical channels self-phase modulation (SPM) forces spectral broadening distortions. Consequently over sampling beyond the bitrate is proposed according to Nyquist theorem. Here received signal over sampling collected with maximum likelihood sequence equalizer is demonstrated, indicating of significant enhancement of inter-symbol-interference mitigation due to SPM.[40] The maximum likelihood sequence estimation (MLSE) has provide increased acceptance to chromatic dispersion (CD) in optical links up to 250 km [41] of Standard Single Mode Fiber (SSMF). MLSE performance was studied in the occurrence of nonlinear effects. [42]-[ 44]. This standard MLSE method, does not take into account the spectral broadening of the SPMinduced signal, therefore is created on one sample per bit. An extended MLSE approach based on increasing the number of Samples Per Bit (SPB) according to the SPM induced spectral broadening. Consequently, a vectorial MLSE (VMLSE) is introduced. Considering Nyquist sampling theorem the increase of the MLSE performance along with the increase of the SPB is enabled by passing a wider portion of the electronic bandwidth of the received analog signal prior to the sampler. This is attained by increasing the photodiode's Bandwidth. A very popular and useful way of the MLSE implementation is the Viterbi algorithm [45] that maximizes the conditional pdf. In the VMLSE, the metric is simply calculated by the sum of the log functions of the conditional pdf of all of the samples of each bit, thus assuming that the samples (in the bit) conditional pdfs are independent. The metric is calculated as follows (π) πΌ π·(π, π (π) ) = β βπΎ π βπ log[π(ππ,π /ππ )]-------(14) Where p(r/s) is the conditional pdf, I is the number of SPB, Rs is the sample rate, Rb is the bit rate, K is the bit sequence length. S(m) is the possible transmitted sequence of bits out of the 2k possible sequences. The rk= [rk,1 β¦..rk,I] is the sample vector of the k's bit. As noted above it is assumed that the samples in the bit are independent. Highly Accurate Compensation Technique for 10-GHz Pulse Intensity Fluctuation: Optical non-linear effects are highly affected by input peak power intensity fluctuation is a serious matter for the all-optical signal processing in communication networks. To compensate for the fluctuation, optical limiter is used because it can output the same intensities for input intensities over a threshold value. Thus far, a lot of optical limiters that utilize saturation properties of some transfer functions of nonlinear phenomena have been proposed. An optical limiter based on such saturation properties can reduce the intensity fluctuation, but not sufficiently. To decrease the residual output intensity fluctuation, the optical limiter must be used continually. The optical intensity is decreased due to the repeated system, several optical amplifiers are required. In a large network, the physical broadcast topology must have a minimum number of optical amplifiers to reduce cost and power consumption [47]. 6 Fig.4 experimental setup of proposed limiter. VOA variable optical attenuator, PM power meter, SOA sampling oscilloscope.[49] Fig.3 principal of proposed all optical intensity fluctuation compensation technique (a) schematic of intensity limiter (b) examples of spectral patterns changed based on SPM with up chirp effect.[46] Toward low power consumption, an SPMbased all-optical intensity limiter relying on a pre-chirping procedure, and tried to reduce the number of optical amplifier. We found the intensity of center wavelength components depends on how the input pulse is chirped. Moreover, by adding an appropriate amount of chirp, we successfully achieved center wavelength intensity stabilization through a single SPM.[48]. A schematic of our proposed limiter that relied on a pre-chirping procedure is shown in Fig.4. It consists of a single EDFA, a dispersion compensation fiber (DCF), a highly nonlinear fiber (HNLF), and an optical band-pass filter (OBPF). The incoming signals are amplified by a single Erbium doped fiber amplifier (EDFA) to reach the power required for optimal peak power equalization. During the transmission in a DCF, an up-chirp is first added to the incoming signals, and the total of up-chirp depends on the length of DCF. Next, in the HNLF, the signals experience SPM providing spectral broadening, which maintains a constant intensity at the center wavelength components because of the prechirping procedure. The fiber output, the resulting signals are filtered by means of an OBPF with the same central wavelength as the signal. Thus, by introducing the prechirp procedure before SPM, our all optical limiter can achieve low power consumption with only a single amplifier, high-speed operation and a highly accurate limiting function. SPM nonlinear spectral broadening and Analysis of SPM: In optical fiber communication systems, we send information from one place to another in the form of light pulses. The non-linear 7 effect come into picture when requirements like high data rates, transmission lengths, number of wavelengths and optical power level increases. Fiber non-linearity includes Stimulated Brillouin scattering (SBS), Stimulated Raman Scattering (SRS), Four wave mixing (FWM), self-phase modulation (SPM) and cross phase modulation (XPM). An optical field modifies its own phase under SPM. Though SPM broadens and reduces the performance of a light wave system but on a positive note, it increases optical switching speed. Kerr effect mainly shows three important non-linear effects; SPM, XPM and FWM. Out of these three only FWM can contribute to gain to one channel at the cost of reducing power from other channels. Both SPM and XPM produce a phase shift in the pulse, broaden the spectrum and increases overall dispersion.[50] Self-phase modulation in an optical system is said to happen when the phase of a beam is modulated non- linearly by its own intensity. The portions of beam which carry high intensity have high refractive index compared to those having low intensities. The refractive index of core in an optical fiber is given by equation (optical Kerr effect). n =π0 +π2 β π π΄πππ ----------(15) Where n0 = linear refractive index of core n2 = nonlinear refractive index P = optical power (in Watts) Aeff = effective area of core Due to the factor n2, a phase shift is created, which is in proposition to the intensity of pulse. Further there in non-uniform spreading of intensity in spectral components due to non-uniformity in the power along the pulse. This phase shift changes the central frequency of the pulse and the difference is called frequency chirp. There is different phase shift in the different parts of the fiber as phase fluctuations are intensity dependent. Hence SPM broadens the optical spectrum non-linearly. As chirping phenomenon increases with increase in input power, SPM develops at high power levels. Furthermore, nowadays erbium doped fiber amplifier EDFAβs are employed to counter attack attenuations and amplify the signal, which increases optical power level and hence contribute to SPM. As can be seen from equation (15), the significance of SPM can be reduced by increasing the effective fiber core area and by operating the systems at low power levels. Here, EDFA noise has not been taken into consideration for the ease of analysis. According to optical Kerr effect: n(I)= π0 + π2 (πΌ) ----------(16) Where n(I) = intensity dependent change in refractive index n0 = linear refractive index n2(I) = nonlinear refractive index (intensity dependent) As refractive index of fiber core is now power dependent, it affects chromatic dispersion in the fiber, which changes the pulse broadening rate throughout the fiber. Conclusion: Nonlinear effects in optical fiber are due to SPM, cross phase modulation, four wave mixing in optical fiber etc this paper is all about how SPM plays its part. SPM can be minimized by selecting suitable cable. At high data rate SPM can occur which can be minimized by operating at minimum GVD. To compensate chromatic dispersion for long haul DCF can be used. As for high bit rate data communication signal waveform is easily damaged by nonlinear effects in such cases optical reshaping is attractive technology. Another promising technique to 8 compensate the nonlinearity is OPC. MLSE has provided increased acceptance to chromatic dispersion in optical links up to 250 km, as MLSE does not consider the spectral broadening. Optical limiter is one of the best methods because it can output the same intensities for input intensities over a threshold value. 11 12 13 Reference: 1 http://en.wikipedia.org/wiki/Selfphase_modulation 2 S. Zhang and R. Hui Impact of optical modulation formats on SPM-induced limitation in dispersion-managed optical systems - A simplified model. 3 N. Kikuchi and S. Sasaki, J. 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K Park, 0 Mizuhara, L D Tzeng, J -M P Delavaux, T V Nguyen, M -L K Kao, P D Yeates, and J Stone, βA 5 Gb/s repeaterless transmission system using Erbium-doped fiber amplifiers,β IEEE Photon Technol Lett, vol 5, no 1, Jan pp 79-82, 1993 23 Noboru Yoshikane, Itsuro Morita, and Noboru Edagawa, Member, IEEE Improvement of Dispersion Tolerance by SPMBased All-Optical Reshaping in Receiver. 24 P. V. Mamyshev, βAll-optical data regeneration based on self-phase modulation effect,β in Proc. ECOCβ98, Madrid, Spain, 1998, pp.475β476. 25 I. Morita, K. Tanaka, N. Edagawa, and M. Suzuki, β40-Gb/s singlechannel soliton transmission by reducing Gordon-haus timing jitter and solitonβsoliton interaction,β J. Lightwave Technol., vol. 17, pp.2506β2511, Dec. 1999. 26 Fig.1 experimental setup. Noboru Yoshikane, Itsuro Morita, and Noboru Edagawa, Member, IEEE Improvement of Dispersion Tolerance by SPM-Based All-Optical Reshaping in Receiver. 27 Xiaosheng Xiao, Changxi Yang, and Ping Shum, Senior Member, IEEE βAnalytical design of SPM limited systems with optical phase conjugationβ 28 X. Xiao et al., βPartial compensation of kerr nonlinearities by optical phase conjugation in optical fiber transmission systems without powersymmetry,β Opt. Commun., vol. 265, no. 1, pp. 326β330, Sep. 2006. 29 P. Minzioni, F. Alberti, and A. Schiffini, βOptimized link design for nonlinearity cancellation by optical phase conjugation,β IEEE Photon. Technol. Lett., vol. 16, no. 3, pp. 813β815, Mar. 2004. 30 P. Minzioni and A. Schiffini, βUnifying theory of compensation techniques for intrachannel nonlinear effects,β Opt. Express, vol. 13, no. 21, pp. 8460β8468, Oct. 2005. 31 G.P Agrawal, Nonlinear Fiber Optics, 3rd ed. San Diego, CA: Academic 2001. 32 P.minzioni I.cristiani V.degiorgio L.marazzi M.matinelli C.langrock and M. M. Fejer, βExperimental demonstration of nonlinearity and dispersion compensation in an embedded link by optical phase conjugation,β IEEE Photon. Technol. Lett., vol. 18, no. 9, pp. 995β 997, May 1, 2006. 33 G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. San Diego, CA: Academic, 2001. 34 X. Xiao, S. Gao, Y. Tian, and C. Yang, βAnalytical optimization of the net residual dispersion in SPM-limited dispersion-managed systems,β J. Lightw. Technol., vol. 24, no. 5, pp. 2038β2044, May 2006. 35 Fig. 2 (a) system setup for general OPC link and (b) the corresponding dispersion map. Xiaosheng Xiao, Changxi Yang, and Ping Shum, Senior Member, IEEE βAnalytical design of SPM limited systems with optical phase conjugationβ 36 Koji Igarashi and Kazuro Kikuchi, Member, IEEE Optical Signal Processing by Phase Modulation and Subsequent Spectral Filtering Aiming at Applications to Ultrafast Optical Communication Systems. 37 P. V. Mamyshev, βAll-optical data regeneration based on self-phase modulation effect,β presented at the Eur. Conf. Opt. Commun. (ECOC98), Madrid, Spain, pp. 475β477. 38 M. Matsumoto, βAnalysis of optical regeneration utilizing self-phase modulation in a highly nonlinear fiber,β IEEE Photon. Technol. Lett, vol. 14, no. 3, pp. 319β321, Mar. 2002. 39 G. Raybon, Y. Su, J. Leuthold, R. J. Essiambre, T. Her, C. Joergensen, P. Steinvurzel, K. Dreyer, and K. Feder, β40Gbit/s pseudo-linear transmissionover one million kilometers,β presented at the Opt. Fiber Commun. Conf. (OFC2002), Anaheim, CA, PD10β1. 40 O. Rozen, D. Sadot, G. Katz, A. Levy, U. Mahlab Electrical and Computer Engineering, Ben-Gurion University, Beer-Sheva, Israel 41 A. Farbert, et al.: Performance of a 10.7 Gb/s Receiver with Digital Equalizer using Maximum Likelihood Sequence Estimation, in Proc. European Conference on Optical Communication (ECOC 20O4),Th.4.1.52004. 10 42 43 44 45 46 Hueda M.R crivelli, D.E. carrer, H.S performance of MLSE based recivers in light wave systems with nonlinear dispersion and amplified spontaneous emission noise global Telecommunications confrernce, 2004, vol .1, pp. 299-303, Nov 2004. W. Sauer-Greff, A. Dittrich, R. Urbansky, H. Haunstein: βMaximum-likelihood sequence estimation in nonlinear optical transmission systemsβ, LEOS 2003, IEEE, vol. 1, pp. 167168, Oct. 2003. J.D. Downie, J. Hurley, M. Sauer: βBehavior of MLSE-EDC With Self-Phase Modulation Limitations and Various Dispersion Levels in 10.7-Gb/s NRZ And duobinary signalsβ ,photonics technology Letters vol. 19, Issue 13, pp. 1017-1019,Jul. 2007. J.G. Proakis, Digital Communications, New York: McGraw-Hill, 1995. Fig.3 principal of proposed all optical intensity fluctuation compensation technique (a) schematic of intensity limiter (b) examples of 47 48 49 50 spectral patterns changed based on SPM with up chirp effect. . Kentaro kawanishi, Florence drouet, kazuyoshi ioth, member,IEEE, and tsyoshi konishi, member, IEEE S. Singh, βPerformance comparison of optical network topologies in the presence of optimized semiconductor optical amplifiers,β J. Opt. Commun. Netw., vol. 1, no. 4, pp. 313β323, Sep. 2009. Kentaro Kawanishi, Florence Drouet, Kazuyoshi Itoh, Member, IEEE, and Tsuyoshi Konishi, Member, IEEE Fig.4 experimental setup of proposed limiter. VOA variable optical attenuator, PM power meter, SOA sampling oscilloscope. Kentaro kawanishi, Florence drouet, kazuyoshi ioth, member,IEEE, and tsyoshi konishi, member, IEEE Monica Bhutani, Abhishek Gagneja Optical Transmission System Simulation for Analysis of Self Phase Modulation Non Linearity. 11