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Optimization of interamplifier separation in WDM transmission systems in the presence of fibre nonlinearities.

Introduction

Wavelength division multiplexing (WDM) can both significantly enhance transmission capacity and provide more flexibility in optical network design [1-3]. Through the use of erbium-doped fibre amplifiers (EDFAs) it is possible to build long distance transparent optical transmission links without electrical regenerators [4]. Although the use of optical amplifiers has extended the optical network dimensions to thousands of kilometers and made the concept of transparent optical networks quite feasible, but at the same time their use introduces some problems like accumulation of Amplified Spontaneous Emission (ASE) noise generated by inline optical amplifiers and aggravation of fiber nonlinearity effects [5, 6]. In such systems, apart from the usual problems of fibre loss (amplifier noise) and dispersion, fibre nonlinearities are likely to impose a transmission limit due to the increased total interaction length [6]. System specifications such as total transmission distance, amplifier spacing, the number of WDM channels, the channel spacing and the power per channel are all affected by the fibre nonlinear effects. Different nonlinear effects include, Stimulated Raman Scattering (SRS), Four Wave Mixing (FWM), Self Phase Modulation (SPM), cross phase modulation (XPM), Stimulated Brillouin Scattering (SBS) and Carrier Induced Phase Modulation.

Yu and Mahony [4] are of the opinion that among all fibre nonlinearities, FWM and SRS are expected to be the dominant nonlinear effects in the amplifier WDM systems. Wu and Way [7] put forward the idea that in Nonzero-dispersion-shifted fibers (NZDSF), FWM is always the dominant nonlinearity at the optimum Dispersion Compensation Ratio. In Single-mode Fibers (SMF), however, SPM, XPM, and FWM are all important nonlinearity impairments to consider in 2.5-Gb/s/6.25GHz systems; and XPM is the dominant nonlinearity in 10-Gb/s/25-GHz systems at the optimum Dispersion Compensation Ratio. Hwang and Tonguz [8] emphasized that among all the fiber nonlinearities, which are a major problem in WDM systems, the FWM is the most serious one because it involves a lower optical input power than other nonlinearities.

An amplifier in long haul optical networks can be used either as a booster amplifier, an in-line amplifier, or as a preamplifier. Rasmussen et al [9] investigated all the configurations thoroughly and concluded that optimal configuration of an EDFA is as a co pumped inline amplifier. Singh et al [10 ] had made comparative study of all the configurations and concluded that placement of optical amplifier as an inline amplifier is the optimal position as it requires minimum power for given probability of error and hence verified the claim by Rasmussen et al. Schadt [11] has shown that the amplifier spacing is an important parameter in the design of very long range multichannel systems with respect to distortion from four-wave mixing.

Keeping in view the findings of the literature, SRS and FWM have been considered as main nonlinearities in our study on NZDSF. We have studied the combined effect of SRS and FWM in the presence of Amplifier Spontaneous Noise (ASE). Configuration of EDFA as an inline amplifier has been considered. The effect of variation of interamplifier spacing (in the case of inline amplifiers) has been studied. An algorithm has been suggested for the optimization of interamplifier spacing to achieve maximum signal to noise ratio. Ratio of modified Signal due to SRS to total noise (combined effect of FWM and ASE) has been chosen as the criterion to find optimum interamplifier spacing (corresponding to maximum signal to noise ratio).

Limitation on Transmitted Optical Power Due to The SRS, FWM and ASE Effect of SRS, FWM and ASE on transmitted optical power is discussed below

Effect of Stimulated Raman Scattering (SRS)

SRS is one of the significant nonlinear effects in dense wavelength division multiplexed (DWDM) based fiber communication systems. In Stimulated Raman Scattering (SRS), the coupled light in the fiber interacts with the molecular vibrations, due to which scattered light is generated at a wavelength longer than that of the coupled light. If another signal is also present having this longer wavelength, it undergoes amplification at the expense of the original signal. This leads to the degradation of the Signal-to-Noise Ratio (SNR) and hence the overall system performance.

Accurate evaluation of amplification and depletion of optical power due to SRS effect is required. The effect of SRS in DWDM fiber optic system has been treated by many authors under various assumptions [5, 6, 12-14]. Singh and Hudiara [15] have given model to calculate SRS without any assumptions ignoring walk off effects. In the equation 1, first term gives the total power transmitted to the kth channel, second term gives the total power depleted from the kth channel by the higher wavelength channels and third term indicates the total power received by the kth channel from the lower wavelength channels.

In equation 2, [g.sub.rmax] is peak raman gain coefficient (cm/W); [lambda]j, [lambda]i are the wavelengths (nm) of jth and ith channels; fi,fj are the centre frequencies (Hz) of the ith and jth channels; Ae is effective core area of optical fiber in [cm.sup.2] and value of b varies from 1 to 2 depending upon the polarization state of the signals at different wavelength channels.

Modified power due to SRS is given by [15]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 1

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 2

Effect of Four Wave Mixing (FWM)

In the SRS effect the optical fiber plays an active role through the participation of molecular vibrations. But in the case of FWM, optical fiber plays a passive role, i.e., it simply mediates the interaction among several copropagating optical signals. In the case of OFDM systems, a number of optical waves copropagate at different wavelengths. Because of the FWM effect, three copropagating optical signals of frequencies say [f.sub.i], [f.sub.j] and [f.sub.k] interact and generate a fourth signal at frequency [f.sub.ijk], where [f.sub.ijk] = [f.sub.i] + [f.sub.j] - [f.sub.k]. So in OFDM systems many such signals copropagate with the original signals and grow at the expense of the original signals. This phenomenon is known as FWM and is due to nonlinear response of a dielectric medium (optical fiber) to the intense light (OFDM signal) [16].

These newly generated signals can interfere with the original signals if there happens to be some frequency match between them, which leads to cross talk and degradation of the system performance. Probability of this frequency match increases if the channels are equally spaced [17-20].Effect of FWM is even more severe in the systems with inline amplification, as due to inline amplification the effective length of the fiber, over which nonlinear interaction takes place, increases.

FWM power generated at the frequency [f.sub.ijk] in this case, i.e., with inline amplifiers, is (assuming equal signal power P launched in all the wavelength channels) [21,22].

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 3

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 4

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 5

n is refractive index of the fiber, [lambda] is centre wavelength, X is third order nonlinear electric susceptibility, P is power injected in the channel, a is fiber attenuation coefficient, M is number of amplifiers, Le is effective system length, Ae is effective area of fiber, dijk is degeneracy factor; and [eta]ijk is FWM efficiency.

Effect of Amplified Spontaneous Emission (ASE) noise

In amplified fibre systems, fibre loss limitation is overcome by periodically spaced inline optical amplifiers. However, inline optical amplifiers generate amplified spontaneous emission (ASE) noise, which is propagating along the fibre together with the signal. The total amount of ASE noise power at the receiver increases with the number of inline optical amplifiers. The influence of ASE noise has been studied by a number of authors [4,23-25]. It has been recognized that for long-distance amplified transmission systems where numerous inline optical amplifiers are used, the dominant noise source is ASE noise and thus BER performance is mainly determined by optical signal-to-noise ratio (defined as the ratio of optical signal power to ASE noise power after predetector optical filtering) rather than the received signal power as in conventional systems without inline optical amplifier repeaters [24, 25].

It is possible to model the signal and noise output photon numbers per second assuming fixed total output power from each amplifier of NP photons per second [5].

S = Np[[(Np + 2nsp Bo)/{Np + (2nsp Bo/A)}].sup.M] (6)

S = Np[1-[[(Np + 2nsp Bo)/{Np + (2nsp Bo/A)}].sup.M]]- (7)

Where Np is photons per second, nsp is population inversion parameter, Bo is rectangular optical bandwidth of an EDFA, A is fiber attenuation coefficient per kilometer and M is number of amplifiers.

In equation 6, s is signal output photon numbers per second and equation 7 gives noise output photons per second denoted by n. And ASE noise power at the output of the Mth amplifier is given as

[P.sub.ASE] = n (h.c/[lambda])- (8)

Where h is plank's constant (6.63 x [10.sup.-34] J.s), [lambda] is centre wavelength and c is velocity of light.

Algorithm for Optimization of Interamplifier Spacing

An algorithm suggested in Figure 1 shows the different steps in the optimization of the interamplifier spacing. Initially, all parameters like Input Power, System Length, Interchannel Separation, Receiver Sensitivity, Data rate except Interamplifier spacing were selected as the fixed inputs. Interamplifier Spacing was varied in steps. Modified signal power due to SRS, Noise power due to FWM and noise power due to ASE were calculated for different values of interamplifier spacing. Ratio of modified signal power and combined noise due to FWM and ASE was evaluated. The process was repeated for all values of interamplifier spacing. In the end, Signal to noise ratio Vs. wavelength for different values of Interamplifier spacing was plotted.

The graph was plotted between signal/ noise ratio vs. wavelength for different values of interamplifier spacing. For one value of interamplifier spacing, the minimum value of signal to noise ratio is considered for comparison considering the worst affected channel. The value of interamplifier spacing corresponding to maximum value of Signal /Noise ratio was noted. This value has been suggested to be the ideal interamplifier spacing for the given set of inputs.

The algorithm was repeated for different values of interchannel spacing and number of channels. All the results are summarised in the graphs [Figure 2-Figure 22].

Program was written in the Matlab 6.1 version to calculate the different values as per relations given in the equations.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

For simulation, WDM fiber optic system with inline optic amplifiers and non-zero dispersion shifted fiber in the anomalous regime (NZDSF+) operating at 1.55 [micro]m transmission window has been considered. Values of some important parameters chosen for the calculations are mentioned below:

Peak Raman gain coefficient = 10.05 x [10.sup.-12]cm/W Input power per channel = 1mW, Centre wavelength = 1.55 x [10.sup.-6]m, Fiber attenuation coefficient at 1.55 [micro]m = 0.205 dB/km, System length = 1000 km, Affective Area of the optical fibre = 5.3 x [10.sup.-7][cm.sup.2] , Fiber chromatic dispersion coefficient at 1.55 [micro]m = 3.0 ps/nm-km, dD/d[lambda] = 0.09 ps/[nm.sup.2]-km, Third order nonlinear electrical susceptibility X = 6 x [10.sup.-14] [m.sup.3]/W. Rectangular optical bandwidth of an EDFA = 30 nm(3.75 THz), Population inversion parameter = 1.3, Data rate per channel = 2.5 Gbits/s Refractive index of the fiber = 1.45 Inter channel separation = varied; 0.4 nm, 0.8 nm, 1 nm. No. of channels = varied; 4, 16, 32.

The interamplifier spacing was initially taken as 25 km and was increased in the steps of 25 km each up to 100 km.

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Results and Discussions

Results of the program have been summarized in the graphical form [Figure 2-Figure22].

Figure 2 shows the variation of noise power due to FWM (Pfwm) Vs. Wavelength for interchannel separation of 1 nm and number of channels to be 4. From this figure, it is clear that FWM noise power is less for high wavelength (channel 4) and low wavelength (channel 1) and maximum for mid range (channel 2,3). Similarly it can be concluded that with decrease in amplifier spacing, FWM effect becomes more severe. This may be due to the fact that for the given system length when amplifier spacing is decreased, the number of amplified segments increases; on the other hand, decrease in the effective length per segment is not that much. So the overall effective length increases, which in turn increase the FWM noise power with decrease in amplifier spacing as reported by Mahony et al and Maeda et al in equation 3, 4, 5 [21,22]. The same trend has been reported by the systems with interchannel separation of 0.4 nm and number of channels to be 16 (Figure 8); interchannel separation of 0.8 nm and number of channels to be 16 (Figure 13); interchannel separation of 0.8 nm and number of channels to be 32 (Figure 18), although the absolute value of the FWM noise has been found varying with changing these values.

Figure 3 depicts the variation of noise power due to ASE (Pase) vs. Wavelength for interchannel separation of 1 nm and number of channels to be 4 which indicates that ASE noise power is constant for different wavelengths but increases with the increase in amplifier spacing. This may be due to the reason that ASE noise introduced by an additional amplifier is proportional to the gain of the amplifier. The gain is adjusted to compensate for the fiber loss and insertion loss due to connectors and isolator in an amplified section [5]. So variation in amplifier separation (length of amplified section) varies the amount of the ASE noise introduced by the amplifier. For smaller amplifier separation the gain required for each amplifier decreases which in turn decreases the amount of ASE noise introduced. This trend has been verified by the systems with interchannel separation of 0.4 nm and number of channels to be 16 (Figure 9); interchannel separation of 0.8 nm and number of channels to be 16(Figure 14); interchannel separation of 0.8 nm and number of channels to be 32 (Figure 19) although the absolute value of the ASE noise has been found varying with changing these values.

Figure 4 describes the combined noise power due to FWM and ASE vs. Wavelength for interchannel separation of 1 nm and number of channels to be 4. Combined noise effect is same as that of FWM noise i.e. with decrease in interamplifier spacing total noise is increasing.The trend of variation of total optical noise is identical to that of FWM noise. This may be ascribed to the higher value of FWM noise power as compared to ASE noise. This is in good agreement with the observation made by Wu and Way [7] and Tonguz [8]. The trend has been strengthened by the systems with interchannel separation of 0.4 nm and number of channels to be 16 (Figure 10); interchannel separation of 0.8 nm and number of channels to be 16(Figure 15); interchannel separation of 0.8 nm and number of channels to be 32 (Figure 20) although the absolute value of the noise has been found varying with changing these values.

The modification in the signal due to SRS effect vs. interamplifier separation has been shown in Figure 5 for interchannel separation of 1 nm and number of channels to be 4. It can be concluded that with the decrease in amplifier spacing SRS effect becomes more severe. This may be due to the fact that for smaller amplified segments, the overall effective length of the system increases which in turn increase the value of D[i,j] as shown by Singh et al in equations 1,2 [15].

The variation of Signal / Noise ratio with Wavelength for different values of interamplifier separation has been reported in Figure 6. It is seen that with the increase in interamplifier separation, signal / noise ratio gets increased. As signal power is continuously increasing with the increase in interamplifier separation and noise power is continuously decreasing with the increase in interamplifier separation, similar results were expected. From Figure 6 it can be concluded that for a given set of input values, the optimum interamplifier separation for maximum signal to noise ratio is 100 km. The same value has been reported by the systems with interchannel separation of 0.4 nm and number of channels to be 16 (Figure 12); interchannel separation of 0.8 nm and number of channels to be 16(Figure 17); interchannel separation of 0.8 nm and number of channels to be 32 (Figure 22) although the absolute value of the Signal/ noise has been found varying with changing these values. Yu and Mahony has also concluded that as a common practice, the amplifier spacing is chosen to be between 50 and 100 km [4]. The result found by our algorithm is in good agreement with that of Yu and Mahony.

Another important observation which can be made from Figure 6 (for interchannel separation of 1 nm and number of channels to be 4), is that the worst affected channel is channel 3 for all values of inter amplifier distances i.e. channel 3 gives the minimum value of signal to noise ratio. To explain this, Figure 7, have to be studied simultaneously which show the variation of Modified signal due to SRS with wavelength for interchannel separation of 1 nm and number of channels to be 4. From these figures, one can visualise that Modified Signal due to SRS increases with the increase in wavelength. In SRS effect, higher wavelength signal grows at the expense of lower wavelength signals as shown in equation 1. Hence signal of high wavelength gets increased and will be minimum for lowest wavelength. Channel 2 and channel 3 experience maximum noise but at channel 3 signal is low as compared to channel 2, hence signal to noise ratio of channel 3 is minimum and it is referred to as the worst affected channel. The same trend in the variation of Modified signal due to SRS with wavelength has been reported by the systems with interchannel separation of 0.4 nm and number of channels to be 16 (Figure 11); interchannel separation of 0.8 nm and number of channels to be 16(Figure 16); interchannel separation of 0.8 nm and number of channels to be 32 (Figure 21).

Comparing Figure 8 (interchannel separation of 0.4 nm) with Figure 13 (interchannel separation of 0.8 nm), one can observe the effect of different interchannel spacing on FWM. It can be concluded that with decrease in interchannel separation FWM effect becomes more severe. This may be due to the increase in phase mismatch with the increase in channel separation as summarised by Mahony et al and Maeda et al in equation 3, 4, 5 [21,22].A similar observation has been reported by the authors elsewhere [26 ].The similar results have been reported by Yu and Mahony[4].

The effect of number of channels on FWM can be seen by studying Figure 13 (number of channels = 16) and Figure 18(number of channels = 32) simultaneously. It can be visualised from the figures that increase in the number of channels here has aggravated the effect of FWM. It may be due to increase in the number of channels in the close proximity as the major part of the FWM noise is generated by the interaction of the channels which are in the close neighbourhood of the worst affected channel.

The effect of different interchannel spacing on ASE can be visualised by comparing Figure 9 (interchannel separation of 0.4 nm) with Figure 14 (interchannel separation of 0.8 nm). Comparison depicts that ASE noise increases with the increase in interchannel separation. This may be due to the reason that channel bandwidth is increased with the increase in channel separation which inturn increases the ASE noise in that channel [26].

The modification in the signal due to SRS effect vs. Wavelength for different interchannel separation has been shown in Figure 11(interchannel separation of 0.4 nm) and Figure 16(interchannel separation of 0.8 nm). It can be concluded that with the decrease in interchannel separation SRS effect becomes more severe. This may be due to the fact that for smaller channel separation, the value of D [I,j] gets decreased as shown by Singh et al in equations 2 [15]. The trend is in good agreement with that observed by Kaur and Singh [26] and Yu and Mahony [4].

The modification in the signal due to SRS effect vs. Wavelength for different number of channels can be seen in Figure 16(number of channels = 16) and Figure 21 (number of channels = 32). It has been observed that with the increase in the number of channels, the effect of SRS has increased. It may be due to the increase in the number of channels falling within the range of Raman gain profile. The similar conclusion is given by Singh and Hudiara [15] in equation 1 cited in this paper.

The variation of Signal / Noise ratio with Wavelength for different values of interchannel separation has been reported in Figure 12 (interchannel separation of 0.4 nm) and Figure 17(interchannel separation of 0.8 nm). It is seen that with the increase in interchannel separation, signal / noise ratio gets increased. As signal power is continuously increasing with the increase in interchannel separation and noise power is continuously decreasing with the increase in interchannel separation, similar results were expected. The authors have reported similar observations in their earlier publication [26].

The variation of Signal / Noise ratio with Wavelength for different values of number of channels has been shown in Figure 17 (number of channels = 16) and Figure 22(number of channels = 32).It can be summarised that with the increase in number of channels from 16 to 32 for given same set of inputs, the signal to noise ratio has decreased. As noise power was increasing with the increase in number of channels, similar results were expected.

An important observation which can be made from Figure 4, Figure 10, Figure 15 and Figure 20 is that although the trends of ASE noise and FWM noise are opposite, still the total optical noise has followed the trend of FWM emphasizing that FWM is the major contributor of noise in WDM fiber optic system with inline optic amplifiers and non-zero dispersion shifted fiber in the anomalous regime (NZDSF+) operating at 1.55 [micro]m transmission window with data rate 2.5 Gb/s. It has been advocated by literature survey as well [3, 4, 7, 8, 27, and 28]. Authors have presented detailed study of FWM noise elsewhere [29].

Conclusion

Following conclusions are presented about the WDM fiber optic system with inline optical amplifiers and non-zero dispersion shifted fiber in the anomalous regime (NZDSF+) operating at 1.55 [micro]m transmission window with data rate 2.5 Gb/s with Peak Raman gain coefficient = 10.05 x [10.sup.-12]cm/W, System length = 1000 km, Rectangular optical bandwidth of an EDFA = 30 nm(3.75 THz):

1. The optimum interamplifier separation for getting maximum signal to noise ratio for given set of values is 100 km.

2. FWM is the major contributor of noise due to fiber nonlinearities.

3. With the increase in interchannel separation, signal / noise ratio gets increased.

The algorithm presented here can be applied for the design of amplified WDM systems in determining the optimum amplifier spacing, when the SRS and FWM are important fiber nonlinearities. Further work to modify the program to optimize interamplifier spacing for different important nonlinearities corresponding to different data rates is under progress.

References

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[21] M. J. O'Mahony, D. Simeonidou, A. Yu and J. Zhou "The design of a European optical network" Journal of Lightwave Technology, vol. 13, no. 5, pp. 817-828, May 1995.

[22] Mari W. Maeda, William B. Sessa, Winston Ingshih Way, A. Yi-Yan, Lyn Curtis, R. Spicer and R. I. Laming, "The effect of four wave mixing in fibers on optical frequency division multiplexed systems" Journal of Lightwave Technology, vol.8, no. 9, pp. 1402-1408, Sep 1990.

[23] N.A. OLSSON, "Lightwave systems with optical amplifiers", Journal of Lightwave Technology, vol.7, pp1071-1082, 1989.

[24] D.MARCUSE,"Derivation of analytical expression for the bit-error probability in lightwave systems with optical amplifiers", Journal of Lightwave Technology,vol 8, pp. 1816-1823,1990.

[25] P.A. HUMBLET, and M. AZIZOGLU,"On the bit error rate of lightwave systems with optical amulifiers", Journal of Lightwave Technology, vol. 9, pp.-1576-1582, 1991. [26] Gurmeet Kaur and M.L. Singh," Optimization of Interchannel Separation in WDM Transmission Systems in the presence of Fibre Nonlinearities", Proc. IFIP International Conference on Wireless and Optical Communications Networks -IEEE, Singapore, 2007.

[27] A.R. Chraplyvy, "What is the actual capacity of single mode fibers in amplified lightwave systems", IEEE Photonics Technol. Lett., vol.5, pp. 665-668, 1993.

[28] K. Sekine, N.Kikuchi, S.Sasaki, and M. Aoki, "10 Gbit/s four-channel WDM transmissions over 500 km with tech- nique for suppressing four-wave-mixing", Electron. Lett., vol.30,no.14, pp. 1150-1151, 1994.

[29] Gurmeet Kaur and M.L.Singh, "Effect of Four Wave Mixing in WDM Optical Fibre Systems," Opt. Int. J. Light Electron. Opt. (2007), In Press.

(a) Gurmeet Kaur, (b) M.L. Singh and (c) M.S. Patterh

(a) Reader, University College of Engineering, Punjabi University, Patiala, India.

E-mail:farishta02@yahoo.co.in

(b) Reader, Department of Electronics Technology, Guru Nanak Dev University, Amritsar, India

E-mail:mlsingh7@yahoo.co.uk

(c) Professor, University College of Engineering, Punjabi University, Patiala, India.

E-mail:mspattar@yahoo.com
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