SRS VE FWM OLAYLARININ DWDM-GPON SİSTEMLERİN AŞAĞI YÖNLÜ KANAL PERFORMANSLARI ÜZERİNDEKİ BİRLEŞİK ETKİSİ

Bu makalede, 7-, 15- ve 31-kanalli yogun dalgaboyu bolmeli cogullamali gigabit pasif optik ag (DWDM-GPON) sistemlerinin merkez asagi yonlu kanallari uzerinde gerceklestirilen isaret-capraz karisim orani (SXR) benzetimleri yardimiyla, uyarilmis Raman sacilmasi (SRS) ve dort dalga karisiminin (FWM), DWDM-GPON asagi yonlu kanal performanslari uzerindeki birlesik etkisi, FWM’nin tekli etkisi ile karsilastirilmistir. Benzetim sonuclari, SRS’nin FWM’nin negatif etkilerini kompanze ettigini ve kompanzasyon belirginliginin artan kanal sayilari ve kanallar arasi bosluk degerleri ile arttigini gostermektedir. 50 GHz ve 100 GHz gibi yuksek kanallar arasi bosluk degerlerinde, SXR degisimi,        0.5 km’lik cok kisa kanal uzunlugu degisimlerinde guclu bir osilasyon davranisi sergilemektedir. Bu kanallar arasi bosluk degerlerinde, SRS ve FWM birlesik etkisi, SXR degisimindeki maksimum osilasyon genligini FWM’nin tekli etkisine gore daha da arttirmaktadir. 0.1-5 mW araliginda, Raman kazancinin kanal giris gucleri ile yaklasik olarak dogrusal degisim sergiledigi gozlenmistir ve Raman kazanci artan fiber uzunluklari, kanallar arasi bosluk degerleri ve kanal sayilari ile artmaktadir. Bu calismanin sonuclari, DWDM-GPON sistemler uzerindeki SRS ve FWM birlesik etkisi ile FWM tekli etkisi arasindaki belirgin farki vurgulamakta ve mevcut DWDM-GPON uygulamalari icin onemli ipuclari vermektedir.


INTRODUCTION
In modern optical communication systems, networks having longer lifetimes, higher speeds, higher bandwidths and lower costs with respect to their alternatives become more important due to ever-increasing demands of customers. Currently, passive optical network (PON) structures, in particular gigabit passive optical networks (GPONs), promise important features for access networks. Allowing information at different channels to be transmitted in various wavelengths through a single fiber at the same time in both upstream and downstream directions, dense wavelength division multiplexed-GPON (DWDM-GPON) systems have proved to be a better choice in increasing the capacity and the flexibility in network design. Telecommunication Standardization Sector of International Telecommunication Union (ITU-T) has standardized the channels spacings for DWDM as 12.5 GHz, 25 GHz, 50 GHz and 100 GHz with Recommendations G.671 (2002) and G.694. 1 (2012). System specifications such as the number of DWDM channels, channel spacings, total transmission length and the input power per channel have important roles in overall system performance as well as the nonlinear effects occurring on the optical fiber during system operation. Among all fiber nonlinearities, four wave mixing (FWM) and stimulated Raman scattering (SRS) are expected to have major impacts on performance limitations in DWDM-GPON systems. There are various papers focusing on long- Karlık, 2016b) while analyses have been carried out for just SRS effects in some papers (Singh and Hudiara, 2004;Kaur et. al., 2015) or for the combined effect of SRS and FWM but in the presence of amplified spontaneous emission (ASE) noise generated by erbium-doped fiber amplifiers (EDFAs) in some others (Kaur and Singh, 2007a; Kaur and Singh, 2007b;Kaur et. al., 2010;Kaur et. al., 2011). However, to the best of our knowledge, there are no papers focusing on the combined impact of SRS and FWM on the downlink channel performance of DWDM-GPON systems. In this paper, using the signal-to-crosstalk ratio (SXR) variations, i.e. variations in the ratio of the power of the modified signal due to SRS to the power of FWM crosstalk, the combined impact of SRS and FWM on the downlink performance of DWDM-GPON systems has been analyzed with Matlab 2013a simulations considering channels spacings of 12.5 GHz, 25 GHz, 50 GHz and 100 GHz. The amplification factor of the Stokes wave in 7-, 15-and 31-channel DWDM-GPON systems has also been analyzed. In Section 2, the theoretical background required for FWM, SRS and PONs is given. Simulation models and necessary system characteristics are introduced in Section 3. Simulations results and their interpretation are presented in Section 4.

Four Wave Mixing (FWM)
During the FWM process, the interaction between three different optical waves propagating through the optical fiber with frequencies f i , f j and f k generates a novel fourth wave with a novel frequency f ijk due to the third order susceptibility of the fiber. The above mentioned process can be described with where indices i, j and k present three different channels of DWDM system satisfying the condition k ǂ i, j. The major impact of FWM on DWDM system occurs when novel optical signals generated by triple combinations of optical signals fall in original DWDM channels and interact with original signals in those channels. If channels are equally spaced in DWDM systems, a significant number of FWM products, i.e. generated optical signals, and original channels may propagate with the same frequencies and hence result in FWM crosstalk, which causes a significant degradation in the system performance The total number of FWM products (M) generated in DWDM systems depends on the number of DWDM channels (N) and can be determined with The FWM power generated at the frequency f ijk can be computed with where d ijk indicates the degeneracy factor, where d ijk = 3 for i = j ǂ k and = 6 for i ǂ j ǂ k, indicates the nonlinearity coefficient, L eff indicates the effective fiber length, P i, P j and P k indicate input powers of channels i, j, k, respectively, indicates the attenuation coefficient of the fiber, indicates the fiber length and ƞ ijk indicates the FWM efficiency, which can be given as where the phase mismatching factor (∆B ijk ) is where is the wavelength of the ℎ channel, c is the speed of light in vacuum, D is the chromatic dispersion coefficient and dD dλ ⁄ is the chromatic dispersion slope. For the case of a DWDM system having equally spaced channels, the total FWM crosstalk in a channel with a frequency f c can be expressed as (Maeda et. al., 1990) The signal-to-crosstalk ratio (SXR) parameter, which can be used for the analysis of FWM crosstalk impact on a specific channel of a DWDM system, can be defined as = 10 10 ( ) where P out is the output power of the channel and is computed with = . − for the input power P in .

Stimulated Raman Scattering (SRS)
In WDM fiber communication systems, SRS is one of the crucial nonlinear effects, which degrades the system performance due to the inter-channel crosstalk and that leads to a decrease in the SNR of the WDM system. In SRS, the incident light interacts with molecular vibrations of the fiber medium and because of this interaction, light can be scattered. Also in SRS, channels with higher frequencies (shorter wavelengths) transfer a part of their power to channels with lower frequencies (higher wavelengths) (Schneider, 2004).
Modified signal powers at various wavelengths due to SRS can be evaluated as (Singh and Hudiara, 2004) In the right hand side of (8) [ , ], gives the total power depleted by the ℎ channel from lower wavelength channels. In where are wavelengths of ℎ and ℎ channels, respectively, in terms of nm; [ ] is the optical power launched in the ℎ channel in terms of mW, is the peak Raman gain coefficient in terms of cm/W; f and f are center frequencies of ℎ and ℎ channels, respectively, in terms of Hz; ( ) is the effective length of the ℎ channel operating at the wavelength in terms of km; is the effective core area of the optical fiber in terms of cm 2 and the value b varies between 1 and 2 according to the polarization state of signals at different wavelength channels.
The actual optical power received at the receiver side of the ℎ channel is defined as In SRS, the power transfer from channels with higher frequencies to the ones with lower frequencies is in fact the light amplification in the channel that has a higher wavelength by the help of the channel that has a lower wavelength. The amplification factor of the Stokes wave (channel that has a higher wavelength), i.e. , can be defined as the ratio of the intensity of the Stokes wave with Raman scattering at the fiber output, i.e. ( ), to the intensity it would have without the Raman scattering at the fiber output, i.e. (0) − (Schneider, 2004).
Since the amplification of the Stokes wave causes a depletion in the pump wave (channel that has a lower wavelength), a depletion factor can be described for the pump wave in a similar way to the amplification factor.
Considering that ( ) = . − and (0) = , (11) can be rewritten as = where represents the modified power due to SRS. The SXR given in (7) can be modified for DWDM systems under combined impacts of SRS and FWM as = 10 10 ( ) (13) where P SRS is the modified signal power due to SRS and P FWM is the FWM crosstalk power.

Passive Optical Networks (PONs)
PON is an optical network technology which uses a point-to-multipoint topology that means a single fiber is used to support multiple users. It includes an Optical Line Termination (OLT), a group of an Optical Network Units (ONUs), a passive optical device or a splitter and optical fibers connecting those devices mentioned above. The OLT is located at the Central Office (CO) where it has an obligation to transmit the data coming from the metropolitan network to ONUs through the downlink stream and the data coming from ONUs to the metropolitan network via the uplink stream. Two wavelengths are used by OLT, one is 1490 nm for the downlink and the other is 1310 nm for the uplink. ONUs are located at customer premises. The optical splitter exists between the OLT and the ONU and it works as a demultiplexer for the downstream transmission and as a multiplexer for the upstream transmission. A PON architecture is shown in Fig. 1. In DWDM-GPON applications, considering the number of end-users in both channels, i.e. downlink and uplink channels, channels can be divided into sub-channels using the splitting ratio (1:N) feature of the optical splitter. 1:128 splitting ratios will be available in applications in the near future.

SIMULATION MODEL AND FIBER PARAMETERS
In this study, with the help of MATLAB 2013a simulation program and mathematical equations given in Section 2, simulations have been performed for center downlink channels of 7-, 15-and 31-channel DWDM-GPON systems, which have equally spaced channels with channel spacing values of 12.5 GHz, 25 GHz, 50 GHz and 100 GHz.
In simulations, G.652 standard single-mode fiber (SSMF) has been used for the downlink channel operating at 1490 nm and important parameter values of this fiber are given in Table 1, where D c indicates the chromatic dispersion, S indicates the chromatic dispersion slope, γ denotes the nonlinearity coefficient and is the attenuation coefficient. In DWDM-GPON systems implemented with SSMFs, center channels are the most badly impacted channels (Harboe et. al., 2008). Therefore, center channels of 7-, 15-and 31-channel DWDM-GPON systems, i.e. 4 th , 8 th and 16 th channels, respectively, are taken into account in simulations. Tables 2-4 show the triple channel combinations that generate FWM products falling into center channels of 7-, 15-and 31-channel systems, respectively.
In Tables 2-4, i, j and k show channel numbers that construct FWM products in the center channel of the related DWDM-GPON system, e.g. in Table 2, channel 3 (i=3), channel 5 (j=5) and channel 4 (k=4) generate a FWM product in the center channel, i.e. the 4 th channel, of the 7-channel DWDM-GPON system. As mentioned before in Section 2, k≠ i, j and only half spaces in Table 2-4 are considered since i and j are interchangeable.  Table 4. Channel combinations that generate FWM products in the center channel of a 31-channel DWDM-GPON system

SIMULATIONS
In this section, simulation results analyzing SXR variations with variations in channel input powers, channel spacing values and channel lengths are explained and interpreted firstly under the single impact of FWM and then under the combined impact of SRS and FWM. Furthermore, simulation results focusing on variations of the amplification factor of the Stokes wave with variations in input powers have also been reported.

SXR-channel input power variations
In this subsection, simulation results exhibiting variation of SXR with channel input powers for center downlink channels of 7-, 15-and 31-channel DWDM-GPON systems have been given in Figs   It has been observed in Figures 2a, 3a, 4a and 5a that SXR value shows an exponential decay with the increase in channel input powers due to the 3 dependence of P FWM for the case of equal channel input powers as given in (3). Furthermore SXR decreases with decreasing channel spacing values since narrower channel spacings cause degradation in the phase mismatching factor ΔB ijk and this increases the FWM efficiency η ijk and subsequently P FWM increases as it can be easily seen from (3)- (5). SXR also decreases with increasing channel Comparing results given in Figs. 2b, 3b, 4b and 5b with Figs. 2a, 3a, 4a and 5a respectively, it can be easily concluded that SXR values under the combined impact of SRS and FWM are significantly greater than those under the single impact of FWM and furthermore contrary to the case under the single impact of FWM, SXR values increase with increasing channel numbers. This is in fact due to the amplification factor of the Stokes wave, i.e. the Raman gain G R , increasing with the increasing channel numbers and resulting in an increase in the modified signal power P SRS for center channels. Therefore SXR increases with the increase in P SRS as it is obvious in (11)  It is clear in Fig. 6 and Tables 7-8 that at fixed channel input powers channel spacing values have more considerable effects on SXR than channel numbers, e.g. at fixed channel numbers SXR values at 100 GHz are greater than those at 12.5 GHz in the range of 36.09-36.14 dB in Table 7 while in the range of 50.90-62.98 dB in Table 8 however at fixed channel spacing values the SXR variation between 7-channel and 31-channel systems is in the rage of 1.74-2.88 dB in Table 7 while it is in 11.99-24.07 dB range in Table 8.

SXR-channel spacing value variations
Results given in this subsection is in good agreement with results given in the previous section about the compensating behavior of SRS on negative impacts of FWM in center downlink channels of DWDM-GPON systems, i.e. all SXR values in Table 8 are greater than related values in Table 7. Considering bold-written SXR values in Tables 7 and 8, the increasing significance of the compensating behavior of SRS with increasing channel numbers and channel spacing values can be easily seen.

SXR-channel length variations
In GHz f=50 GHz f=100 GHz

Amplification factor of the Stokes wave-channel input power variations
In this subsection, simulation results displaying variation of amplification factor of the Stokes wave, i.e. G R , with channel input powers for center downlink channels of 7-, 15-and 31-channel DWDM-GPON systems have been shown in Figs. 10-12.

CONCLUSION
Comparative analysis of the single impact of FWM and combined impact of SRS and FWM on the performance of center downlink channels of 7-, 15-, 31-channel DWDM-GPON systems have been carried out. The system performance has been evaluated by focusing on SXR variations with varying channel input powers, channel spacing values and channel link lengths under the single impact of FWM and the combined impact of SRS and FWM. Furthermore, variation of the amplification factor of the Stokes wave, i.e. the Raman gain G R , with varying channel input powers has been also investigated.
The most remarkable point emphasized by comparative simulation results about SXR-channel input power variations is that SRS compensates negative impacts of FWM in center downlink channels of DWDM-GPON systems and significance of compensation enhances with increasing channel numbers and channel spacing values.
Simulation results obtained for SXR-channel spacing value variations show that at fixed channel input powers, channel spacing values have more considerable effects on SXR than channel numbers. Simulation results of SXR-channel length variations state that a strong oscillatory behavior occurs on the SXR variation in very short channel length variations of 0.5 km especially at high channel spacing values of 50 GHz and 100 GHz. The combined impact of SRS and FWM enhances the maximum oscillation amplitude of the SXR variation with respect to the case under the single impact of FWM.
Simulation results display an approximately linear variation between the Raman gain and channel input powers in the range of 0.1-5 mW. Furthermore, the Raman gain increases with increasing fiber lengths, channel spacing values and channel numbers.
Results of this research exhibit that the combined impact of SRS and FWM on DWDM-GPON systems differs significantly from the single impact of FWM and give important hints for current DWDM-GPON implementations.