Effects of Four Wave Mixing on an Optical WDM System by using Dispersion Shifted Fibre

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1 International Journal of Engineering and Tehnology Volume No. 7, July, 01 Effets of Four Wave Mixing on an Optial WDM System by using Dispersion Shifted Fibre Nahyan Al Mahmud, Bobby Barua Department of EEE, Ahsanullah University of Siene and Tehnology Dhaka, Bangladesh ABSTRACT The trend toward higher bit rates in lightwave ommuniation has interest in dispersion-shifted fibre to minimize dispersion penalties. At the same time optial amplifiers have inreased interest in wavelength multiplexing. These two methods of inreasing system apaity if used together an result in severe degradation due to fibre nonlinearity. So the et of dispersion, input power, fibre length and hannel spaing on the bit error rate and reeived or resultant power are investigated in our study. The performanes are analyzed in terms of transmitted hannel power, hannel spaing and bit error rate (BER) of the system. Keywords: Dispersion shifted fibre (DSF), four-wave mixing (FWM), signal to noise ratio (SNR), bit error rate (BER), wavelength division multiplexing (WDM). 1. INTRODUCTION Optial fibre ommuniation provides a very large bandwidth (50 THz) and it beomes the most modern means of ommuniation. To utilize the available bandwidth, we an multiplex numerous hannels on the same fibre and to inrease system margins, higher transmitter power or lower fibre losses are required [1]. Optial wavelength division multiplexing (WDM) systems using low dispersion fibres and erbium-doped fibre amplifier (EDFA) are very attrative to meet up the growing demand for broadband information distribution networks. WDM systems having high bit rate with a span of thousands of kilometer have beome a reality [-4]. However, these networks suffer performane degradation beause of fibre nonlinear ets, suh as stimulated Raman sattering, stimulated Brillouin sattering, self and ross phase modulation and, more importantly, Four wave mixing(fwm) [5-6]. FWM et generates new frequeny omponents some of whih may interfere with the transmitted signals [6]. Unequal hannel spaing an be employed so that no FWM omponent has the same frequeny as that of any hannel [7]. So interferene will be greatly redued. Even when unequal hannel spaing is used, the system may suffer from power depletion beause of new FWM omponents. Uniform hromati dispersion et favors the generation of FWM omponents [8]. In this paper we try to analyze the performane of an optial WDM ommuniation system under the et of FWM. The ratio of generated mixingprodut power to transmitted hannel power versus hannel spaing and bit error rate (BER) of an optial WDM system by using dispersion shifted fibre are evaluated.. METHODS The four-wave mixing phenomenon is one of the dominating nonlinearities in optial fibres. The other nonlinear ets by whih the degradation of the transmission harateristis in Wavelength Division Multiplexing (WDM) using dispersion shifted fibre ours are Stimulated Raman Sattering (SRS), Stimulated Brillouin Sattering (SBS), hromati dispersion, self and ross-phase modulation. The FWM harateristis are related to frequeny alloation of hannels. In FWM interations, a forth wavelength light is generated from three lights of different wavelengths. With the inrease in number of hannel the number of FWM light is drastially inreased. When three light passes through an optial transmission system a fourth light frequeny is produed by the interations among those three intelligene lights. This newly produed light is known as FWM light and the phenomenon is known as Four wave mixing. It originates from the weak dependene of the fibre refrative index on the intensity of the optial wave propagating along the fibre through the third order non linear suseptibility.it is analogous to third order intermodulation distortion whereby two or more optial waves at different wavelengths mix to produe new optial waves at other wavelengths. The simplest embodiment is shown in figure 1. ISSN: IJET ubliations UK. All rights reserved. 116

2 International Journal of Engineering and Tehnology (IJET) Volume No. 7, July, 01 Two o-propagating waves at frequenies f 1 and f mix and generate sidebands at f 1 -f and f -f 1.These sidebands opropagate with the initial waves and grow at their expense. Similarly, three opropagating waves will generate nine new optial waves at frequenies f ijk =f i +f j -f k where i,j,k an be 1, or 3.If the hannels are equally spaed, some of the generated waves will have the same frequenies as the injeted waves. Clearly the appearane of the additional waves as well as the depletion of the initial waves will degrade multihannel systems by rosstalk or exess attenuation. f 1 -f f -f 1 f 1 f Figure 1: Four wave mixing with injeted wave at frequeny f 1 and f 3. EFFECT OF FWM By FWM the following et ours in the optial fibre i. To produe the new optial waves the signal power is redued. This is known as power depletion. ii. In multihannel system several hannels are transmitted with several equally spaed frequenies. So some of these mixing produts will our at or near some of the operating wavelengths. These new optial waves interfere destrutively with the signal and degrade the system performane. 4. THEORETICAL ANALYSIS Four-photon mixing is a third-order nonlinearity in silia fibres, whih is analogous to intermodulation distortion in eletrial systems, so that in multihannel systems three optial frequenies mix to generate a fourth f g = f i + f j + f k (1) If we assume that the input signals are not depleted by the generation of mixing produts, the magnitude of this new optial signal is given by (in esu) g dχ1111L 4 αl A n i j k e η () Where is the refrative index, is the wavelength of the light, is the speed of light, i, j, k are the input powers of the hannels, L is the etive length of the fibre, given by 1 L = 1 e L (3) with the fibre loss, here taken to be 0. db/km. A is the etive area of the fibre, d is the degeneray fator, whih takes value 1 and for degenerate and nondegenerate terms, respetively, and 1111 = esu is the nonlinear suseptibility. The nonlinear suseptibility an be expressed in terms of the nonlinear index of refration n, in the ase of a single polarization, as n 480π 1111 [esu]= n [m /W] (4) The iieny is given by α η β 4e 1 L sin ΔβL/ L 1 e The quantity is the differene of the propagation onstants of the various waves due to dispersion and for a two-tone produt with hannel spaing f, is given by g + k - j - i = π λ f D f λ dd d Where the dispersion D and its slope are omputed at k. This analysis has been extended to multiple amplified spans. For suffiiently low fibre hromati dispersion 0 and 1. If in addition all hannels have the same power in, the ratio of the generated power g to the transmitted power of the hannel out an be written as g out (5) (6) π dχ L (7) n 4 λ A in ISSN: IJET ubliations UK. All rights reserved. 117

3 Bit error Rate International Journal of Engineering and Tehnology (IJET) Volume No. 7, July, 01 For theoretial analysis here we use the following equation κl e L η (8) g i j k Table 1: System arameters used for omputation arameter roperties Length 50km Where, Loss.5dB/km 6 104π 1 κ 3 n λ A 4 (9) Dispersion dd/d=.07ps/nm -km (Dispersionshifted) D=17ps/nm-km (Nondispersion-shifted) The probability of error an be expressed as 1 t e exp[ ] dt Q 5. RESULTS AND DISCUSSION (10) Following the analytial approah presented in setion 4, we evaluated the performane in terms of transmitted hannel power, hannel spaing, bit error rate (BER) and the power penalty of the system. For the onveniene of the readers the parameters used for omputation in this paper are shown in table 1. Nonlinearity m - W - (Dispersion-shifted) m - W - (nondispersionshifted) In figure we represent the plots of bit-error-ratio urves for the D=-0.ps/nm-km ase at three different launhed powers. Values quoted are for the total launhed power of the three hannels. The plots show that, with the inrease in reeived power the bit error rate dereases. Again for the same reeived power as input power inreases bit error rate inreases Bit error Rate vs reeived power varying input power pin=7dbm pin=11dbm pin=15dbm 10-4 Dispersion= -0.ps/nm-km Channel spaing=1 nm Reeived ower Figure : lots of bit-error-rate vs. reeived power varying input power ISSN: IJET ubliations UK. All rights reserved. 118

4 Bit error Rate International Journal of Engineering and Tehnology (IJET) Volume No. 7, July, Bit error Rate vs reeived power varying hannel spaing Channel spaing=1 nm Channel spaing= nm Channel spaing=3 nm 10-4 Dispersion= -0.ps/nm-km Total input power=1dbm Reeived ower Figure 3: lots of bit error rate vs. reeived power varying hannel spaing Figure 4: lots of bit error rate vs. reeived power varying dispersion ISSN: IJET ubliations UK. All rights reserved. 119

5 International Journal of Engineering and Tehnology (IJET) Volume No. 7, July, 01 figure 3 shows the plots of bit error rate vs. reeived power with varying hannel spaing. From the above figure we found that, for the same reeived power if hannel spaing is inreased then bit error rate will derease. Figure 4 represents the plots of bit error rate vs. reeived power with varying dispersion. From the plots it is lear that for the same reeived power if dispersion inreases then bit error rate dereases. 6. CONCLUSION We have investigated the et of FWM in an optial wavelength division multiplexed (WDM) ommuniation system. FWM lights degrade the performane of the system and as the number of hannel inreases, the no. of FWM lights inreases almost exponentially. To redue this nonlinear phenomenon we an use equal hannel spaing sheme. But it produes large number of FWM light with the same frequeny of the intelligene signals. Then we an use unequal hannel spaing so that FWM lights produed do not oinide with the intelligene hannel. This has the problem of requiring large bandwidth. The management of fibre dispersion an also redue the et of FWM in a WDM system. Low hromati dispersion fibre auses high FWM iieny, but if dispersion is inreased with hannel spaing then the FWM iieny is redued. REFERENCES [1] Chraplyvy, A.R. 00. Limitations on Lightwave Communiations Imposed by Optial-Fiber Nonlinearities, J. Lightwave Tehnology, vol. 10, no. 8, pp [] Brakett, C. A. Is there an emerging onsensus on WDM networking J. Lightwave Tehnology, vol. 14, pp , June 000. [3] Kogelnik, H. WDM networks: A U.S. perspetive, in ro. ECOC 1996, MoA., pp , [4] Mizrahi, V. et al., The future of WDM systems, in ro. ECOC 1997, pp [5] Chang, K., Yang, G., Kwong, C Determination of FWM roduts in Unequal- Spaed-Channel WDM Lightwave Systems, J. Lightwave Tehnology, vol.18, no.1. [6] Singh, S.., Kar, S., Jain, V.K. 007 erformane of All-optial WDM Network in resene of Four-wave Mixing, Optial Amplifier Noise, and Wavelength Converter Noise Volume 6, Issue, 007 pages [7] Forghieri, F., Tkah, R. W., Chraplyvy, A. R WDM systems with unequally spaed hannels, J.Lightwave Tehnol., vol 13, no. 5, pp [8] Eiselt, M Limits on WDM Systems Due to Four-Wave Mixing: A Statistial Approah, J. Lightwave Tehnology, vol. 17, no.11, pp ISSN: IJET ubliations UK. All rights reserved. 1130