Analysis of FWM Penalties in DWDM Systems Based on G.652, G.653, and G.655 Optical Fibers

Transcription

1 Vol:, No:1, 8 Analysis of FWM Penalties in DWDM Systems Based on G.65, G.653, and G.655 Otical Fibes Paula B. Haboe, Edilson da Silva, and José R. Souza Abstact This ae esents an investigation of the owe enalties imosed by fou-wave mixing (FWM on G.65 (Single- Mode Fibe - SMF, G.653 (Disesion-Shifted Fibe - DSF, and G.655 (Non-Zeo Disesion-Shifted Fibe - NZDSF comliant fibes, consideing the DWDM gids suggested by the ITU-T Recommendations G.69, and G.694.1, with unifom channel sacing of 1, 5, 5, and 1.5 GHz. The mathematical/numeical model assumes undeleted uming, and shows vey clealy the deleteious effect of FWM on the efomance of DWDM systems, measued by the signal-to-noise atio (SNR. The esults make it evident that non-unifom channel sacing is actically mandatoy fo WDM systems based on DSF fibes.. Keywods DWDM systems, Fou-Wave Mixing (FWM, G.65, G.653, G.655 comliant fibes, Signal-to-noise atio. D I. INTRODUCTION ENSE wavelength-division-multilexing (DWDM is the key technology to enable the vey high-caacity hotonic netwoks euied by ou communication thisty society. In moden WDM systems, the imay nonlinea effects ae coss hase modulation (XPM, and the fou-wave mixing (FWM. The XPM mechanism was studied by the authos eviously [1], [], and two imotant effects associated with XPM wee investigated: feuency shifting, and the geneation of dak ulse tains fom CW light. The latte is used in the context of high seed otical netwoks fo wavelength convesion. On the othe hand, FWM geneates new otical feuencies (o FWM oducts that may cause channel cosstalk, and is the object of the study eoted in this ae. The occuence of FWM deends on seveal factos, such as the feuency sacing between channels, the inut owe e channel, the disesion chaacteistics of the otical fibe, and the distance along which the channels inteact. In long haul links, the P. B. Haboe is with the Deatment of Telecommunication Engineeing, Fedeal Fluminense Univesity (UFF, Niteói RJ, Bazil (coesonding autho to ovide hone: ; fax: ; aula@telecom.uff.b. E. da Silva was with the Deatment of Telecommunication Engineeing, Fedeal Fluminense Univesity (UFF, Niteói RJ, Bazil ( edilsondasilva@gmail.com. J. R. Souza is with the Deatment of Electonics and Telecommunications, Rio de Janeio State Univesity (UERJ, Rio de Janeio RJ, Bazil ( jsouza@uej.b. deloyment of otical amlifies aggavates the oblem, as not only the tansmitted signal ae amlified, but also the geneated FWM oducts, which mix again with the signals, giving ise to new oducts. In addition, if disesion-shifted fibes (DSF ae used, the FWM mechanism is enhanced, due to a eduction of the hase mismatch associated to the fibe's chomatic disesion. The ITU-T Recommendation G.69 (/98 secifies otical intefaces fo the oeation of amlified WDM systems on fibes that confom to ecommendations G.65 (Single-Mode Fibe - SMF, G.653 (Disesion-Shifted Fibe - DSF, and G.655 (Non-Zeo Disesion-Shifted Fibe - NZDSF. Initially, two eually saced channel gids wee defined, with the channels saced by 1 and 5 GHz. Late on, the ecommendation G.69 eceived as an addendum a efeence to ecommendation G (6/, and two new channel gids wee incooated, with 5 and 1.5 GHz channel sacing. Such naowe channel sacing will be indisensable in the nea futue to ovide fo the inceased caacity euied by futhe ogess of infomation technology. The cosstalk caused by FWM becomes moe intense as the sacing between channels diminishes. Also, the deloyment of the eually saced channel gids ecommended by ITU-T heightens the FWM henomenon, as most of the new feuencies coincide with the existing channel feuencies, esulting in coheent intefeence that is bit-atten deendent. In conseuence, the detected signal owe will fluctuate consideably. Theefoe, the nonlinea ocess of FWM mechanism is the one of the majo limitations to moden DWDM communication systems based on otical fibes. Diffeent techniues have been oosed to educe the deleteious effects of FWM, such as [3]: sectal allocation of the channels so that the sacing between neighboing channels is as lage as ossible, sectal allocation of the channels as fa as ossible fom the zeo-disesion wavelength ( ZD, deloyment of non-zeo disesion-shifted fibe (NZDSF, and sectal allocation of uneually saced channels, which euies a comlex system design. Although much wok has aleady been dedicated to the analysis of the FWM henomenon, a eview of the liteatue shows that the majoity of the aes tackle the oblem fom Intenational Scholaly and Scientific Reseach & Innovation ( schola.waset.og/ /734

2 Vol:, No:1, 8 the oint of view of a geneic disesive, nonlinea otical fibe. Howeve, the commecial fibes, as well as the hotonic systems/netwoks, comly with etinent ITU-T ecommendations, and the authos feel that moe infomation egading the occuence and effects of FWM in such a context is needed. This ae then investigates the FWM enalties imosed on DWDM systems based on G.65, G.653, and G.655 fibes, consideing eually saced channel gids of 1, 5, 5, and 1.5 GHz. Also, the aid evolution of the DWDM technology with inceasing channel density, and bit ate e channel, as well as the occuancy of new wavelength bands has fosteed the develoment of a vaiety of fibes. Each tye of fibe euies a secific aoach to the balancing of disesion, nonlinea effects, channel sacing, inut signal owe and chi. The designe is then faced with new challenges to match the ight fibe technology to the DWDM netwok secifications. Theefoe, by comaing the effects of the diffeent fibe tyes on the system efomance, the study caied out in this ae aims at oviding infomation that is useful fo the eduction of the FWM cosstalk. A numeical model develoed ealie [4], which consideed only two channels, was extended and imoved to accommodate a geneal DWDM system, with abitay numbe of channels, and channel sacing. II. MATHEMATICAL MODEL The evolution of the amlitude of a FWM signal along the length of a monomode fibe is descibed by [4]-[7]: d n A (z A (z i F * F F A (za (za (zex i F z dz caeff (1 whee A F (z is the amlitude of the FWM signal geneated at the feuency f F = f + f f = F /, (,, = 1,..., N;,, A s (z (s =,, is the amlitude of one of the N channels, of feuency f s, oiginally injected in the fibe, s (s =,, is the hase constant, z is the osition along the fibe, is the fibe loss coefficient, n is the nonlinea efactive index coefficient, c is the velocity of light in vacuum, A eff is the effective aea of the fibe coe, i = 1, and * indicates the comlex conjugate. The fibe disesion chaacteistics ae included indiectly though the vaiation of the hase constant with feuency. Euation (1 assumes CW oeation (which eesents the wost-case scenaio fo FWM geneation, and no um deletion, i.e. the um (channel waves ae consideed much moe intense than the geneated FWM waves. Afte a length L of fibe, the solution of (1 is witten as [4]-[7]: ( il in e 1 A (L F * L / F A (A (A ( e. caeff i ( with = F The aveage FWM owe geneated at the feuency F = c/ is then calculated as: P F (L AF(L (3 f f f ff f f ( il 4 n e 1 d P (P (P ( ex L Aeff i In (3, is the wavelength of the geneated FWM signal, and d is the so called degeneacy facto: d = 1 if =, and d = if ; the tem eesents the hase mismatch, i.e., the diffeence between the hase constants of the vaious waves. The smalle this hase mismatch, the moe efficient is the FWM geneation. An analytical exession fo the aamete is obtained exanding the hase constant in a Taylo seies in the neighbohood of a cetain feuency f = c/, which can be the feuency of one channel, the feuency of the disesion zeo of the fibe, o any suitable feuency. Afte some calculation, is finally given by [4]- [7]: ( f (f (f (f F (f f (f f (f (f f f [(f (f f f (f f (f f ] (f D f c 4 D dd (4 c d In (4, D is the disesion aamete of the fibe, and dd/d is the coesonding disesion sloe. The euation is valid in a feuency ange aound f, whee the disesion sloe is linea, i.e., a feuency ange whee the second ode disesion is constant. Accoding to (4, the hase mismatch deends on the tye of fibe, though D, and dd/d, and the sacing between neighboing channels. The hase matching condition, =, is theefoe aoximately satisfied at wavelengths close to the zeo-disesion wavelength of the fibe. In actice it is imotant to guaantee that the WDM system has a good SNR, so that the tansmitted infomation can be ecoveed with no ambiguity. Not knowing the details of tansmitte and eceive deloyed in the system, it is assumed that a minimum SNR of db is euied [8], consideing that the noise is totally due to the geneated FWM, and the signal owe loss is due solely to the fibe attenuation. The signal-to-noise ation is then defined as: P signal SNR (db 1log 1 (5 P FWM Fo the calculation of the SNR, it is then necessay to identify all the FWM oducts that fall within the ass band of the otical filte esonsible fo the channel seaation; the Intenational Scholaly and Scientific Reseach & Innovation ( schola.waset.og/ /734

3 Vol:, No:1, 8 coesonding FWM owes ae then added togethe. Geneally, the cosstalk vaies with the osition of the channel in the gid: the cosstalk of the cente channels diffes fom the cosstalk of the edge channels. Theefoe, the SNR analysis will be based on the wost case among the channels, as exlained late on. Euations (1-(5 eesent all the mathematical fomalism needed to investigate the effect of the FWM mechanism in WDM systems. Theses euations wee imlemented in the numeical model used in the simulations esented next. Befoe discussing the esults, it is woth mentioning that this wok focuses the secific context of the ITU-T Recommendations G.69, and G that suggest eually saced channel gids. Howeve, both the mathematical fomulation, and the esulting numeical model ae comletely geneal, and can be alied to uneually saced channel gids as well [9], [1]. III. CASE ANALYSIS AND RESULTS In a evious wok [4], the authos veified that, fo eually saced channels, seveal of the geneated FWM oducts coincide in feuency with the channels injected into the fibe, giving ise to sevee cosstalk. Additionally, the esults then obtained showed that, in a single-mode fibe (SMF, the FWM owe deceases vey aidly as the channel sacing inceases. Howeve, fo DSF fibes, the FWM owe can be vey high, indeendent of the sacing between channels, if the channels ae allocated in the 155 nm window. As this is exactly the scenaio fo the majoity of the long haul otical communication systems, it will be the focus of the esent analysis. Thee case analyses ae esented. The fist one investigates how the ositioning of the channels in the 155 nm window affects the signal-to-noise atio of systems based on DSF, and NZDSF fibes. The second case investigates how the channel sacing affects the FWM owe gowth, consideing SMF, DSF, and NZDSF fibes. The thid and final case investigates how the inut owe e channel vaies with the length of the fibe, also fo the thee fibes.to hel the undestanding of the hysical ocesses involved, systems with 3, 5, 7, 9, and 11 channels ae consideed, as well as the fou WDM gids: 1, 5, 5, and 1.5 GHz. Befoe discussing the effects of FWM on the system efomance, it is necessay to detemine which channel is the most affected. In systems with eually saced channels that emloy DSF fibe, the wost case is always that of the channel that coincides with the fibe's zeo-disesion wavelength, indeendent of the numbe of channels. With SMF, and NZDSF fibes, the wost case is that of the cente channels, as moe FWM oducts coincide with these channels. Fo examle, with just 3 channels, nine FWM oducts will be geneated, and one coincides with the middle channel (channel no.. It is not difficult to veify that, with 11 channels, 37 FWM oducts will coincide with the cente channel. A. SNR and Positioning of the Channels in the 155 nm Window To investigate how the system SNR is influenced by the ositioning of the channels in the 155 nm window, fo a cetain WDM gid with a given numbe of channels, the middle channel is shifted in wavelength fom 1515 nm to 1585 nm, and the whole gid follows suit. Fig. 1 shows the vaiation of the system SNR as a function of the wavelength of the middle channel fo systems with 3, 5, 7, 9, and 11 channels; in Fig. 1(a the channels ae saced by 1 GHz, and in Fig. 1(b by 5 GHz. The coesonding cuves fo the FWM owes have exactly the same shae, but u side down, theefoe they ae not shown. In both cases, the inut owe e channel is 1 mw ( dbm. Fig. 1 efes to a DSF fibe, whose aametes at 155 nm ae: D =, dd/d =.7 s/km-nm, A eff = 5 m, =. db/km. A length of fibe L = km is consideed. Fig. 1 Vaiation of the system SNR as a function of the wavelength with channel sacing of (a 1 GHz, and (b 5 GHz. In Fig. 1(a, it is aaent that, indeendent of the numbe of channels, the signal-to-noise atio is minimal at 155 nm (the zeo-disesion wavelength of the DSF fibe, and inceases as the middle channel is shifted fom this wavelength, indicating that the FWM owe deceases as the middle channel is shifted fom ZD. Howeve, the SNR deceases vey aidly as the numbe of channels inceases, as moe FWM oducts ae geneated at the osition of the Intenational Scholaly and Scientific Reseach & Innovation ( schola.waset.og/ /734

4 Vol:, No:1, 8 middle channel. The oscillations seen in the SNR cuves ae associated with the behavio of the hase mismatch, accoding to (4. If the ange of obsevation encomasses all of the C band ( nm, the incease in the SNR and coesonding decay of the FWM owe is aaently fast. Nevetheless, fo oeation close to 155 nm, and consideing the naowlysaced channel gids suggested by the ITU-T ecommendations, the enalties imosed on the system by the FWM mechanism ae still too sevee. Fo examle, consideing 11 channels saced by 1 GHz (.8 nm, the esulting SNR is as low as 1 db, as shown in Fig. 1(a. The situation is aggavated when the channel sacing is educed to 5 GHz (.4 nm, with the esulting SNR as low as 8 db, as illustated in Fig. 1(b. The esults summaized in Fig. 1 indicate that the use of DSF fibe is not ecommended, as fa as the geneation of FWM oducts is concened, even fo a small numbe of channels. The influence of the channel sacing on the system efomance is investigated next. Fig. shows the vaiation of the system SNR as a function of the wavelength of the middle channel, fo an 11-channel DSF fibe system, with the channel sacing as a aamete. It is evident fom this figue that, when the channels ae saced by 1, 5, and 5 GHz, the middle channel must be at least 5 nm away fom the zeodisesion wavelength, so that an SNR of about 3 db can be obtained. When the channels ae saced by 1.5 GHz o less, the situation is even moe citical, and the esulting SNR values ae unaccetably low. Fig. Vaiation of the system SNR as a function of the wavelength fo an 11-channel DSF fibe system. A DSF seems an ideal means to maximize the each of otical communication systems in the 155 nm window, and it is indeed suitable fo TDM o single-channel alications. Howeve, as the evious esults show, having zeo-disesion at 155 nm is a negative condition fo DWDM alications: the absence of chomatic disesion enhances not only the FWM henomenon, but also othe citical nonlinea imaiments, like coss-hase modulation (XPM. Togethe, these effects basically limit the ultimate system efomance. To counteact the ole of nonlinea effects in DWDM systems, and still benefit fom educed disesion in the 155 nm egion, a new geneation of fibes has been develoed: the so called non-zeo disesion-shifted fibes (NZDSF. In ode to mitigate coss-channel nonlinea effects (FWM and XPM, a cetain level of chomatic disesion is actually desiable. Next, an NZDSF fibe is addessed, with the following disesion aametes at 155 nm: D = 3.7 s/km-nm, and dd/d =.7 s/km-nm ; the othe aametes and length ae the same as those of the DSF used eviously. Fig. 3 shows the esults fo the system SNR, consideing an 11-channel system. The geneal behavio of the cuves is simila to that obseved in Fig.. The fact that the disesion aamete D is small but non zeo causes a shifting of the cuves towads the shote wavelengths, with a valley nea 15 nm. In the egion of inteest, aound 155 nm, it is seen that the cuves exhibit a slowe vaiation than in the case of DSF fibes, and that SNR values above 3 db ae easily obtained with channel sacing as small as 5 GHz. This indicates that the use of NZDSF does indeed educe the deleteious effects of the FWM mechanism, while keeing total disesion low. Howeve, fo 1.5 GHz, and smalle channel sacing, the SNR emains ohibitively low. Fig. 3 Vaiation of the system SNR as a function of the wavelength fo an 11-channel NZDSF fibe system. B. FWM Powe and Channel Sacing To investigate how the fibe disesion chaacteistics affect the FWM owe gowth, G.65 (SMF, G.653 (DSF, and G.655 (NZDSF comliant fibes ae consideed. The disesion chaacteistics of the DSF, and NZDSF fibes wee aleady listed; fo the SMF fibe, the following values ae used at 155 nm: D = 17 s/km-nm, dd/d =.55 s/kmnm ; the othe data ae the same as in Fig. 1. Fig. 4 shows, fo a 9-channel system, the vaiation of the FWM owe as a function of the channel sacing. It is seen that the FWM owe is maximum with the DSF fibe, and, with esect to the othe fibes, actically constant and indeendent of the channel sacing. One can also conclude that SNR values in excess of db ae obtainable only if the channels ae seaated by GHz o moe. With the NZDSF, and SMF fibes, the FWM owe shows an oscillatoy behavio, which decays as the channel sacing inceases. Intenational Scholaly and Scientific Reseach & Innovation ( schola.waset.og/ /734

5 Vol:, No:1, 8 Fo examle, with the SMF fibe, the FWM owe is lowe than -45 dbm, fo channel sacing geate than 5 GHz; with the NZDSF fibe, a simila behavio is obseved fo channel sacing above 5 GHz, which, accoding to (3-(5, guaantees an excellent signal-to-noise atio. Fig. 4 Vaiation of the FWM owe as a function of the channel sacing fo a 9-channel system. The esults eoted in Fig. 4 can also be exlained fom (4, which, fo the DSF fibe, indicates that the coesonding hase mismatch deends only on the disesion sloe, and also that (i it is nil, and indeendent of the channel sacing (f, in the case of thee channels, and (ii it vaies with f 3 fo moe than thee channels. Fo the NZDSF, and SMF fibes, the hase mismatch vaies with f 3, but it now deends on both the disesion sloe, and on the disesion aamete D. It is woth mentioning that the oscillation obseved in the cuves fo the NZDSF, and SMF fibes ae totally associated with the behavio of the hase mismatch, and do not deend on the numbe of channels. This fact is illustated in Fig. 5 fo the NZDSF fibe, consideing 3-, 5-, 7-, 9-, and 11-channel systems. It is clea in this figue that the influence of the numbe of channels deceases as the channel sacing inceases. Fig. 5 Vaiation of the FWM owe as a function of the channel sacing fo a NZDSF fibe system. Theefoe, the evious esults indicate that when the channels ae saced by 1, and 5 GHz (many WDM systems still deloy such seaations between channels, the FWM is not a eal concen with NZDSF, and SMF fibes, fo a educed numbe of channels (u to channels. Howeve, FWM can become a sevee oblem with NZDSF fibes when smalle sacing - 5 GHz o 1.5 GHz - is adoted. C. Inut Powe e Channel and Fibe Length To comlete the analysis and bette undestand all the factos that affect the system signal-to-noise atio, new simulations wee efomed, vaying both the inut owe e channel, and the fibe length. Fig. 6 shows, fo a 7-channel system, the inut owe e channel needed to guaantee a minimum SNR of 3 db as the length of the fibe inceases, and consideing (a NZDSF, and (b DSF fibes. Fo the latte, a wide channel sacing of GHz is included. Fig. 6 Vaiation of the inut owe e channel as a function of the fibe length fo a 7-channel system: (a NZDSF, and (b DSF fibes. It is seen in Fig. 6(a that, fo a given length of fibe, the accetable inut owe levels decay as the channel sacing deceases, as the FWM mechanism becomes moe intense. It is also seen that the oscillatoy behavio of the cuve stengthens as the channel sacing inceases; accoding to (4, this is due to the lage hase mismatch. The figue indicates that, fo the 5 GHz channel sacing, u to dbm can be injected in each channel fo fibe lengths smalle than 7 km; if the channel sacing is educed to 1.5 GHz, values of the Intenational Scholaly and Scientific Reseach & Innovation ( schola.waset.og/ /734

6 Vol:, No:1, 8 inut owe of about -4 dbm aleady excite the FWM mechanism in NZDSF fibes. Othe simulations showed simila esults fo lage numbes of channels, but the accetable owe levels decease as the numbe of channels inceases, as moe FWM owe is geneated. Fo the DSF fibe, the hase matching condition is actically satisfied, and the occuence of FWM is significant, and deends only slightly on the channel sacing. This is aaent in Fig. 6(b, whee the accetable levels of inut owe e channel (to guaantee a minimum SNR of 3 db decay exonentially - as dictated by (3 - fo small lengths of fibe. Fo fibe length above 3 km, the inut owe vaies vey little. Only fo channel sacing of GHz can the inut owe levels be alleviated to moe easonable values. This fact becomes moe noticeable as the numbe of channels inceases, due to the highe numbe of FWM oducts coinciding with the egaded channel. Results of othe simulations, e.g. fo an 11-channel system with f 1 GHz, and L ~ 3 km, indicate that the inut owe must be educed by at least 3 db in comaison with the f = GHz case. Fig. 7 shows esults fo an 11-channel system, with f = 1 GHz, consideing the thee tyes of fibe. The SMF fibe, with a high disesion aamete at 155 nm, favos the hase mismatch, thus educing the FWM efficiency. The cuve fo the SMF fibe indicates that an SNR of 3 db is easily obtained fo inut owe of u to 5 mw. The same obsevation alies to the NZDSF fibe, with f = GHz. The oscillatoy behavio obseved in the othe cuves is also seen in the cuve fo the SMF fibe, ovided the scales ae adjusted accodingly. Fig. 7 Vaiation of the inut owe e channel as a function of the fibe length fo an 11-channel system. Othe simulations that wee efomed - consideing systems of u to channels, as well as all the evious comments, assue that the DSF fibe offes the most favoable conditions to excite the FWM mechanism, and thus imoses the most sevee enalties on WDM systems, esulting in accetably low values of signal-to-noise atio, even fo channel sacing as wide as GHz. Fo this eason, DSF fibes ae no longe commecialized, and gadually the newe DWDM installations benefit fom the enomous vaiety of NZDSF fibes available in the maket. IV. CONCLUSION This ae esented an analysis of the enalties imosed by the FWM henomenon on WDM systems using G.65, G.653, G.655 comliant fibes, in the secific context of the ITU-T Recommendations G.69, and G.694.1, which secify unifom sacing 1, 5, 5, and 1.5 GHz between channels. Conditions fo wost-case scenaio wee identified and exloed. The numeical model develoed - based on the undeleted um hyothesis - allows fo the evaluation of the hase mismatch, geneated FWM owe, and the system signal-to-noise atio. The vaious esults indicate that a eduction of the deleteious effects of the FWM henomenon is ossible, in at, by allocating the WDM channels away fom the zeodisesion wavelength of a DSF fibe. The esults show that the NZDSF fibe, with a local low but non-zeo disesion at 155 nm and also a lage effective aea, may alleviate the nonlinea cosstalk between channels. The esults also show that fo the SMF fibe (lagely deloyed all ove the wold the FWM oblem is ielevant, due to the high hase mismatch. Howeve, the SMF-based systems euie comlex and exensive schemes fo comensating the disesion accumulated along the fibe link. The esults futhe indicate that the system SNR deends mostly on the disesion chaacteistics of the otical fibe, on the channel sacing, and on the inut owe e channel. Theefoe, in those systems that euie the channels to be vey closely saced, the owe levels cannot be too high. The numeous simulations efomed cooboate the oositions ut fowad in the ITU-T Recommendations G.69, and G.694.1, and also make it clea that non-unifom channel sacing is actically mandatoy in WDM systems based on DSF fibes. Such channel allocating schemes wee aleady incooated in the numeical model, and the esults ae eoted elsewhee [6], [9], [1]. REFERENCES [1] P. B. Haboe, D. S. Godoy, and J. R. Souza, WDM simulato fo disesive, nonlinea, and lossy otical fibes, in Poc. MOMAG 6: 1 th SBMO Bazilian Micowave and Otoelectonics Symosium, and 7 th CBMAG Bazilian Congess on Electomagnetism, São Caetano do Sul SP, Bazil, Setembe 6 (in Potuguese. [] [] D. S. Godoy, WDM simulato fo disesive, nonlinea, and lossy otical fibes, MSc dissetation esented to the Deatment of Telecommunication Engineeing of the Fedeal Fluminense Univesity, Niteói RJ, Bazil, Decembe 6 (in Potuguese. [3] [3] G. P. Agawal, Nonlinea Fibe Otics (4 th edition, Academic Pess, San Diego, USA, 6. [4] [4] P. B. Haboe, and J. R. Souza, Analysis of fou-wave mixing in otical fibe links with non-unifom chomatic disesion, Micowave and Otical Tech. Lettes, vol. 39, no.,. 1-15, Octobe 3. [5] [5] W. Zeile, Modeling of fou-wave mixing in otical multiwavelength tansmission systems using disesion management, Reseach Reot, Univesity College London, London, Novembe [6] [6] E. da Silva, Analysis of enalties imosed by FWM on WDM systems, MSc dissetation esented to the Deatment of Intenational Scholaly and Scientific Reseach & Innovation ( schola.waset.og/ /734

7 Vol:, No:1, 8 Telecommunication Engineeing of the Fedeal Fluminense Univesity, Niteói RJ, Bazil, July 8 (in Potuguese. [7] [7] P. B. Haboe, E. da Silva, and J. R. Souza, WDM simulato fo the analysis of owe enalties imosed by FWM in G.65, G.653, and G.655 comliant fibes, in Poc. MOMAG 8: 13 th SBMO Bazilian Micowave and Otoelectonics Symosium, and 8 th CBMAG Bazilian Congess on Electomagnetism, Floianóolis SC, Bazil, Setembe 8 (in Potuguese. [8] [8] K. Nakajima, M. Ohashi, Y. Miyajima, and K. Shiaki, Assessment of disesion vaying fibe in WDM system, Electonics Lettes, vol. 33, no. 1, , June [9] [9] P. B. Haboe, E. da Silva, and J. R. Souza, FWM in DWDM systems: non-unifom vesus unifom channel sacing, in Poc. SBT'8: XXVI Bazilian Telecommunication Symosium, Rio de Janeio RJ, Bazil, Setembe 8 (in Potuguese. [1] [1] S. Kojima, and T. Numai, Theoetical analysis of modified eeated uneually saced feuency allocations in FDM lightwave tansmission systems, J. Lightwave Tech., vol. 4, no. 7, , July 6. Intenational Scholaly and Scientific Reseach & Innovation ( schola.waset.og/ /734