Indian Journal of Pure & Applied Physics Vol. 4 1. March 2003, pp. 217-222

Non-linear cross-talk analysis in fiber Raman amplifiers V K Chaubey, V Jagannathan , R Raj agopalan & R Seshadrinathan

Electrical and Electronics Engineering Department, Birla In stitute of Technology and Science. Pil ani . 333 03 1

Received 5 June 2002; revised 20 September 2002; accepted 22 Janu ary 2003

Optical non-linearitics limit the optical power and information capaci ty of li ght-wave systems. These non-lincarities introduce different types of frequency and phase distortions. which lead to cross-talk. Various non-linear effects that aiTcct Raman amplificati on have been discussed and an evaluation or the cross- talk induced clue to these effects. has been presented . The maximum input power that can be transmi tted in a WDM system without degrading its performance has also been evalu ated.

1 Introduction

Since the first low-loss fiber in 1970, fiber­optics emerged from being a laboratory curiosity to constitut ing a significant portion of the communications and sensors business. Throughout the world, optical cables are carrying plain , old telephone serv ice across land and sea, along with data and video, at rates exceeding several gigabytes per second 1

• Optica l fiber communication systems have made dramatic progress over the past years. Both bandwidth and wavelength utili zation have significantly improved and continue to do so. Within this decade, dense WDM systems are ex pected to span the entire low-loss range in silica fibers of 1.2 to 1.7 ~lin (Ref. 2).

This huge bandwidth will on ly be accessible, if suitabl e optical amplifiers are avai lab le. EDFAs have some advantages such as, large avai I able power amplification , relative ly good, overall power efficien cy, small size and small dependence of amp lifi cation on optical polarization' . EDFAs used in WDM transmiss ion systems are so-call ed lumped amplifiers in which , the ga in is lumped at a point of the transmission line. Such amp lifiers are often cascaded to overcome the fibre loss 111 a communicati on channel, but, in such system, amplified spontaneous emission (ASE), accumu lates to affec t the gain and deteriorates the SNR at the rece iver. On the other hand , distributed ampl ifi ers, such as, fiber Raman amplifier, retain the optical signal leve l over a long distance along the transmission line and provides better system performance~. Although, it was even before EDFAs that Raman amp lifiers were used in experiments,

using large sca le solid-state lasers. They were not actually deployed in real fi e ld systems until recently, when high power diode pump sources became commercially availabl e' . Studies on Raman amplifiers have been continually conducted to suggest two critical merits of Raman amplifi ers; one is low noise and the other is arbitrary gain band . Raman amplifiers can work at any wavelength as long as the pump wave length is suitabl y chosen. The wide wavelength range of pump light in a wide and flat compos ite gain spectrum of Raman amplifier is suitable for multi-channe l systemsr' 7 in the low loss region of li ght-wave system. In practice, the gain spectrum is flattened by usin g several pumps at different wavelengths, yie lding a super-posed flat gain spectra. ln general , such pump beams are also affected by Raman scattering as well , with the WDM channels. This would result in power exchange between WDM channels . The cross-talk in such WDM channels leads to signal degradation due to stimulated Raman scattering (SRS), cross phase modulati on (XPM), interaction with group ve loc ity dispersion (GV D). se lf phase modulation (SPM) , four wave mi xing (FWM ), etc .

In this paper, one of the issues that degrades the performance of Raman amp! i fiers i.e. channe l cross­talk is taken up . In WDM , li ght at numerous wavelengths is inj ected into the fiber and the signal s at longer wavelengths will be amplifieJ not onl y by the pump but also by other signals at shorter wave lengths. This is a serious problem in Raman amp lifi ers . Here, a detail ed analysis of the various factors that cause cross-ta lk in Raman amplifiers pumped in one direction and al so bi-direc ti onall y

2 1R INDIAN J PURE & APPL PHYS, VOL 41 , MARCH 2003

pumped Raman amp lifiers has been done. The maximum power th at can be transmitted through the fiber without degrad ing system performance is al so es timated.

2 Theory

Stimul ated Raman scattering is an important non-linear process that can turn optical fibers into broad-band amp! i fi ers and tunable Raman lasers . Raman scattering can be viewed as modulation of li ght by molecular vibrations in the si lica matrix.

In Raman scattering, a pump photon is annihilated and a Stokes photon is created along with quantum vibrati onal e ergy in the scattering molecule. If a probe signal at Stokes frequency is co-inj ected into Raman active medium, the probe will be amp lified at the expense of the pump. The strength of this amplification IS ex ponentially dependent on pump intensity.

. . . ( I )

where P is the injected pump power, A" is the effec ti ve area of propagat ing waves, L" is the effective fiber length to account for fiber loss, and b is the relati ve polari zation factor of the ampli fi er. Effective area is approx imated as nw~ with a mode­fi eld diameter w. The effective length in case of ex ponenti al decay of power wi ll be given as:

L,. = ( I - e·•lL )/a ... (2)

where a is the loss coeffici ent of the fiber.

The sa me phenomenon of SRS that is benefi cial for making fiber amp lifi ers is al so detrimental to multi-channel communication systems employing wave length di vision multi plex ing. The reason is th at, the short wave length channel can ac t as a pump for longer wavelength channels and transfer part of the pul se energy to the nei ghbouring channels. This leads to Raman-induced cross-talk among channels th at can affect the system performance considerably . Channel cross-talk is induced due to various non­linear effects of whic h SRS, XPM, SPM, FWM and stimulated Brillouin scattering (SBS) are important.

There are two types of Raman ampl ifiers; d isc rete Raman amplifi er and Distributed Raman amplifi er. They differ in two ways: I ) Fiber type and length ; 2) Pumping geometry. In both , there i.;; a fundamenta l des ign compromi se between band width and low noise operati on. In di screte Raman

amplifier noi se figure will be 5-6 dB at shorter wavelengths due to mcrease 1n spontaneous emi ss ion for the signal wavelength closer to pump wavelength . Wh ile for di stributed Raman amplifier, it has always an improvement in noise figurex.

The Raman gain coefficient increases linearl y with pump probe frequency separati on up to 500 cm-1 ( I 5000 GHz) . This gives us an easy and efficient way fo r obtaining the Raman ga in coeffi cient profil e by using linear and exponenti al approx imations in the respecti ve reg ions of the spectrum. This model has been used for theoret ica l estimation of st imulated Raman cross-talk in the multi -wave opt ical channel. Moreover, s1nce, transmitted optica l powers for analog CATV signals carried by the fiber typicall y need to be in the order of I 0 dBm. This high power level induces a variety of fiber non-linear effects leading to system impairment , particularly in WDM systems. Amongst these effects cross-talk due to stimulated Raman scatterin g~ (S RS), se lf-phase modu lat ion, cross­phase modulation (XPM) 10

, Brillouin scattering 11

and four wave mixing 12 are predominant.

The total cross-talk due to SRS and XPM is given byl ' :

{ [e·aL cos (dL) - I + aL ]+ j [e·ul. sin (dL )- dL]} f

... (3)

where P, is the transmitted power per carri er, a is the fiber-loss coeffici ent , y is th .__ fiber Kerr coeffi cient, g is the Raman-gain coeffic ient , Li s the fiber length , d=2DQD))A. is the walk-off parameter between the two carriers, Q is the modulati on freq uency, D" is the chromati c di spersion and oA. is the wavelength separati on between optical channels. The first term is, the SRS cross-talk term and the second and third are XPM terms.

Combining the non-linear effects of the Bri llouin scattering and four-wave mix ing, the total cross-talk comes out to be:

XT = P.,2 r ( - <a-Jtt )l . - 1)] Dd".O"y ' " ' ? ? L+ g e . (x_- + d - m:(a- .Jd)

{[e·aL cos (dL) - I + aL ]+j [e·<>L sin (dL)- dL ])]

CHAUBEY et a/.: FIBER RAMAN AMPLIFIERS 219

+{ gBu /c L, (F-j f llQ)/(llQ2+F) -aL} +{(11/P,) ( 1024nr·; n~'),}c1) (X,,,,f(LJAcflf

.. . (4)

where gao is the Brill ouin-gain coeffi c ient , /c is the

pump li ght intensity, lln = j~ -I-f~ .. ~, is the pump frequency, I is the signal frequency, In is the

freq uency of Brillouin-gain, r·• is the acoust ic

phonon I ife-time, and X 1111 is the third-order non­linear susceptibility.

(a)

Modu lat ion Frequency (GHz)

-16 0

-16.5

(]) -17.0 1J ~

-"" -17.5 2 1/1 -18.0 1/1 0 '-u -18 .5

-19.0

-19.5 0 2.0

Modulation Frequency (GHz)

Fig. I - (a) Variation of total cmss-talk due to various non­linear effects (S RS. XPM. SBS and FWM ) with modul ation frequency in di screte Raman amplifiers: (h) Variation of total cross- talk due to various non -linear effects (SRS, XPM , SBS and FWM) with modu lati on frequency in di stributed Raman amp I i tiers

In this paper, two channe l WDM system with signal wavelengths 1542 and 1553 nm, respectively, has been taken into cons iderati on. The transmission fibe r is a 25 km long, standard, sing le- mode fiber

(SMF), w ith a=0.22 dB/km and D,= 17ps/(nm-km).

The cross-ta lk for discrete Raman ampl ifier (pu mped in one d irection) was eva luated and the p lot of cross-talk versus modulation frequenc y is obtained. In d istributed Raman amplification (ORA), both forwa rd and backward pumping is done. For DRA configuration, it reduces the fiber

attenuation and a must be replaced by some a' whi ch corresponds to zero, when the Raman-ga in cancels out fiber loss. The c ross-talk variat ion with modu lation freq uency was dete rmined fo r DRA, using the above equati on and typical curves have been obta ined.

-19.0

- 19 5

(]) -20.5 1J

-210 """ 0 -21 .5 .... til

-220 1/1 0 ....

-22. 5 u

-23.0

-23. 5 0 0.002 0.004 0.006 0.008 0.01

Input Power (W)

- 160

-16.5 (b)

-17.0 (]) 1J -17.5 -"' - 18.0 0 ..... til -18.5 1/1 0 .... u

- 19.5

-20.0

-20.5 0 0.006 0.008 0.01

lnpu t Power (W)

Fig. 2- (a) Variation o f" cross-ta lk with the transmitted input power in discrete Raman amplifiers; (h ) Variation or cross-tal k with the transmitled input power in distributed Raman amplifiers

Stimu lated Raman scattering and stimul ated Brillouin scatte ring pose ser ious limitations to the input power that can be transmitted through an y optical system '~. The cr itica l power that can be transmitted throu !lh the system without decrracl in cr ._.. b C'

220 INDIAN 1 PURE & APPL PHYS, VOL 4 1, MARCH 2003

the pe rformance was also evaluated for both the cases 15

.

-18.0

-18 .5 {a)

-19.0

-19.5 en -20.0 :s -""

0 _,

"' lfl 0 L

u

-22.5 -23.0

0 0.5 1.0 1.5 2.0 2.5

Input Power (W)

-17 {b)

- 18

en -19 2

-"" 0 -20 +' lfl lfl 0 -2 1 '-u

-22

-23 0 0.5 2.5

Input Power (W)

Fig. 3 - (a) V ariation of cross-talk (neglecting SBS) with input power in di screte Raman amp li fiers: (b) Vari ation of cross-ta lk (neglecting SBS ) wit h input power in di stributed Raman amplifiers

3 Results and Discussion

Us ing Eq. (4) , the to ta l cross-talk in case of discrete Raman amp lifi e r and di stributed Raman amplifi e r has been numerically estimated as shown in Figs I (a) and (b).

It is evident that , in discrete Raman amplifier pumped from one end , power will attenuate , as it propagates, giv ing a lesser cross-talk and hence expone nlial decremen t w ith modul ati on frequency wi II be lesser as compared to the DRA case. In case o f ORA, the attenuati on fac to rs ge t red uced , and impose a large r scatte ring cross- ta lk .

It is clear from Figs I (a) and (b) that , as modulation frequency inc reases the cross-talk decreases, more rapidly, in the case of ORA. However, the order of magnitude of c ross-talk is lesser in the case of di sc rete Raman amplifier, which may be attributed to hi ghe r attenuation compared with the di stributed case.

-20.0

crJ -21.0 "0

0 -"' "' 0 '-u -24.0

-" 0 -"' "' 0 '-u

0.006 0,008 0,01 Input Power ( W)

-1 4.0 r-.--,--,-~.---r-r--.---..--.,

-15.0

-16 0

s.znm

- 23. 0 '-.-l...--1..-L-.J...........J....---l._.L_....,L......J.._ 0 0.002 0.004 0.006 0.008 0.01

Input Power ( W)

Fig. 4 - (a) Variation of cross-talk wit h input power for diiTerent values of wavelength diiTerences between signals for the case of distribu ted Raman amplifiers: (b ) V ariati on or cross­talk wi th input power ror di!Terent val ue; or wavelength ditlcrences between si gnals

In order to find out the maximum input power that can be trans mitted without degrading system performance, the variation of cross-ralk with input power has been obtained for the case of disc re te and distributed Raman amplifiers, taking Brillouin and four-wave mi xing cross-ta lk into cons ide ra ti on. The numerical estimation of cross-talk , u ~ i ng Eq . (4) has been shown in Figs 2(a) and (b).

It may be infe rred from Figs 2(a) and (b) that , as the input power inc reases, the c ross-ta lk le ve l a lso

CHAUBEY et a/.:FIB ER RAMAN AMPLIFIERS 221

mcreases for both di sc rete and di stributed Raman amplifie rs because of a larger power scatte ring and thi s sets a limit to the max imum input powe r that can be transmitted through the system. It can a lso be seen that, the order o f magnitude of c ross-ta lk reaches higher leve ls, for lower input power leve ls, in the case of di stributed Raman amplifiers, as compared to di scre te Raman ampli f ie rs. Thi s is obvious as in case o f di stributed Raman amplifie r, s ignal le ve l maintain s a hi gher leve l in the channe l whi ch causes more non-linear scattering. Thi s gives a scope that, for a g iven no ise margin , the input power requirement for di stributed Raman amplifie r w ill be smalle r as compared to di screte R aman amplifi er. The study has been ex tended to see the effect of SRS, XPM and FWM only . These are shown in Figs 3(a) and (b).

It may be conc luded from the Figs 3(a) and (b) that, the input power leve ls that can be transmitted , dras ti ca ll y inc rease, when c ross-ta lk due to Brill ouin scatte ring is neglected . It is once again seen that , more power can be transmitted in the case of di sc rete Raman amplifie r as compared to di stributed Raman amplifiers, s ince the cross-ta lk reaches hi gher le ve ls, for lower input power leve ls in di stributed Raman amplifie rs, as compared to di sc rete Raman amplifie rs. It is al so c lear that, the Brill ouin scatte ring puts a severe constra int towards cross-talk.

Fina ll y, the authors have tri ed to evalu ate the vari ati on of cross-ta lk w ith input power, by varying the diffe rence between the wave lengths of the two signal s that are transmitted in a two-channe l WDM system. They have cons idered a wider channe l spac ing to avo id large c ross-ta lk level in the present ana lys is . However, thi s is appli cable to narrow WDM with wave length less than I nm. The result is shown in Fi gs 4(a) and (b).

It can be seen fro m Figs 4 (a) and (b) that, as the wavelength di ffe rence be tween the two channe ls increases, the c ross-ta lk leve l fo r a parti cul a r input power decreases, for both di sc re te and d istributed Raman amplifica ti on. lt can also be observed that, in the case of di stributed Raman amplifi e rs, when the wave length di ffe rence approaches c loser to zero, the re is a sharp increase in the c ross-ta lk level due to la rger e ffecti ve scatte ring . The graph illustrates that, fo r low input powe r, c ross-ta lk is very small and attain s a saturated va lue for a given channel

separation . This g ives a scope to se lec t the appropriate channe l spac ing, for a given input power, at a des ired cross-talk .

4 Conclusion

In the present analys is, the contributi ons of SRS, XPM , SBS and FWM towards c ross-ta lk have been analyzed . The theore ti cal estimati ons of c ross- ta lk in case of di screte and di s tributed Raman amplifi ers have been presented . The study has al so been ex tended to find the input power limitation, considering the various types of non-linear c ross­ta lk .

It has been veri f ied that , Brill ouin scattering is the most dominant effect in induc ing c ross-talk in a WDM system. Thi s pheno menon dominates in the backward pumping case, the reby, resulting in a hi gher magnitude c ross-talk in di stributed Raman amplifie r, compared to disc rete Raman amplifi e r where only forward pumping is done. It is a lso infe rred from the s tudy th at, the four-wave mi x ing, least affects the channe l c ross-ta lk in the WDM systems considered in the present study.

It is observed that, an inc rease in input power results an inc rease in the c hanne l c ross-talk . Thi s imposes a limit on the maximum input po wer th at can be transmitted through a WDM sys te m. In the absence of Brill ouin scatte ring, the input power leve ls that can be transmitted, dras ti call y inc rease for both discrete and di stributed Raman amplifi er. So, if by some mean s the Brill ouin scatte ring is e liminated, then larger input powers can be transmitted . It is a lso infe rred that, sma lle r channe l spacing imposes a hi gher c ross-ta lk, w hich becomes more severe in ORA sys te m.

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