The 5th International Conference on Optical Internet (COIN 2006) TuAl -4Hyatt Regency Jeju, Korea / July 9 - 13, 2006

Cross-gain Modulation in TDM PumpedRaman Fiber Amplifiers

Vineetha Kalavally1, Malin Premaratne2, Tin Win'(Department of Electrical and Computer Systems Engineering School of Engineering, Monash University Malaysia

Bandar Sunway, 46150 Petaling Jaya, Selangor, Malaysia Tel: +603-56360600, Fax: +603-56329314

2Advanced Computing and Simulation Laboratory, Department of Electrical and Computer Systems Engineering,

Monash University Clayton 3 800 Victoria Australia. E-mail:

Abstract

Signal-to-signal cross- gain modulation characteristics for

a counter-pumped Raman fiber amplifier (RFA) is

investigated when Time Division Multiplexed (TDM)

Gaussian Pulse Stream is used for pumping. Crosstalk

dependence on the pump pulseFull Width Half Maximum

(FWHM) is investigated.

1 Introduction

Multiple pump sources are used in Raman amplifiedDense Wavelength Division Multiplexed (DWDM)

optical transmission systems to obtain flat gain in the

transmission band. However, presence of multiple Raman

pumps introduces non-linear impairments such as Four

Wave Mixing (FWM) among pump signals and

undesirable exchange of power from shorter to longer

wavelengths due to Raman scattering. To reduce theseundesirable effects without affecting the gain performance

of Raman amplifiers, researchers have proposed time

division multiplexing (TDM) of pump wavelengths. Dueto the reduced interaction between pumps, this scheme

also provide flexibility for reconfiguration of pump

powers and wavelengths to achieve flat gain. TDM

pumping may be done either by using discrete time

division multiplexing (DTDM) which refers to

sequentially switching on and off a discrete set of pump

lasers or electronically sweeping the frequency of a singlelaser (SWEPT wavelength). More recently, Time

Division Multiplexed Gaussian Pulse Stream has been

used for pumping which is hereafter referred to as

Gaussian Time Division Multiplexing (GTDM) The use

of incoherent pump sources has also been suggested to

reduce the effects ofFWM.

Crosstalk magnitude between two signal channels

mediated by the pump is dependent on the pumping

scheme used. Due to the interaction between signal and

pump, modulation in signal channel induces power

modulations in the pump channel. Noting that gain is

directly dependent on the pump power, any modulationsin the pump channel is seen by other signal channels as

gain modulations, resulting in crosstalk between signal

channels. Crosstalk results in power penalty and needs to

be compensated. Frequency response of crosstalk of this

nature has been investigated for continuous wave (CW)

pumping for co- and counter-pumped configuration in [1]

and it was established that counter pumping results in a

significant reduction of the crosstalk bandwidth due to the

difference in the relative speeds between the signal and

the pump. It was shown that crosstalk in two

wavelength channels of a counter pumped RFA is

comparable to that in Erbium Doped Fiber Amplifiers in

[2]. Cross-gain modulation was used for studying theeffects of channel loss in r]. Degradation in crosstalk

performance and its dependency on the frequency of

DTDM pumped counter-pumped RFAs was reported in

[4]. TDM pumped RFA investigations such as opticalsignal to noise ratio in [5] employs GTDM. To the best of

the author's knowledge, no work has been reported so far

on crosst alk issues in GTDM counter pumped RFAs.

2 Numerical Modeling

In this paper, we investigate the cross-gain modulation

associated with GTDM pumping and the impact ofFWHM on its magnitude using numerical simulations.

89-955301-4-6 98560 @2006 OSIA - 277 -

signal fiber

sI1 (t) + S2() signal~~~~~~~~~~~~~~~~IOGTDM pump

?,=1420 nm, ?2=1439 nm, ?3=1473 nm

P1=75mW P2=9OmW P3=300mW

Fig. 1 Schematic of Counter -pumped RFA usingGTDM

Pump power

Fig. 2 GTDM pump pattern

Consider a span of 15km dispersion compensated fiber

(DCF) counter-pumped RFA shown in figure 1. The pumplasers using Gaussian pulses are sequentially switched on

and off; pump period, TDM period and FWHM are

illustrated in figure 2. There are three pump lasers at

wavelengths, 1420hm, 1439nm and 1473nm with average

output power of 75mW, 90mW and 300mW, respectively.The average power is maintained regardless of the choiceof FWHM. Signal wavelengths of 1560 and 1550 nm are

used to provide the input signals s(t) and s2(t); s1(t) is

sinusoidally amplitude modulated using a modulation

depth of 100% and modulation frequency (f); S2(t) is a

constant power CW signal. The signal power launched

into the DCF fiber is 2mW/channel. The loss coefficient

at pump wavelengths is 0.46 dB/km and that at signalwavelength is 0.60 dB/km, assumed to be the same for

both channels. The modulation frequency of s1(t) ranges

from lOOOHz to 3 MHz.

The RFA model is based on numerical solution using finite

differencing of coupled propagation equations (1)-(3) forforward signals and backward propagating pump [4].

pJ(z-±A, t + At) - f (,t) =

P,(,ye x p (-gs , IPI,(Z; t)+P(2g(z, t)]Az -apAz (2)

(z +AX t +,At) - P I (z, t)=Ps I (z,t) exp(gs Pp (z, t)Az- as Az) (2)

P 2(Z +A; t +A0) - PS2(Z, t)=Ps2(z, 0 exp(gsl (z,t) Az - a6sA) (3)

where PP (z, t) Psl (z,t), Ps2(z, t) are respectively thepump power and the input signal powers represented asfunctions of position along the fiber, z, and time, t. vp and

Vs are the group velocity at pump frequency and signalfrequency respectively, A and A are the pump andsignal wavelengths respectively, as and axp are theattenuation coefficients at signal and pump frequenciesrespectively, gs is the Raman gain efficiency for thefrequency difference corresponding toA andA . Theinitial launch distributions of pump and signal powers are

calculated using un-depleted pump approximation. Sgnalpower at the end of the fiber is computed using finitedifference equations. When the TDM frequency andFWHM are selected, GTDM pumping can be implementedby injecting the appropriate pump power and wavelengthat each step. If ? z is the incremental fiber lengthspecified by the number of fiber sections, the simulationprocess is now discrete in the time domain wlh a stepsize At= Az/ v , where vg = V= v (assumed) is thegroup velocity.

3 Results

Magnitude of cross-gain modulation between s1(t) and s2(t)is defined as the modulation index of ~(t) when s4(t) is

modulated, normalized to s2(t) when s1(t) is un-modulated.

The modulation frequency spectral components of s2(t) is

computed using Fast Fourier Transform for different pulseFWHMs. A TDM frequency of 200 kHz is used to

thoroughly average the pump power for counter-pumpedRaman amplifiers [5]. Crosstalk is found to be stronglydependent on the FWHM of the pulse for GTDM

pumping in figure 3. The narrower the pulse that mediates

the gain process, the larger the cross transfer of

modulation between signals.

For a GTDM pumped RFA employing pulse FWHM, 1/4 iof pump period, elimination of signal components below0.1MHz will ensure crosstalk less than -6dB, but it can go

up to 0.3MHz for FWHM, 16h pump period and 1MHz

- 278-

for FWHM, 1/12thpump period. The RFA design requires

the resulting power penalty to be compensated.

I-- :--I-- ll------------

I----- I -1-

---FWHM-m----- e

-6__j_ FWHM 126 pump period %

---FWHM =I/1 pumpperiod - v \.1

===FWM=11puppeid

.14 _ ______.___

.16 __ %___.___

.18 __ _ ______.____3 3.5 4 4.5 5 5.5 6 6.

log(modulation frequency, Hz)

Fig.3 Frequency response of cross-gain modulation

for GTDM repeat frequency = 200kHz.

7000 -------- ___-l I-----FWHM=1/4 pumpp

ll |---~~~~~~~~FWHM=1/6 pump period6000k - --- FWHM=1/12 pump peniodl I--------1---

'3000 -- ------ -_

i2000,i------|---

1000.+

lI Il

0.98 0.99 1 1.01 1.02 1.03 1.04 1.0'frequency (H-1z) x 105

Fig.4 FFT ofs2(t)

[Srs2(t)F slft) FV7HM 112 pump period2 ds ti frequency 200kHz

a)n\x L/'jlkJf'.Ii- %.t

7500 8000 8500 9000

FW IM -1/6 pump period2 fren_;en_v=-2___-_

7500 8000 8500 9000

FW ;HM = 1/4 pump period

1 4, 2,3; \ - I

7500 8000 8500 9000

of the output signal s(t) is compared for FWHM set toth th1/4t, 1/6 and 1/12 of the pump period in figure 4. The

time domain comparison between si(t) and s2(t)

(normalized to un-modulated ~(t) and s2(t) ) in figure 5

demonstrates the increase in cross transfer of modulation

for narrower pulses.

4 C onclusion

Although crosstalk envelope decreases steadily asmodulation frequency increases in counter-pumped RFA,

the roll off is dependent on the FWHM of the pulse used

in the case of GTDM pumping. It has been found that the

maximum signal frequency component that can be

ignored to ensure crosstalk of less than -6dB for 100%

modulation can change by an order of 1, for FWHM

ranging from 14l to 1/12t of the pump period. A sound

design for RFA employing GTDM requires knowledge of

crosstalk magnitude and associated power penalty.

5 References

1. F. Forghieri, R.W. Tkach and A. R. Chraplyvy,

"Bandwidth of cross talk in Raman Amplifiers", Optical Fiber

Communications Conference, FC6, Anaheim, 1994.

2. Jun Shan Wey, Douglas L.Butler, Michael F.Van Leeuwen,

Lance G.Joneckis and Julius Goldhar, "Cross Talk Bandwidth

in Backward Pumped Fiber Amplifiers", IEEE Photon. Technol.

Lett., vol.11, no.11, pp. 1417-1419, November, 1999.

3. M. Menif, M.Karasek, L.A.Rusch, " Cross- Gain Modulation

in Raman Fiber Amplifier: Experimentation and Modeling",

IEEE Photon. Technol. Lett., vol.14, no.9, pp 1261-1263,

September 2002.

4. V. Kalavally, M. Premaratne, and T. Win, 'Crosstalk in

counter-pumped distributed Raman amplifiers with DTDM

pumping', pp 205 - 209, IEEE computer society Proceedings,DELTA 2006, Malaysia, 2006

5. M. Karasek, J. Kanka, J. Radil, and J. Vojtech, "Large Signal

Model of TDM-Pumped Raman Fiber Amplifier", IEEE

Photon. Technol. Lett., vol. 17, no. 9, pp. 1848-1850,

September 2005

- 279 -

v)

0

v1)v

time, n

Fig. 5 Effect ofFWHM on cross-gain modulation

(time = n?t)

The modulation frequency spectral component (0. IMHz)

a

-.. 1,Ii.-ki if -jk, 0 v