Simultaneously Stokes and anti-Stokes Raman amplification in silica fiber

Victor G. BespalovRussian Research Center

"S. I. Vavilov State Optical Institute"

Nikolai S. MakarovSaint-Petersburg State

Institute of Fine Mechanics and Optics (Technical

University)

Outline

•The main goal•Principle of quasi-phase matching

•System of SRS equations•Properties of quasi-phase matching

•Numerical simulations results•Conclusions•References

2

EDFA-amplification

3

- It is necessary to

provide amplification with an error

no more than 5 dB in the

whole spectral band of the amplifier.

SRS amplification in silica fiber

4

- With pump=1480 nm, due to

the broadband of SRS-

amplification stokes=1550 -

1580 nm.

- For opening of 1310 nm amplification window we offer to use simultaneously Stokes and anti-Stokes quasi-phase matching stimulated

Raman scattering amplification

Combined EDFA andStokes SRS amplification

5

- Flattening of amplification

curve is possible with

combined using of EDFA and Stokes SRS amplifier.

Principle of quasi-phase matching

Nonlinearity (2) Nonlinearity (3)

6

Raman active medium

Principleof quasi-phase matching at SRS

- Generalized phase=2p-a-s-(ka+ks-2kp)r,

where ki – is the wave vector of interacting wave, that describes

the direction of energy conversion “pump – Stokes –

anti-Stokes”, on passive layers input (0, 2) and active layers input (1, 3) do not practically

change, that in a final result provides a realization of quasi-

phase matching conditions.(3)0 (3)=07

System of steady-state SRS equations

In this system the waves mismatching and Raman gain are the functions of coordinate for nonlinear ((3)0) and

linear ((3)=0) layers.

– wave mismatching, g – steady-state Raman gain

coefficient, i – frequencies of

interacting waves, Aj –

complex wave amplitudes.

8

Optimum ratio ofinput Stokes/pump intensities

9

- There is an optimum value of input Stokes/pump waves

intensities ratio.

- This dependence can be

approximated as Is/Ip,opt=0,1359g-2,6146.

Comparison ofquasi-phase and phase matching

Hydrogen = 3.84 rad/cmg = 3.0 cm/GW1 - quasi-phase

matching2 - without (quasi-)

phase matching3 - phase matching.

- Conversion efficiency at quasi-phase matching is lower than at phase matching and higher than at simple focusing in

Raman media.10

Critical pump wave intensity

11

- There is a critical value

of pump intensity.

- This dependence

can be approximated as Icr.p=0.4Δ/g.

SRS in silica fiber

12

- For amplification in both windows it is

possible to use simultaneously amplification of Stokes and anti-

Stokes radiation at condition of quasi-

phase matching.- The structure is quasi-periodic.

SimultaneouslyStokes and anti-Stokes amplification

13

- Stokes and anti-Stokes

amplification provides

amplification peaks at

wavelengths of 1389 and 1583 nm with pump

1480 nm.

Analytical model ofquasi-phase matching SRS

14

)(

)(

arccos)1,(

js

ja

II

joptactl

])(exp[ )1,()()(2

)()1( jopt

actjs

ja

gjp

jp lIIEE

s

p

)1,(2)1,(

)1,()(2

)1,()(2

)(

2)(2

2

)(2

2)(2

*)()()1(

])(

)()

([

joptpasspai

s

a

s

a

s

ajopt

act

joptact

jps

agjoptact

jps

ag

lkk

jp

g

jp

gjp

gil

lIjs

lIja

ja

eI

iIIe

eEeEE

pass

jp

ja

jsjopt

passl

2

2)1,()2/1()2/1()2/1(

Analytical model ofquasi-phase matching SRS

15

)1,(2

21)1,(

21

)1,(

2

)()(2

1

)()()(

*)(2

1

2)(*)(2

)1(2

])1(

)1([

joptpasspsi

joptact

s

s

joptact

s

s

lkkjs

iljs

jp

ja

gil

js

jp

gjs

eEie

EE

Eie

EEE

)1,(2)1,(

)1,()0(2

)1,()0(2

)(

2)(2

2

)(2

2)(2

*)()()1(

])(

)()

([

joptpasspsi

joptact

joptactp

gjoptactp

g

lkk

jp

g

jp

gjp

gil

lIja

lIjs

js

eI

iIIe

eEeEEImprovement of calculation rate with constant calculation accuracy is ~120 times

16

)11lg()(

)(

)arccos(

5)(

)(

)(

ja

jsIg

II I

Ijps

a

js

ja

1 - attenuation zone,2 - amplification zone

- With losses about 0.3 dB/km (characteristic value for today optical fiber) the amplification occurs practically in whole medium.

Calculating losses in silica fiber

Conclusion

•Stokes-Anti-Stokes SRS amplification is useful for improvement of EDFA amplification curve and creating of amplified channel in 1310 nm

transparency window.•Layers lengths do not depend on input waves intensities if the ratio between pump/Stokes/anti-Stokes waves intensities does not change.

•The analytical model of quasi-phase matched stimulated Raman scattering in silica fiber is formulated and the recurrent formulas for

layers lengths and amplitudes of interacting waves are received.•The analytical model allow significant improvement of calculation rate

with same accuracy.•The obtained results are promising for the development of new effective

optical amplifiers.

17

References

•G. Randy, L. I. Tingyc, "Optical amplifiers transform long distance lightvoice telecommunications", Proc. IEEE, 84, pp. 870-883, 1996.•P. Urquhart, "Review of rare-earth-doped fiber lasers amplifiers", IEE Proc, 6, 385-407, 1988.•M. H. Ahmed, M. Shalaby, F. M. Misk, "Combined erbium and Raman amplification at 1.55 m in submarine links using backward pumping at 1.48 m", Pure Appl. Opt., 7, 659-666, 1998.•V. G. Bespalov, N. S. Makarov, "Quasi-phase matching anti-Stokes SRS generation", Proc. SPIE, vol. 4268, 2001, pp. 109-116.•J. J. Ottusch, M. S. Mangir, D. A. Rockwell, "Efficient anti-Stokes Raman conversion by four-wave mixing in gases", J. Opt. Soc. Am. B 8, pp. 68-77, 1991.

18