Post on 14-Dec-2015
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.
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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
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)(
)(
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.
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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.
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