Raman threshold and optical gain bandwidth in silica fibers
Nonlinearity of the stimulated Raman scattering (SRS) process in single-mode
 fibers is the creation basis of the new class of modern photonic devices such as fiber
 Raman lasers and fiber Raman amplifiers. The quantitative analysis of the gain start
 conditions and the Raman...
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| Опубліковано в: : | Semiconductor Physics Quantum Electronics & Optoelectronics |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2008
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| Цитувати: | Raman threshold and optical gain bandwidth in silica fibers / G.S.Felinskyi, P.A.Korotkov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 4. — С. 360-363. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860222602758324224 |
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| author | Felinskyi, G.S. Korotkov, P.A. |
| author_facet | Felinskyi, G.S. Korotkov, P.A. |
| citation_txt | Raman threshold and optical gain bandwidth in silica fibers / G.S.Felinskyi, P.A.Korotkov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 4. — С. 360-363. — Бібліогр.: 8 назв. — англ. |
| collection | DSpace DC |
| container_title | Semiconductor Physics Quantum Electronics & Optoelectronics |
| description | Nonlinearity of the stimulated Raman scattering (SRS) process in single-mode
fibers is the creation basis of the new class of modern photonic devices such as fiber
Raman lasers and fiber Raman amplifiers. The quantitative analysis of the gain start
conditions and the Raman laser threshold in the single mode fibers from the viewpoint of
the strong gain description of active laser materials have been made in this work. It has
been shown that the absolute transparency regime for optical transmission in fibers and
Raman laser threshold for a monochrome signal wave can be directly obtained from the
standard coupled equations using only fundamental fiber parameters. Limiting condition
when material of fiber core starts transformation from the natural state with attenuation
of the Stokes wave to the state in which the Stokes wave is amplified due to the pumping
power may be expressed in a simple analytical form. The numerical data of laser
threshold as a function of the wavelength and the examples of gain bandwidth
determination for several widespread Raman fibers have been presented.
|
| first_indexed | 2025-12-07T18:18:25Z |
| format | Article |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 4. P. 360-363.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
360
PACS 42.65.Yj, 42.81.-i
Raman threshold and optical gain bandwidth in silica fibers
G.S. Felinskyi1, P.A. Korotkov2
Taras Shevchenko Kyiv National University, 2, Academician Glushkov prospect, 03022 Kyiv, Ukraine,
Phone: +38-044-526-0570, fax: +38-044-526-1073,
E-mail:1felinskyi@yahoo.com ,2pak@mail.univ.kiev.ua
Abstract. Nonlinearity of the stimulated Raman scattering (SRS) process in single-mode
fibers is the creation basis of the new class of modern photonic devices such as fiber
Raman lasers and fiber Raman amplifiers. The quantitative analysis of the gain start
conditions and the Raman laser threshold in the single mode fibers from the viewpoint of
the strong gain description of active laser materials have been made in this work. It has
been shown that the absolute transparency regime for optical transmission in fibers and
Raman laser threshold for a monochrome signal wave can be directly obtained from the
standard coupled equations using only fundamental fiber parameters. Limiting condition
when material of fiber core starts transformation from the natural state with attenuation
of the Stokes wave to the state in which the Stokes wave is amplified due to the pumping
power may be expressed in a simple analytical form. The numerical data of laser
threshold as a function of the wavelength and the examples of gain bandwidth
determination for several widespread Raman fibers have been presented.
Keywords: optical fiber communication, fiber Raman laser, fiber Raman amplifier.
Manuscript received 23.09.08; accepted for publication 20.10.08; published online 11.11.08.
1. Introduction
The light amplification arising at stimulated Raman
scattering (SRS) is widely applied to development of
such photonic devices as fiber Raman lasers (FRL) [1]
and fiber Raman amplifiers (FRA) [2]. SRS is nonlinear
optical process and amplification of optical radiation
results from coherent accumulation of Stokes wave
intensity and it has strongly pronounced threshold
character. The Raman gain threshold is defined doubly:
first, as equality between the generated power of Stokes
noise and pumping power at the fiber output [3] or
second, as a laser threshold for the monochromatic
wave, when fiber losses are fully compensated due to the
Raman gain in single-mode fiber [4]. We will use the
laser threshold definition for the analysis and
quantitative calculations of occurrence conditions for the
full transparency regime for optical signal transmission
and the generation mode of coherent light in several
widely used single-mode fibers in this work.
2. Modeling basis
Initial growth of the Stokes wave is defined by the
pumping power, and it is described by the Raman gain
coefficient gR. The interaction between pumping and
Stokes waves should be considered for calculation of the
Raman gain threshold. In the CW case, interaction of
these propagated waves in the same direction is
described by the following system of two coupled
equations:
( ) ( ) ( ) ( ) ( )ωα−ωω=
ω ,,)(g,
R zIzzIzI
dz
zdI
sssp
s , (1)
( ) ( ) ( ) ( ) ( )ωα−ωω
ω
ω
= ,,)(gR zIzzIzI
dz
zdI
ppsp
s
pp , (2)
where the absorption coefficients αs and αр account for the
fiber losses at the Stokes and pumping frequencies,
accordingly, Is is the Stokes intensity, Ip is the pumping
intensity. It should be noted that within the transparency
windows of fiber αs ≈ αр = α, and attenuations α
practically do not change within the whole band of Stokes
shifted components of ~1000 cm–1. For the transparency
window near to 1.55 µm, this band corresponds to the
range of wavelengths approximately 100 nm, where
attenuation α does not depend on the frequency and has a
constant value in the diapason from 0.2 up to 1.0 dB/km,
depending on the type of silica fiber.
Besides, it is considered that in Eqs. (1) and (2) the
pumping is provided with a monochromatic wave
possessing so narrow generated line that its spectral
width can be neglected. Alternatively, the Stokes wave
amplification gR(ω) takes place in a sufficiently wide
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 4. P. 360-363.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
361
bandwidth of optical frequencies. Accordingly, the
Stokes wave intensity is the function not only of the
variable z, but also ω as a parameter. The Raman gain
coefficient is coupled to the cross-section of spontaneous
Raman scattering which is experimentally measured
size. It is possible to directly check up that the laser
threshold is not only naturally determined using the
standard coupled equations (1) and (2) for the SRS
process, but also its frequency dependence can be
obtained in the quantitative form being based only on
fundamental material parameters of the fiber, that is,
gR(ω) and α(ω).
Really, the differential equation (1) can have a
special point in its right part, if the pumping power will
change within the range wide enough. Therefore three
cases are possible:
(i) if dIs /dz < 0, then there is attenuation of the
Stokes wave;
(ii) if dIs /dz > 0, then there is amplification of the
Stokes wave;
(iii) if dIs /dz = 0, then there is a special point.
The case (i) dIs /dz < 0 takes place when pumping is
absent or at the low pumping power, and it corresponds
to attenuation of a Stokes wave during distribution
caused by its own losses in the fiber. Raman
amplification (ii) of the Stokes wave is described by the
product gRIp, and it arises with growth of the pumping
intensity Ip, when its absolute value starts to exceed the
own losses α. In this case, the fiber is transformed to the
active gain media as the condition dIs/dz > 0 corresponds
to some increase of the running Stokes wave in the
propagation process along the fiber. In the intermediate
case (iii) dIs /dz = 0, there comes an absolute trans-
parency regime for Stokes wave propagation in the fiber
as the Stokes intensity remains constant along fiber
length because of full compensation of fiber losses.
The physical sense of the absolute transparency
condition for a fiber closely corresponds to a laser
threshold definition in the SRS process. As the pumping
power Pp(ω) can be expressed using the pumping
intensity Ip(ω) and the fiber effective area Aeff, the
equation dIs /dz = 0 together with the equation (1) results
in the following quantitative form:
)(gR
effth
ω
α
=
A
P s
p
(3)
for the limiting condition when the fiber core material
starts its transformation from a natural state with
dumping the Stokes wave to the state with Stokes wave
amplification, when applying the pumping power. In
contrast to the experimental threshold [5], the laser
threshold (3) is defined using only material parameters
of the fiber, and it does not depend on experimental
arrangement, in particular, it does not depend on the
fiber length. Often, as the th
pP value is chosen, its
minimum takes place at maxRmaxR )( gg =ω . Convenience
of the given definition of the gain threshold will consist
in the following. We shall assume that the pumping
power value Pp is known to us in some point z of the
fiber as a result of measurements or calculation. Then,
using the known constant α and the determined function
gR(ω) one can directly check the inequality th)( pp PP <> .
If th
pp PP > , then not only set of frequencies satisfying
the full transparency condition of the fiber is defined, but
also the amplification (generation) band located between
the pair of adjacent frequencies can be easily calculated.
Specific examples of this modeling for the several
widespread fibers are presented in the following section.
Thus, it is possible to directly calculate the Raman
laser threshold as a function of frequency (or wave-
length) in the Stokes shift range for any wavelength of a
pumping source using (3), if the Raman gain profile
gR(ω) is perfectly obtained. Sometimes, the gain profile
gR(ω) is described using the simplified Lorentz lineform
approximation. However, real fibers have so complex
structure of amplification that satisfactory performance
of gR(ω) function needs the special modeling. The exact
enough model of multimode decomposition of the
Raman spectrum on Gaussian type components has been
developed by us recently [7].
Our model analysis of the Raman spectrum with
Gaussian profiles is based on the following expression
∑
= ⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
Γ
ω−ω
−ω
mN
i i
iv
iAg
1
2
2
,
R
)(
exp~)( , (4)
where Nm is the number of modes used for decom-
position and can be chosen in accord with the spectral
range (typically, Nm lies within the range of 10 to 13),
ωv,i is the central frequency of the ith Gaussian profile,
parameter ( ) iii FWHM6.02ln2FWHM ⋅≈=Γ , where
FWHMi – full width at half maximum parameter of the
ith Gaussian profile that is usually used in spectroscopy.
Amplitudes Ai together with ωv,i and Γi we use as
parameters for a nonlinear fitting procedure.
The result of Raman gain profile approximation is
the individual set of 3Nm numerical parameters for each
fiber [7], which gives the performance gR(ω) as the sum
of exponents in (4). Exact approximation allows to
essentially simplify the quantitative determination
procedure of the pumping power that causes the full
transparency regime for wave propagation in a specific
fiber type.
3. Modeling results and discussion
Four types of silica fibers widely applied in optical
communication for creation FRA and FRL were used for
modeling [8]. Experimental gain profiles gR(ω) and the
maximal values of the Raman gain coefficients gR max
were perfectly measured earlier and taken from [6]:
gR max = 0.4 (W⋅km)–1 for standard silica fiber,
gR max = 0.71 (W⋅km)–1 for TrueWave RSTM fiber type,
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 4. P. 360-363.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
362
Wavelength, µm
1.45 1.50 1.55 1.60
(a) Pure Silica Fiber
20
15
10
25
30
0.3 dB/km
1.45 1.50 1.55 1.60
(b) True Wave RSTM
1.45 1.50 1.55 1.60
(c) DCF Fiber
100
1000
10
0.5
0.2 dB/km 3.8 THz
6.7 THz
0.3 dB/km
(Cabling penalty)
7.3 THz
0.2 dB/km
10.2 THz
17.6 THz
0.2 dB/km
0.3
Pp, dBm Pp, mW
200
Fig. 1. Raman gain threshold (λp = 1.45 nm) as a function of the wavelength in single-mode fibers: (a) – pure silica fiber; (b) –
True Wave RSTM; (c) – dispersion compensated fiber (DCF). Every curve is the set of points of fiber full transparency. Gain
bandwidth is shown for all fiber types at the probe pumping power of 200 mW.
gR max = 3.1 (W⋅km)–1 for dispersion compensated fiber
(DCF), and
gR max = 6.3 (W⋅km)–1 for the special Raman fiber.
First three fiber types have received wide
application in long distant communication links for
optical signal transmission, and the fourth fiber type is
mainly used in FRL. Pumping powers for Raman
threshold causes the full fiber transparency as a function
of the wavelength are shown in Fig. 1 for three types of
communication fibers.
We used the pumping source with λp = 1.45 µm
supposed for definite calculation. Then the full
transparency mode in the pure silica fiber (Fig. 1a) starts
at the wavelength of 1.55 µm when the pumping power
achieves the value equal to 20.7 dBm (117.5 mW).
These values can be simply obtained graphically as
follows. The horizontal line (marker) in Fig. 1
corresponds to the certain pumping power level of Pp,
the latter moves from below upwards and displays how
the pumping power grows. In the case of standard silica
fiber (Fig. 1a) when the pumping power reaches
117.5 mW, the marker line has one common point
(touch) with the full transparency curve for this fiber.
The cross point with abscissa corresponds to the
wavelength 1.55 µm. If the pumping power grows, then
the marker line will move upwards. Next, it is formed at
least two crossing points of marker with the full
transparency curve. The cross point with abscissa for
this pumping power level corresponds to the wavelength
of the full transparency when both absorption and
amplification of a Stokes wave are equal to zero in
accuracy for a studied fiber. The interval between these
wavelengths of full transparency actually corresponds to
the amplification bandwidth, as for every wavelength
from this interval Raman gain exceeds own losses.
Alternatively, outside the specified interval the Raman
gain appears to be insufficient for full compensation of
own losses, and signals with these frequencies will
decay when propagating in the fiber.
In particular, the amplification band is equal to
6.7 THz (from 1513 up to 1566 nm) in a standard silica
fiber at the pumping power of 200 mW and the fiber
losses α = 0.2 dB/km (Fig. 1a). The definition influence
of the own losses on the Raman gain band of fibers is also
enough simple. If the standard silica fiber will have losses
of 0.3 dB/km, then the gain band for this fiber is
essentially narrowed almost by 2 times up to 3.8 THz
(from 1533 up to 1563 nm). The curve of the full trans-
parency for this fiber is shown by a dotted line in Fig. 1a.
The amplification bands for both TrueWave RSTM
fiber and DCF type used for communication are
determined by us similarly between crossing points of
the full transparency curve with the marker level of the
pumping power, and results are shown in Figs 1b-c,
accordingly. The pumping power was considered equal
to 200 mW at all calculations for comparison.
The own losses α normally do not exceed
0.2 dB/km for TrueWave RSTM fiber type. The level of
0.3 dB/km shown in Fig. 1b can be considered as the top
limit allowing to take into account additional losses in a
cable (microbends, pressure, etc.) laid in real field
conditions. In this case, the gain band of 10.2 THz for
α = 0.2 dB/km is reduced down to 7.3 THz, but remains
essentially more wide as compared to the amplification
band in the pure silica fiber at the same pumping power.
The special fiber to dispersion compensation (DCF)
is most often applied for simultaneous Raman
amplification of signals, as it has the greatest coefficient
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 4. P. 360-363.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
363
gR max among the considered communication fibers. As a
result, the amplification band in this fiber exceeds
17 THz even if the fiber losses are equal to 0.5 dB/km
(see Fig. 1c). It should be noted that is its value almost
2 times larger than the total bandwidth of C+L
telecommunication windows. Therefore, it is possible to
use considerably smaller pumping powers for effective
Raman amplification in this fiber, because of the full
transparency in this fiber is possible to start since
20 mW of the pumping power.
In contrast to the considered communication fibers,
the special Raman fiber has gR max = 6.3 (W⋅km)–1, but it
is mainly used for FRL fabrication. The matter is that the
essential increase in Raman amplification of this fiber is
achieved by an increased doping concentration of fiber
core with GeO2 molecules (usually up to ~20 %) during
manufacturing this specialized Raman fiber. Unfortu-
nately, this process is accompanied by appreciable
increase of the own losses of the fiber that do not
manage to be lowered less than down to the values α ~
0.3-1.0 dB/km. Thus, the Raman laser thresholds
(λp = 1.45 µm) as a function of the wavelength for this
special Raman fiber are submitted in Fig. 2 with various
values of their own losses that change within the range
from 0.2 up to 1.0 dB/km. If the pumping power lies
below the level of the laser threshold, which is located in
the area under the curve in Fig. 2, Stokes waves possess
attenuation, and Raman amplification takes place in the
area above curves.
Naturally, the threshold power for a monochromatic
Stokes signal at λs = 1.55 µm will increase approximately
from 9 up to 40 mW when the own fiber losses are
increased from 0.2 up to 1.0 dB/km. Nevertheless, it is
obvious from Fig. 2 that for rather small powers of
pumping (Pp = 100 mW) in the Raman fiber with losses
α = 0.5 dB/km, the laser generation threshold begins at
the wavelength of 1466 nm and is ended at the
wavelength of 1613 nm. The FRL retuning band
potentially exceeds 140 nm in this case and covers both
telecommunication windows. It is possible to expand the
retuning bandwidth of the laser even more, when the
pumping power is increased or the own losses of the
Raman fiber are decreased. The central wavelength inside
this band of optical frequencies may be changed only by
variation of the pumping wavelength, but not changing the
active Raman fiber parameters.
4. Conclusion
The calculation technique to determine absolute values of
the threshold pumping power that causes the full
transparency conditions and the Raman amplification
band in an arbitrary fiber were developed in this work for
the set wavelength and power of a pumping source. The
method is based only on frequency dependence of key
fiber parameters such as Raman gain coefficient gR(ω)
and the fiber attenuation parameter α(ω). Quantitative
ratings for the full optical transparency conditions at
Raman amplification are presented for silica fibers widely
used in optical communication. Modeling results on
Raman gain bands above 10 THz and nominal pumping
powers are given for these fibers. It is shown that the laser
threshold for a monochromatic Stokes signal will be
observed irrespective of real fiber losses in a sufficiently
wide spectral range, if power of pumping is raised up to
several hundred milliwatts. In this case, laser generation
can be received in the range approximately from 1.5 up to
1.6 µm with the pumping wavelength λp = 1.45 µm that
corresponds to a full width of the maximal transparency
window in silica fibers.
References
1. E.M. Dianov, A.M. Prokhorov, Medium-power CW
Raman fiber lasers // IEEE J. Sel. Top. Quantum
Electron. 6(6), p. 1022-1028 (2000).
2. M.N. Islam, Raman amplifiers for telecommu-
nications // IEEE J. Sel. Top. Quantum. Electron.
8(3), p. 548-559 (2002).
3. R.H. Stolen, C. Lee, and R.K. Jain, Development of
the stimulated Raman spectrum in single-mode
silica fibres // J. Opt. Soc. Amer. B 1, p. 652 (1984).
4. P.A. Korotkov, G.S. Felinskyi, Fiber Raman CW
lasers // Rev. Ukr. J. Phys. 3(2), p. 126-150 (2006).
5. G.P. Agrawal, Nonlinear Fiber Optics, Second ed.
Academic., San Diego, CA, 1995.
6. K. Rottwitt, J. Bromage, A.J. Stentz, L. Leng, M.E.
Lines, and H. Smith, Scaling of the Raman gain
coefficient: applications to germanosilicate fibres //
J. Lightwave Techn. 21(7), p. 1652-1662 (2003).
7. G.S. Felinskyi, Spectroscopic multiple-vibrational-
modelling of Raman gain for FRA design // Proc.
SPIE/Ukraine 6(1-6), p. 418-426 (2006).
8. G.S. Felinskyi, P.A. Korotkov, Full transparency
regime for optical transmission and lasing threshold
in silica fibers due to nonlinear Raman interaction //
Proc. 9th Intern. Conf. on Laser and Fiber-Optical
Networks Modeling (LFNM 2008), Oct. 2-4,
Alushta, Crimea, Ukraine, p. 79-81 (2008).
Raman Fiber
Wavelength, µm
1.45 1.50 1.55 1.60
1000
100
10
30
25
20
15
10
5
147 nm
0.2 dB/km
0.3
0.5
0.7
1.0
Pp, dBm Pp, mW
Fig. 2. Lasing threshold in a Raman fiber.
|
| id | nasplib_isofts_kiev_ua-123456789-119070 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2025-12-07T18:18:25Z |
| publishDate | 2008 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Felinskyi, G.S. Korotkov, P.A. 2017-06-03T05:03:05Z 2017-06-03T05:03:05Z 2008 Raman threshold and optical gain bandwidth in silica fibers / G.S.Felinskyi, P.A.Korotkov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 4. — С. 360-363. — Бібліогр.: 8 назв. — англ. 1560-8034 PACS 42.65.Yj, 42.81.-i https://nasplib.isofts.kiev.ua/handle/123456789/119070 Nonlinearity of the stimulated Raman scattering (SRS) process in single-mode
 fibers is the creation basis of the new class of modern photonic devices such as fiber
 Raman lasers and fiber Raman amplifiers. The quantitative analysis of the gain start
 conditions and the Raman laser threshold in the single mode fibers from the viewpoint of
 the strong gain description of active laser materials have been made in this work. It has
 been shown that the absolute transparency regime for optical transmission in fibers and
 Raman laser threshold for a monochrome signal wave can be directly obtained from the
 standard coupled equations using only fundamental fiber parameters. Limiting condition
 when material of fiber core starts transformation from the natural state with attenuation
 of the Stokes wave to the state in which the Stokes wave is amplified due to the pumping
 power may be expressed in a simple analytical form. The numerical data of laser
 threshold as a function of the wavelength and the examples of gain bandwidth
 determination for several widespread Raman fibers have been presented. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Raman threshold and optical gain bandwidth in silica fibers Article published earlier |
| spellingShingle | Raman threshold and optical gain bandwidth in silica fibers Felinskyi, G.S. Korotkov, P.A. |
| title | Raman threshold and optical gain bandwidth in silica fibers |
| title_full | Raman threshold and optical gain bandwidth in silica fibers |
| title_fullStr | Raman threshold and optical gain bandwidth in silica fibers |
| title_full_unstemmed | Raman threshold and optical gain bandwidth in silica fibers |
| title_short | Raman threshold and optical gain bandwidth in silica fibers |
| title_sort | raman threshold and optical gain bandwidth in silica fibers |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/119070 |
| work_keys_str_mv | AT felinskyigs ramanthresholdandopticalgainbandwidthinsilicafibers AT korotkovpa ramanthresholdandopticalgainbandwidthinsilicafibers |