Experimental and theoretical study of stimulated Raman scattering indicatrix asymmetry
The paper provides experimental and theoretical results of stimulated Raman scattering Stokes component indicatrix asymmetry study. Theoretical results demonstrate that asymmetry is caused by influence of Stokes/anti-Stokes parametric processes. Stokes/anti-Stokes parametric process provides addi...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2012
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| Цитувати: | Experimental and theoretical study of stimulated Raman scattering indicatrix asymmetry / M. V. Dmitriev, O. Iu. Isaienko, А. І. Ivanisik, P. A. Korotkov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2012. — Т. 15, № 1. — С. 44-47. — Бібліогр.: 9 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1182562025-06-03T16:28:46Z Experimental and theoretical study of stimulated Raman scattering indicatrix asymmetry Dmitriev, M.V. Isaienko, O.Iu. Ivanisik, А.І. Korotkov, P.A. The paper provides experimental and theoretical results of stimulated Raman scattering Stokes component indicatrix asymmetry study. Theoretical results demonstrate that asymmetry is caused by influence of Stokes/anti-Stokes parametric processes. Stokes/anti-Stokes parametric process provides additional photons to the forward Stokes component. This excess of photons compared to a backward Stokes component increases due to combinational mechanism of stimulated scattering during further propagation of waves along the medium. Thus, under competition of forward and backward Stokes components generation, the process of forward stimulated Raman scattering takes significant advantage. Obtained in this paper is satisfactory matching between theoretical calculations and experimental results for benzene under excitation by laser pulses with the duration 25 ns and wavelength 694.3 nm. 2012 Article Experimental and theoretical study of stimulated Raman scattering indicatrix asymmetry / M. V. Dmitriev, O. Iu. Isaienko, А. І. Ivanisik, P. A. Korotkov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2012. — Т. 15, № 1. — С. 44-47. — Бібліогр.: 9 назв. — англ. 1560-8034 PACS 42.65.Dr https://nasplib.isofts.kiev.ua/handle/123456789/118256 en Semiconductor Physics Quantum Electronics & Optoelectronics application/pdf Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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English |
| description |
The paper provides experimental and theoretical results of stimulated Raman
scattering Stokes component indicatrix asymmetry study. Theoretical results demonstrate
that asymmetry is caused by influence of Stokes/anti-Stokes parametric processes.
Stokes/anti-Stokes parametric process provides additional photons to the forward Stokes
component. This excess of photons compared to a backward Stokes component increases
due to combinational mechanism of stimulated scattering during further propagation of
waves along the medium. Thus, under competition of forward and backward Stokes
components generation, the process of forward stimulated Raman scattering takes
significant advantage. Obtained in this paper is satisfactory matching between theoretical
calculations and experimental results for benzene under excitation by laser pulses with
the duration 25 ns and wavelength 694.3 nm. |
| format |
Article |
| author |
Dmitriev, M.V. Isaienko, O.Iu. Ivanisik, А.І. Korotkov, P.A. |
| spellingShingle |
Dmitriev, M.V. Isaienko, O.Iu. Ivanisik, А.І. Korotkov, P.A. Experimental and theoretical study of stimulated Raman scattering indicatrix asymmetry Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Dmitriev, M.V. Isaienko, O.Iu. Ivanisik, А.І. Korotkov, P.A. |
| author_sort |
Dmitriev, M.V. |
| title |
Experimental and theoretical study of stimulated Raman scattering indicatrix asymmetry |
| title_short |
Experimental and theoretical study of stimulated Raman scattering indicatrix asymmetry |
| title_full |
Experimental and theoretical study of stimulated Raman scattering indicatrix asymmetry |
| title_fullStr |
Experimental and theoretical study of stimulated Raman scattering indicatrix asymmetry |
| title_full_unstemmed |
Experimental and theoretical study of stimulated Raman scattering indicatrix asymmetry |
| title_sort |
experimental and theoretical study of stimulated raman scattering indicatrix asymmetry |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2012 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/118256 |
| citation_txt |
Experimental and theoretical study of stimulated
Raman scattering indicatrix asymmetry / M. V. Dmitriev, O. Iu. Isaienko, А. І. Ivanisik, P. A. Korotkov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2012. — Т. 15, № 1. — С. 44-47. — Бібліогр.: 9 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT dmitrievmv experimentalandtheoreticalstudyofstimulatedramanscatteringindicatrixasymmetry AT isaienkooiu experimentalandtheoreticalstudyofstimulatedramanscatteringindicatrixasymmetry AT ivanisikaí experimentalandtheoreticalstudyofstimulatedramanscatteringindicatrixasymmetry AT korotkovpa experimentalandtheoreticalstudyofstimulatedramanscatteringindicatrixasymmetry |
| first_indexed |
2025-11-26T09:52:26Z |
| last_indexed |
2025-11-26T09:52:26Z |
| _version_ |
1849846146392915968 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 1. P. 44-47.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
44
PACS 42.65.Dr
Experimental and theoretical study of stimulated
Raman scattering indicatrix asymmetry
M.V. Dmitriev, O.Iu. Isaienko, А.І. Ivanisik, P.A. Korotkov
Taras Shevchenko Kyiv National University
4g, Academician Glushkov Avenue, 03127 Kyiv, Ukraine
Phone: +380-44-526-0570; e-mail: aivan@univ.kiev.ua
Abstract. The paper provides experimental and theoretical results of stimulated Raman
scattering Stokes component indicatrix asymmetry study. Theoretical results demonstrate
that asymmetry is caused by influence of Stokes/anti-Stokes parametric processes.
Stokes/anti-Stokes parametric process provides additional photons to the forward Stokes
component. This excess of photons compared to a backward Stokes component increases
due to combinational mechanism of stimulated scattering during further propagation of
waves along the medium. Thus, under competition of forward and backward Stokes
components generation, the process of forward stimulated Raman scattering takes
significant advantage. Obtained in this paper is satisfactory matching between theoretical
calculations and experimental results for benzene under excitation by laser pulses with
the duration 25 ns and wavelength 694.3 nm.
Keywords: stimulated Raman scattering, parametric process, indicatrix.
Manuscript received 30.11.11; revised version received 29.12.11; accepted for
publication 26.01.12; published online 29.02.12.
1. Introduction
According to Placzek’s theory [1], the cross-section of
Raman scattering that propagates along the exciting
beam is the same in both forward and backward
directions. However, experimental observations of
spontaneous scattering sometimes show slight
asymmetry [2]. Furthermore, in case of stimulated
Raman scattering (SRS) Stokes component this
asymmetry is essential in almost all experimental
conditions. Intensity of the forward SRS first Stokes
component is usually much higher than the intensity of
the backward scattering, which propagates in the
opposite direction with respect to the exciting laser
beam. However, the nature of SRS indicatrix asymmetry
is still controversial.
Many physical mechanisms explaining the SRS
indicatrix asymmetry have been proposed. One of the
earliest views was based on the fact that damping of
coherent molecular vibrations wave generated by forward
scattering is less than damping of the same wave
generated by backward scattering, because its wave vector
in the first case is much higher. Due to this difference in
damping, scattering mostly propagates in the forward
direction [3]. But this view didn’t get any further
evidences. A similar situation has developed with the
following statement. Under the forward scattering, field
transfers less momentum to molecules than that in case of
backward scattering, therefore such different recoil effects
substantially amplify the forward scattering [4].
Other views are more fundamental. In particular,
attention has been drawn to the fact that Raman
amplification in the forward direction is inversely
proportional to the width of the spontaneous Raman
scattering line. Raman amplification in the backward
direction is less intensive, because it is inversely
proportional to the total width of the spontaneous
scattering line and the width of the exciting radiation
spectrum [5]. Obviously, this mechanism is significant
only in those rare cases where the width of exciting
radiation spectrum is comparable to the width of the
SRS line.
For ultra-short pulses, the length of the forward
scattering path is limited by the SRS-active medium
length, and the length of backward scattering is limited
by the pulse length. Under these conditions forward
scattering dominates [5].
Due to the change of refractive index during
medium excitation pulse, phase modulation of
interacting waves occurs, primarily improving the
conditions for backward scattering [6].
Scattering occurs mainly in the focal region
(focusing or self-focusing), and rest of the medium acts
as an amplifier. If the focal region location does not
coincide with the medium center, then the scattering will
have a corresponding asymmetry [5].
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 1. P. 44-47.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
45
There are acceptable and proven views that
describe backward asymmetry. For example,
amplification of backward SRS pulses occurs in the field
of non-depleted exciting radiation thus leading to
dominating backward scattering [7].
There is another approach that seems to be logical,
but controversal. Due to interaction of exciting radiation
and the forward Stokes wave by parametric mechanism,
anti-Stokes component is generated. The energy outflow
restrains forward Stokes wave amplification. In case of
perfect phase matching between Stokes and anti-Stokes
waves, none of them is able to exponentially amplify,
and so parametric suppression of forward scattering
takes place. As for the backward scattering, matching
conditions for parametric process are not met in the
described environment. As a result, dominating forward
Stokes wave is generated [5, 8].
The aim of this work is experimental and
theoretical study of Stokes/anti-Stokes parametric
process influence on the SRS Stokes component
indicatrix asymmetry. It is interesting, because forward
and backward SRS are widely used in fiber Raman
amplifiers [9].
2. Experimental study
Our experiment consisted of simultaneous energy
registration in forward and backward SRS pulses. The
experimental setup has been presented in Fig. 1.
Al2O3:Cr3+ crystal laser worked on one longitudinal
mode, generating radiation pulses with duration 25 ns,
wavelength 694.3 nm, spectral width 0.01 cm1, energy
0.6 J, divergence 5′ (arcmin). Laser radiation was
damped using calibrating light filters and collimated to
the center of the cuvette (length L = 1 m) using the lens
with the focal length f = 1 m, cuvette was benzene-filled
(active molecular vibrations are at 992 cm1). The light,
scattered in forward and backward directions, passed
through blue-green filters BGF20 that completely absorb
laser radiation, and directed to calorimetric energy
meters of IMO2N type with sensitivity 0.1 mJ.
Particular attention was paid to defining the relevant
sensitivities that both energy meters provide on forward
and backward scattering channels. An optical scheme
based on equal division of laser beam was constructed to
achieve this goal.
f =1m
BGF20BGF20
Laser
С6Н6IMO2N IMO2N
50%
Fig. 1. The experimental setup.
To avoid the influence of parasitic link between the
cuvette and laser caused by stimulated Brillouin-
Mandelstam scattering (SBMS), dual optical distance
between the lens focal point in the cuvette and laser was
chosen at 4.5 m, which corresponds to the timed
feedback delay 15 ns. In addition, the 50% mirror was
placed on the path between laser and the cuvette, which
further lowered efficiency of “SBMS mirror” by 4 times,
even without taking into account the light attenuation
filters (that were used at low excitation levels) and losses
on other optical elements.
Non-parallelism of cuvette windows between each
other and their non-perpendicularity to laser beam
exceeded 5°. Other optical elements deviated from the
normal at the angle 1°.
The peak intensity of radiation was calculated at
the cuvette inlet for similar to Gaussian laser pulses with
the maximum energy EL0 = 310 mJ, duration 25 ns,
average beam radius 3.4 mm at 1/е level, and the
obtained result was IL0 = 3.91011 W/m2.
Fig. 2 shows measurement results for calculated
logarithm of E↑S (forward Stokes component energy) to
E↓S (backward Stokes component energy) ratio with
respect to exciting radiation energy EL0. Energy values
are given considering losses in the cuvette windows and
all optical elements.
For the maximum energy EL0 = 310 mJ, the
average values were E↑S = 220 mJ, E↓S = 1.1 mJ, and
Lg [E↑S / E↓S] 2.3. Thus, the energy asymmetry
coefficient reached k↑↓E = E↑S / E↓S 200. With EL0
decrease the forward SRS energy decreased faster. For
energy EL0 = 70 mJ, average values of E↑S and E↓S were
0.25 mJ (k↑↓E 1).
2.0
2.5
1.5
1.0
0.5
0
50 100 150 200 250 300 3500
EL0, mJ
Lg[E↑S/E↓S]
Fig. 2. Experimental dependence of E↑S to E↓S ratio on the
laser pulses energy EL0.
3. Theoretical study
It was supposed that the laser beam, Stokes component,
and anti-Stokes component propagate along z axis, and
phase matching conditions are achieved, and that only
the Stokes component propagates in the backward
direction, since the phase matching of anti-Stokes
component is impossible. We’ve numerically solved the
coupled system of equations for the electric field
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 1. P. 44-47.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
46
amplitudes EL of laser wave and fields ES↑, ES↓, EA of
forward Stokes, backward Stokes, and anti-Stokes
components, accordingly:
2 2' '
2''
2 2''
2 2' ''
2'
2 ;
;
;
.
L
L L L LS S
L L A L L AS
S
S L S A LS
A
A A L A LS
S
S LS
dE
g E E g E E
dz
g E E E g E E
dE
g E E g E E
dz
dE
g E E g E E
dz
dE
g E E
dz
(1)
If wave frequencies are distant from electronic
resonances, refractive indices at laser radiation
frequency L , Stokes S , and anti-Stokes A
frequencies are almost equal. By neglecting the non-
resonant cubic susceptibility factors in (1), the following
equations are valid for g:
/ / / ,
, , .
S S L L A A
S S S L L L A A
g g g
g g g g g g g g
(2)
For benzene, Sg 2.79·10-14 m/V2 [5].
The values ES↑ (z = 0) = ES↓ (z = L) = 2·104 V/m
were used for forward Stokes component field ES↑ (z = 0)
at the cuvette inlet and backward Stokes component field
ES↓ (z = L) at the cuvette outlet, thus providing initial
symmetry and efficient generation of forward Stokes
components, which are comparable to experimental
results at the maximum calculated field of laser radiation
EL (z = 0) = 1.4·107 V/m. The anti-Stokes field EA (z = 0)
was considered to be zero. The medium length L was
1 m.
0.2 0.4 0.6 0.8 1
I, W/m2
L, m
0
41011
31011
21011
11011
0
IL
IS
IS
IA
Fig. 3. Radiation intensities in medium considering parametric
process in case of IL0 = 3.91011 W/m2.
The intensity of corresponding components (IL, IS↑,
IS↓, IA) was calculated using the electric field amplitude:
2232
0 mWVW1025.0 EEncI , (3)
where 0 is the dielectric constant. Under the boundary
conditions, it is IS↑(z = 0) = IS↓(z = 0) = 8105 W/m2.
Ignoring the parametric process ASL 2
in (1) leads to symmetric indicatrix. If parametric
process is considered, the forward Stokes component
reaches a much higher intensity (Fig. 3). The anti-Stokes
component is also observed at the medium output.
Dependence of Stokes component indicatrix
asymmetry coefficient (by intensity) k↑↓I =
IS↓ (z = L) / IS↑ (z = 0) on the output laser radiation
intensity is shown in Fig. 4 in logarithmic scale.
In the given range of laser radiation intensities, k↑↓I
varies from 1 to 49. At IL0 = 3.91011 W/m2 (EL0 =
1.4107 V/m), we obtain k↑↓I = 40 (Lg [k↑↓I] = 1.6).
1
1.2
1.4
1.6
0
3 4 5 6 72
Lg[IS↑/IS↓]
IL0·1011 W/m2
Fig. 4. Theoretical dependence of IS↑ (forward SRS Stokes
component intensity) to I↓ (backward component intensity at
z = 0) ratio on laser intensity IL (z = 0) at L = 1 m.
4. Conclusions
The main result of this research is that the predominance
of the forward SRS over backward scattering can be
caused by the influence of Stokes/anti-Stokes parametric
process. The result presents a contrast to the classical
notions [5] that do not provide sufficient experimental
and theoretical reasoning and, in general, indicates a
reverse asymmetry.
The competition between forward and backward
scattering processes is important. Stokes/anti-Stokes
parametric process provides additional photons to the
forward SRS Stokes component. This excess of photons
compared to a backward Stokes component increases
due to combinational mechanism of stimulated scattering
during further propagation of waves along the medium.
Thus, during competition in generation of forward and
backward Stokes components, the process of forward
SRS takes significant advantage.
The calculated logarithm of the scattering
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 1. P. 44-47.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
47
asymmetry coefficient by intensity in similar experi-
mental conditions reaches the value close to 1.6 at
maximal laser radiation intensities. Experimental values
of the asymmetry coefficient logarithm by energy are
much higher and reach 2.3.
Differences of experimental and theoretical results
might have appeared due to neglection of radiation
intensity change during the laser pulse. However, the
more important is presence of self-phase modulation,
despite the fact that benzene does not reveal distinct self-
focusing properties.
References
1. G. Placzek, Rayleigh Scattering and the Raman
Effect. Moscow-Leningrad, Gostekhizdat, 1935 (in
Russian).
2. I.I. Kondilenko, P.A. Korotkov, On the asymmetry
of the Raman scattering indicatrix // Optika i
Spektroscopiya, 24, p. 466-468 (1968), in Russian.
3. N. Bloembergen and Y.R. Shen, Coupling between
vibrations and light waves in Raman media // Phys.
Rev. Lett. 12(18), p. 504-507 (1964).
4. P.D. Maker and R.W. Terhune, Study of optical
effects due to an induced polarization third order in
electric field strength // Phys. Rev. 137(3A), p. 801-
818 (1965).
5. Y.R. Shen, The Principles of Nonlinear Optics. New
York, Wiley, 1984.
6. V.V. Kuzmin, Disruption of phase matching in
stimulated light scattering // Trudy FIAN, 207, p. 3-
39 (1991), in Russian.
7. А.V. Kaczynski, G.G. Kotaev, I.V. Pilipovich,
Competition between backward and forward SRS
and compression of picosecond pulses //
Kvantovaya Elektronika, 19(6), p. 550-553 (1992),
in Russian.
8. Iu. E. D’yakov, S.Iu. Nikitin, On the interaction and
competition between forward and backward SRS
scattering // Kvantovaya Elektronika, 9(6), p. 1258-
1261 (1982), in Russian.
9. G.S. Felinskiy, P.A. Korotkov, Simulation of
multiwave pumped fiber Raman amplifiers //
Semiconductor Physics, Quantum Electronics &
Optoelectronics 9(3), p. 35-39 (2006).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 1. P. 44-47.
PACS 42.65.Dr
Experimental and theoretical study of stimulated
Raman scattering indicatrix asymmetry
M.V. Dmitriev, O.Iu. Isaienko, А.І. Ivanisik, P.A. Korotkov
Taras Shevchenko Kyiv National University
4g, Academician Glushkov Avenue, 03127 Kyiv, Ukraine
Phone: +380-44-526-0570; e-mail: aivan@univ.kiev.ua
Abstract. The paper provides experimental and theoretical results of stimulated Raman scattering Stokes component indicatrix asymmetry study. Theoretical results demonstrate that asymmetry is caused by influence of Stokes/anti-Stokes parametric processes. Stokes/anti-Stokes parametric process provides additional photons to the forward Stokes component. This excess of photons compared to a backward Stokes component increases due to combinational mechanism of stimulated scattering during further propagation of waves along the medium. Thus, under competition of forward and backward Stokes components generation, the process of forward stimulated Raman scattering takes significant advantage. Obtained in this paper is satisfactory matching between theoretical calculations and experimental results for benzene under excitation by laser pulses with the duration 25 ns and wavelength 694.3 nm.
Keywords: stimulated Raman scattering, parametric process, indicatrix.
Manuscript received 30.11.11; revised version received 29.12.11; accepted for publication 26.01.12; published online 29.02.12.
1. Introduction
According to Placzek’s theory [1], the cross-section of Raman scattering that propagates along the exciting beam is the same in both forward and backward directions. However, experimental observations of spontaneous scattering sometimes show slight asymmetry [2]. Furthermore, in case of stimulated Raman scattering (SRS) Stokes component this asymmetry is essential in almost all experimental conditions. Intensity of the forward SRS first Stokes component is usually much higher than the intensity of the backward scattering, which propagates in the opposite direction with respect to the exciting laser beam. However, the nature of SRS indicatrix asymmetry is still controversial.
Many physical mechanisms explaining the SRS indicatrix asymmetry have been proposed. One of the earliest views was based on the fact that damping of coherent molecular vibrations wave generated by forward scattering is less than damping of the same wave generated by backward scattering, because its wave vector in the first case is much higher. Due to this difference in damping, scattering mostly propagates in the forward direction [3]. But this view didn’t get any further evidences. A similar situation has developed with the following statement. Under the forward scattering, field transfers less momentum to molecules than that in case of backward scattering, therefore such different recoil effects substantially amplify the forward scattering [4].
Other views are more fundamental. In particular, attention has been drawn to the fact that Raman amplification in the forward direction is inversely proportional to the width of the spontaneous Raman scattering line. Raman amplification in the backward direction is less intensive, because it is inversely proportional to the total width of the spontaneous scattering line and the width of the exciting radiation spectrum [5]. Obviously, this mechanism is significant only in those rare cases where the width of exciting radiation spectrum is comparable to the width of the SRS line.
For ultra-short pulses, the length of the forward scattering path is limited by the SRS-active medium length, and the length of backward scattering is limited by the pulse length. Under these conditions forward scattering dominates [5].
Due to the change of refractive index during medium excitation pulse, phase modulation of interacting waves occurs, primarily improving the conditions for backward scattering [6].
Scattering occurs mainly in the focal region (focusing or self-focusing), and rest of the medium acts as an amplifier. If the focal region location does not coincide with the medium center, then the scattering will have a corresponding asymmetry [5].
There are acceptable and proven views that describe backward asymmetry. For example, amplification of backward SRS pulses occurs in the field of non-depleted exciting radiation thus leading to dominating backward scattering [7].
There is another approach that seems to be logical, but controversal. Due to interaction of exciting radiation and the forward Stokes wave by parametric mechanism, anti-Stokes component is generated. The energy outflow restrains forward Stokes wave amplification. In case of perfect phase matching between Stokes and anti-Stokes waves, none of them is able to exponentially amplify, and so parametric suppression of forward scattering takes place. As for the backward scattering, matching conditions for parametric process are not met in the described environment. As a result, dominating forward Stokes wave is generated [5, 8].
The aim of this work is experimental and theoretical study of Stokes/anti-Stokes parametric process influence on the SRS Stokes component indicatrix asymmetry. It is interesting, because forward and backward SRS are widely used in fiber Raman amplifiers [9].
2. Experimental study
Our experiment consisted of simultaneous energy registration in forward and backward SRS pulses. The experimental setup has been presented in Fig. 1.
Al2O3:Cr3+ crystal laser worked on one longitudinal mode, generating radiation pulses with duration 25 ns, wavelength 694.3 nm, spectral width (0.01 cm(1, energy (0.6 J, divergence 5′ (arcmin). Laser radiation was damped using calibrating light filters and collimated to the center of the cuvette (length L = 1 m) using the lens with the focal length f = 1 m, cuvette was benzene-filled (active molecular vibrations are at 992 cm(1). The light, scattered in forward and backward directions, passed through blue-green filters BGF20 that completely absorb laser radiation, and directed to calorimetric energy meters of IMO(2N type with sensitivity (0.1 mJ. Particular attention was paid to defining the relevant sensitivities that both energy meters provide on forward and backward scattering channels. An optical scheme based on equal division of laser beam was constructed to achieve this goal.
f =1m
BGF20 BGF20
Laser
С
6
Н
6
IMO2N
IMO2N
50%
Fig. 1. The experimental setup.
To avoid the influence of parasitic link between the cuvette and laser caused by stimulated Brillouin-Mandelstam scattering (SBMS), dual optical distance between the lens focal point in the cuvette and laser was chosen at (4.5 m, which corresponds to the timed feedback delay (15 ns. In addition, the 50% mirror was placed on the path between laser and the cuvette, which further lowered efficiency of “SBMS mirror” by 4 times, even without taking into account the light attenuation filters (that were used at low excitation levels) and losses on other optical elements.
Non-parallelism of cuvette windows between each other and their non-perpendicularity to laser beam exceeded 5°. Other optical elements deviated from the normal at the angle (1°.
The peak intensity of radiation was calculated at the cuvette inlet for similar to Gaussian laser pulses with the maximum energy EL0 = 310 mJ, duration 25 ns, average beam radius 3.4 mm at 1/е level, and the obtained result was IL0 = 3.9(1011 W/m2.
Fig. 2 shows measurement results for calculated logarithm of E↑S (forward Stokes component energy) to E↓S (backward Stokes component energy) ratio with respect to exciting radiation energy EL0. Energy values are given considering losses in the cuvette windows and all optical elements.
For the maximum energy EL0 = 310 mJ, the average values were E↑S = 220 mJ, E↓S = 1.1 mJ, and Lg [E↑S / E↓S] ( 2.3. Thus, the energy asymmetry coefficient reached k↑↓E = E↑S / E↓S ( 200. With EL0 decrease the forward SRS energy decreased faster. For energy EL0 = 70 mJ, average values of E↑S and E↓S were (0.25 mJ (k↑↓E ( 1).
2.0
2.5
1.5
1.0
0.5
0
50
100
150 200
250
300
350
0
E
L0
, mJ
Lg[E
↑S
/E
↓S
]
Fig. 2. Experimental dependence of E↑S to E↓S ratio on the laser pulses energy EL0.
3. Theoretical study
It was supposed that the laser beam, Stokes component, and anti-Stokes component propagate along z axis, and phase matching conditions are achieved, and that only the Stokes component propagates in the backward direction, since the phase matching of anti-Stokes component is impossible. We’ve numerically solved the coupled system of equations for the electric field amplitudes EL of laser wave and fields ES↑, ES↓, EA of forward Stokes, backward Stokes, and anti-Stokes components, accordingly:
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
22
''
2
''
22
''
22
'''
2
'
2;
;
;
.
L
LLLL
SS
LLALLA
S
S
SLSAL
S
A
AALAL
S
S
SL
S
dE
gEEgEE
dz
gEEEgEE
dE
gEEgEE
dz
dE
gEEgEE
dz
dE
gEE
dz
¯
¯
¯
ì
ï
=--
ï
ï
-+
ï
ï
ï
=+
í
ï
ï
=-+
ï
ï
ï
=-
ï
î
(1)
If wave frequencies are distant from electronic resonances, refractive indices at laser radiation frequency
L
w
, Stokes
S
w
, and anti-Stokes
A
w
frequencies are almost equal. By neglecting the non-resonant cubic susceptibility factors in (1), the following equations are valid for g:
///,
,,.
SSLLAA
SSSLLLAA
ggg
gggggggg
w=w=w
¢¢¢¢¢¢¢¢¢
=====
(2)
For benzene,
S
g
=
2.79·10-14 m/V2 [5].
The values ES↑ (z = 0) = ES↓ (z = L) = 2·104 V/m were used for forward Stokes component field ES↑ (z = 0) at the cuvette inlet and backward Stokes component field ES↓ (z = L) at the cuvette outlet, thus providing initial symmetry and efficient generation of forward Stokes components, which are comparable to experimental results at the maximum calculated field of laser radiation EL (z = 0) = 1.4·107 V/m. The anti-Stokes field EA (z = 0) was considered to be zero. The medium length L was 1 m.
0.2 0.4 0.6 0.8 1
I, W/m
2
L, m
0
410
11
310
11
210
11
110
11
0
I
L
I
S
I
S
I
A
Fig. 3. Radiation intensities in medium considering parametric process in case of IL0 = 3.9(1011 W/m2.
The intensity of corresponding components (IL, IS↑, IS↓, IA) was calculated using the electric field amplitude:
[
]
[
]
(
)
2
2
3
2
0
m
W
V
W
10
2
5
.
0
E
E
n
c
I
-
×
»
e
=
,
(3)
where
0
e
is the dielectric constant. Under the boundary conditions, it is IS↑(z = 0) = IS↓(z = 0) = 8(105 W/m2.
Ignoring the parametric process
A
S
L
w
+
w
=
w
h
h
h
2
in (1) leads to symmetric indicatrix. If parametric process is considered, the forward Stokes component reaches a much higher intensity (Fig. 3). The anti-Stokes component is also observed at the medium output.
Dependence of Stokes component indicatrix asymmetry coefficient (by intensity) k↑↓I = IS↓ (z = L) / IS↑ (z = 0) on the output laser radiation intensity is shown in Fig. 4 in logarithmic scale.
In the given range of laser radiation intensities, k↑↓I varies from 1 to 49. At IL0 = 3.9(1011 W/m2 (EL0 = 1.4(107 V/m), we obtain k↑↓I = 40 (Lg [k↑↓I] = 1.6).
1
1.2
1.4
1.6
0
3
4 5 6 7
2
Lg[I
S↑
/I
S↓
]
I
L0
·10
11
W/m
2
Fig. 4. Theoretical dependence of IS↑ (forward SRS Stokes component intensity) to I↓ (backward component intensity at z = 0) ratio on laser intensity IL (z = 0) at L = 1 m.
4. Conclusions
The main result of this research is that the predominance of the forward SRS over backward scattering can be caused by the influence of Stokes/anti-Stokes parametric process. The result presents a contrast to the classical notions [5] that do not provide sufficient experimental and theoretical reasoning and, in general, indicates a reverse asymmetry.
The competition between forward and backward scattering processes is important. Stokes/anti-Stokes parametric process provides additional photons to the forward SRS Stokes component. This excess of photons compared to a backward Stokes component increases due to combinational mechanism of stimulated scattering during further propagation of waves along the medium. Thus, during competition in generation of forward and backward Stokes components, the process of forward SRS takes significant advantage.
The calculated logarithm of the scattering asymmetry coefficient by intensity in similar experi-mental conditions reaches the value close to 1.6 at maximal laser radiation intensities. Experimental values of the asymmetry coefficient logarithm by energy are much higher and reach (2.3.
Differences of experimental and theoretical results might have appeared due to neglection of radiation intensity change during the laser pulse. However, the more important is presence of self-phase modulation, despite the fact that benzene does not reveal distinct self-focusing properties.
References
1. G. Placzek, Rayleigh Scattering and the Raman Effect. Moscow-Leningrad, Gostekhizdat, 1935 (in Russian).
2. I.I. Kondilenko, P.A. Korotkov, On the asymmetry of the Raman scattering indicatrix // Optika i Spektroscopiya, 24, p. 466-468 (1968), in Russian.
3. N. Bloembergen and Y.R. Shen, Coupling between vibrations and light waves in Raman media // Phys. Rev. Lett. 12(18), p. 504-507 (1964).
4. P.D. Maker and R.W. Terhune, Study of optical effects due to an induced polarization third order in electric field strength // Phys. Rev. 137(3A), p. 801-818 (1965).
5. Y.R. Shen, The Principles of Nonlinear Optics. New York, Wiley, 1984.
6. V.V. Kuzmin, Disruption of phase matching in stimulated light scattering // Trudy FIAN, 207, p. 3-39 (1991), in Russian.
7. А.V. Kaczynski, G.G. Kotaev, I.V. Pilipovich, Competition between backward and forward SRS and compression of picosecond pulses // Kvantovaya Elektronika, 19(6), p. 550-553 (1992), in Russian.
8. Iu. E. D’yakov, S.Iu. Nikitin, On the interaction and competition between forward and backward SRS scattering // Kvantovaya Elektronika, 9(6), p. 1258-1261 (1982), in Russian.
9. G.S. Felinskiy, P.A. Korotkov, Simulation of multiwave pumped fiber Raman amplifiers // Semiconductor Physics, Quantum Electronics & Optoelectronics 9(3), p. 35-39 (2006).
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
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_1391932984.doc
0.2
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1
I, W/m2
L, m
0
4(1011
3(1011
2(1011
1(1011
0
IL
IS(
IS(
IA
_1395567995.unknown
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_1391932218.doc
Laser
BGF20
50%
С6Н6
BGF20
IMO(2N
f =1m
IMO(2N
_1391932317.doc
2.0
2.5
1.5
1.0
0.5
0
50
100
150
200
250
300
350
0
EL0, mJ
Lg[E↑S/E↓S]
_1391932828.doc
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1.6
0
3
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6
7
2
Lg[IS↑/IS↓]
IL0·1011 W/m2
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