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Correlations between the intensities of pump, depleted pump and Stokes waves in superbroadband stimulated Raman scattering
s.__
IS April 1996
lliz e.
OPTICS COMMUNICATIONS
__
ELSEVIER
Optics Communications 125 ( 1996) 243-249
Correlations between the intensities of pump, depleted pump and Stokes waves in superbroadband stimulated Raman scattering A.I. Vodchitz, V.P. Kozich, P.A. Apanasevich,
V.A. Orlovich
Received 28 December 1994; revised version received 30 June 1995; accepted 9 October 199.5
Abstract The pair correlations between the intensities of input pump laser radiation with spectral bandwidth of 250 cm- ‘, which has femtosecond and picosecond noise structures, output depleted pump radiation and Stokes light generated through stimulated Raman scattering ( SRS) in compressed hydrogen have been studied experimentally under weak and strong pump depletion. The third order correlation functions were measured by means of time-delayed four-wave mixing in a Kerr-shutter scheme with two noise light beams under investigation. The data obtained show that the Stokes wave is well correlated with the input pump wave up to an energy conversion efficiency of about 30%. The measured functions display the considerable suppression of the femtosecond amplitude fluctuations in the depleted pump beam upon increasing the efficiency of SRS and pump depletion. Such a result shows a possible way for preparing superbroadband light with smooth temporal envelope and predominant phase fluctuations using SRS. The picosecond part of the correlations between the depleted pump and Stokes waves is characterized by the asymmetrical shape that is probably caused by the fact that picosecond peaks in the noise structure of the depleted pump and Stokes waves have opposite temporal profiles.
1. Introduction The statistical properties of the Stokes light and nonlinear interactions in stimulated Raman generation and amplification with broad-bandwidth pump have drawn considerable attention both from the side of investigators of the processes and users of the light generated through stimulated Raman scattering (SRS) [ I-131. The Stokes wave generation is a convenient way to produce a frequency-shifted field which is well correlated with the pump field [l-3]. Such fields can be widely used in transient spectroscopy with incoherent light [9-I I ] and other applications [ 131. Intensity cross-correlation functions in SRS of colored chaotic light without pump depletion have been studied theoretically by Trippenbach and Cao Long Van 1 I 1. 0030.40 18/96/S
12.OO0 I996 Elsevier Science E3.V. All rights
SSD/OO30-JOI 8(95)00714-8
reserved
An experimental and theoretical investigation of the temporal correlations between the intensities of multimode laser radiation and Stokes light in stimulated Raman generation was carried out by Westling and Raymer [ 21. The investigation was also done under the absence of pump depletion and small spectral bandwidth of pump radiation. In this paper we present experimental studies of the temporal correlations between the intensities of a superbroad-bandwidth pump, depleted pump and Stokes beams in pairs at SRS in compressed molecular hydrogen. Input pump broadband radiation was characterized by the presence of two noise structures in the dependence of the instantaneous intensity on time - one with femtosecond correlation time and the other with picosecond correlation time. It allowed to study and compare the transformation of noise properties through
244
A.I. Vodchitz et al. /Optics
Cotntnunications
SRS in these time scales under different levels of pump depletion from weak to strong when the pump to Stokes energy conversion efficiency varied from 3% up to about 30%.
2. Experiment The studies of temporal correlations were carried out on the set-up the scheme of which is shown in Fig. 1. A I5 mJ dye-laser (3) pumped by 50 mJ second harmonic (SH) pulses of a nanosecond Nd:YAG-laser ( I ) with nonselective resonator served as an exciting source for stimulated Raman generation. The g-shaped cavity of the dye laser without any spectral selecting elements consisted of three highly reflective mirrors and an output one with reflection coefficient of 10%. The cavity dye cell with a circulating ethanol solution of Rhodamine 6G was oriented at Brewster’s angle to the pumping SH-beam. Such a scheme of the laser allowed to realize the conditions near to superluminescent lasing with multiple passing the multimode amplitied radiation through the active medium and obtain a powerful output laser beam with a small divergence of 0.8 mrad. The 6 ns (full width at half maximum or FWHM) dye-laser pulse with a spectral bandwidth of
s/j?
1 6
Fig.
I-
!
L
!
9
10
I,
e-9
(1)
0
12
11
SRS in compressed hydrogen (see details in the
Nd:YAG-laser;
2 - KDP-crystal; 3 -broadband
dye laser;
4, 14 - fully reflective mirrors; 5 - dividing mirror: 6, 19, 20 replaceable neutral filters; 7. 9. 25 -focusing with compressed hydrogen; 10 -replaceable able dividing mirror; 12 -constant
lenses; 8 - Raman cell color filter;
I I -replace-
optical delay line; 13. 16, 18,22,
24 - replaceable fully reflective mirrors; IS - introduced opaque shield: I7
about 250 cm ’ (FWHM) had femtosecond and picosecond noise structures. The picosecond structure originated from the intensity fluctuations of the pumping SH-radiation from the multimode YAG:Nd-laser. Dyelaser light centered at a wavelength of 560 nm was shifted to the other spectral region near 730 nm through Stokes vibrational Raman generation in a molecular hydrogen gas compressed to 75 atm. For this purpose the dye-laser beam was divided in proportion of 7:3 and its more intensive part was focused into a 22 cm long hydrogen cell (8). The focal length of the focusing lens (7) was equal to 30 cm. The energy efficiency of the Stokes generation was varied from 3 to about 30% by attenuating the pump beam with neutral filters (6) to observe the effect of Raman gain and pump depletion on the intensities correlations. The output energy of dye laser was sustained at the same level in all measurements to be sure that the light statistical properties would be reproducible. The third order intensity correlations were studied in pairs between the two beams of noise light by means of time-delayed four-wave mixing (TDFWM) in a Kerr-shutter configuration. Because of the degeneracy on the two wave-vector this scheme of TDFWM has a substantial advantage in the use for coherent interactions of noise light, as phase matching is fulfilled here automatically. TDFWM was realized in a I or 3 mm thick plate of glass, a medium with instantaneous cubic nonlinear response. Under these conditions the TDFWM-signal measured as a function of’ the relative time delay Tbetween the two beams under investigation was proportional to the intensity correlation function oftype [9-II]
I
experimental setup for studying intensities correlations in
wperbroadband text ):
I
?‘
8
7
I. An
I
125 (1996) 243-249
variable optical delay line; 21. 23 - polarizers (Glan
prisms): 26 - glass plate; 27 - diaphragm; 28 - analyzer (Clan prism): 29 - photomultiplier: 30 - data acquisition system.
Here IpumpandIpmhcare the instantaneous
intensities of pumping and probing beams participating in the TDFWM-process in the Kerr-shutter scheme and the symbol (. .) means statistical averaging. Under our assumptions (see below and Refs. [9-l 1] ) that noise light is described by a stationary Gaussian random process which is ergodic, the statistical averaging was equivalent to temporal averaging. It significantly simplified the experimental measurements. Using noise radiation flows of input pump, depleted pump and Stokes as such beams with the intensities ofZi,, Iclpand I,,, respectively, we have studied the correlations between the different flows.
A.I. Vodchin et al. / Oprics Comtnunicutions
Experimentally the intensity correlations were studied in the following way. The pumping beam for TDFWM passed through the variable automatically controlled optical delay line ( 17) and a polarizer (21) and then it was focused into the glass plate (26) with a lens (25 ) having a focal length of 15 cm. The probing beam passed through the constant optical delay line ( 12) and a polarizer (23 ). It was also focused into the plate with the same lens. The polarization plane of the probing beam was horizontal and that of the pumping one was oriented at an angle of 45 degrees to the first one. The informational TDFWM-signal passed through an analyzer (28) crossed with the polarization plane of the probing beam and was detected with a photomultiplier (39) and accumulated with a data acquisition system (30). All experimental curves were registered in an automatized regime. The minima1 step of tuning the delay was equal to 28 fs. During the study of the intensity autocorrelation of input pump radiation we used the less intensive part of the output dye laser beam passing through a dividing mirror (5 1 as a pumping beam in the Kerr-shutter scheme. The beam passed through the Raman cell in the &sense of SRS and recollimating lens (9) (focal length of 30 cm) was used as a probing beam. Such a scheme was also used under measurement of the crosscorrelations between the intensities of the input and depleted pump waves and the input pump and Stokes waves. But in this case the depleted pump or Stokes radiation passed through replaceable yellow orred filter ( IO). For studying the intensity autocorrelations of the depleted pump or Stokes beams and crosscorrelations between them an opaque shield ( 15) was introduced into the beam after a mirror ( 14) and suitable replaceable mirrors ( I I ) and ( 16) were used for obtaining pumping and probing beams for the Kerr-shutter scheme. The mirrors ( l3), (l8), (22) and (24) were also replaceable and suitable for studying definite correlations. All the mirrors had broadbanddielectriccoatings with spccilied suitable reflectances in the yellow or red spectral region. For optimizing the intensities of the pumping and probing beams into the glass plate the rcplaccable neutral filters ( 19) and (20) were used. 3. Results and discussion The curve ( a) in Fig. 2 shows the measured intensity correlation function between the input and output pump
I25
(1996) 243-249
Fig. 2. The experimental laser (a) and
ACF (I;,( I) I,,,( I + 7)) of broadband
CCF (If,(r) I,,,,(/+ 7))
between the intensities
dye
of the
input pump and depleted pump beams at pump to Stokes energy conversion
efficiencies
of
IS (b)
and 30%~ ( c 1.
fields below the threshold of SRS, i.e. an autocorrelation function (ACF) of dye-laser radiation. It is seen that there are two features in this function - a picosecond-width “dome” due to the picosecond noise structure of the laser light and an ultrafast coherent spike due to the femtosecond structure [ 9-1 I 1. For the theoretical modeling of the experimental curve the amplitude of the noise light field E(t) was assumed to be represented as the product of the fast and slow independent random functions &I) and q(t), respectively which describe the stationary Gaussian random processes with different correlation times: E(r) = (y(f) x 5(r) x 77(f) ,
(2)
where a( I) is a slow function describing the pulse envelope. These random processes are characterized by the amplitude autocorrelation functions s(7)=(&f)*
<(t+7)
and H(7) =(7(f)*
v(t+~)).
(3)
Accounting these assumptions one can obtain the Ihllowing theoretical expression for ACF: G,(~)=(I~~(f)lip(t+T))l(I,p(t))~ =4[1+2~‘(~)]x(I+2H’(~)].
(3)
A.I. Vodchitz et (11./Optics Communications I25 (1996) 243-249
h \ :
a
01
1
0 Time
-1 Delay
I
1 (ps)
Fig. 3. The femtosecond parts of the correlation functions (a), (b). (c ). shown in Fig. 2 measured with higher resolution near zero time delay.
Fitting the calculated ACF (4) to the experimental, one shows that the fast random process t(t) is best described by E(T) written as S”(T) =exp(
-i/<,-)
,
pedestal ratio) of the fast part of the correlation function diminishes considerably with increasing r] and the width of the femtosecond correlation peak (FWHM) becomes slightly wider. It indicates a partial smoothing of the femtosecond noise spikes in the output pump field due to the depletion effect. The contrast of the slow part of the CCF is not changed substantially. The ACF of the Stokes radiation G,,(T) = (ZzL(t) XZ,,( t+ T)) measured at pump to Stokes energy conversion efficiency of 30% is shown in Fig. 4a, b. Fitting the model calculations based on the same assumptions as above to the experimental G,,(T) we have found that fast and slow intensities correlations are characterized by ~,r = 160 5 30 fs and rcP = 45 f. 5 ps, respectively. Comparing the curve (a) in Fig. 2 and Fig. 4. one can conclude that the statistical properties of the superbroad-bandwidth pump are well transferred to the generated Stokes wave up to an efficiency of SRS of about 30%, despite the substantial pump depletion here. The transfer of the pump light statistics to the generated Stokes radiation is corroborated as well by the measured CCF between the intensities of input undepleted pump and Stokes waves (ZfP(r) Z\,(~+T)) which is shown in Fig. 5. The two CCF (Z&(t) I,,([+ T)) between the inten-
(5)
with femtosecond correlation time ~,r= 160-130 fs. The slow process q(t) is modelled well as a random one with a phase diffusion, for which the amplitude autocorrelation function is written in the form H(T) =exp(
- 1-rj /T,~) ,
’
b
i\ I i
a
(6)
and the measured picosecond correlation time T,,, is equal to 50 + 5 ps. The curve (b) in Fig. 2 displays the measured crosscorrelation function (CCF) of the intensities (Z&(t) X I,,,( r-t T) ) between the input and depleted pump light for the pump to Stokes conversion efficiency q= 15%. The analogous CCF is represented by the curve (c) in Fig. 2 for 77= 30%. The curves (a), (b), (c ) in Fig. 3 show the fast parts of these correlation functions at the same values of 7 measured with more high resolution near zero time delay. Also we have measured the ACF of the depleted pump radiation (Z&(t) I,,,( t+ T)) at pump to Stokes conversion efliciencies of 15 and 30%. Similar data were obtained. From these results one can see that the contrast (peak/
0
i..
-50
I..
-25 Time
L _~~~~
i
0
25 Delay
5b (ps)
Fig.4. (a) ACFof Stokes radiation G,,( 7) = (I:,( r) I,,(! + 7)) measured at T= 30%; (b) the femtosecond part of G,,( ~1 measured with higher resolution near zero time delay.
A.I. Vodchitz et al. /Optics
o-i--
1
I
30
60
1
0
-30
Time
Delay
Communications
125 (1996) 243-249
OL
-100
I
-50 Time
(ps)
Fig. 7. The measured CCF (I&(f) Fig. 5. The experimental CCF between the intensities of input unde-
241
0 Delay
_l__-.
50
100
(ps)
I,,(t + 7)) between the intensities
of the depleted output pump and Stokes beams at q = 32%.
pleted pump and Stokes waves (I$( t) I,,( I + T)) at T= 30%.
sities of the depleted output pump and Stokes beams are shown in Figs. 6 and 7 for the pump to Stokes conversion efficiencies of 22 and 32%, respectively. The sharp peak corresponding to the femtosecond correlations has substantially diminished and the slow picosecond part of CCF has become very asymmetrical
(f--J I
1
-50
-25 Time
1
I
0 Delay
Fig. 6. The experimental CCF (I&(r)
25 (ps) I,,(
I + 7))
50
75
between the inten-
sities of the depleted output pump and Stokes beams at ~=22%.
with its maximum retarded relative to the point T= 0 marked by the femtosecond peak. Changing asymmetry of the CCF between the depleted pump and Stokes beams was observed by interchanging these beams in a TDFWM scheme of the nonlinear interaction, i.e. during measurement of CCF of type (Z:,(r) Z,,(r-- 7)). This CCF did not display such a strong asymmetry as the function (Z&(r) X I,,( t + T) ) did. The difference between these third order correlation functions consists in its intensity, either the intensity of the depleted pump beam or the Stokes one is squared. Because the two beams are not equivalent in the measured CCF the difference in the temporal shape of the noise spikes of these beams may result in a different shape of CCF. We did not observe a noticeable influence of interchanging the beams to the shape of the other cross-correlation functions. In the studies carried out all the ACF and CCF had a symmetrical form besides those discussed above. To understand the observed asymmetry of the correlation functions between the depleted pump and Stokes waves while the others are symmetrical, we have done a simple theoretical modeling. The third order intensity correlation functions for the pulsed signals having asymmetrical envelopes have been calculated. We have found that when the pulses have the same temporal shape then ACF and CCF do not display asymmetry. On the other hand, CCF for two pulses one
which has a sharp front and a long tail and the other a long front and a sharp tail is asymmetrical. So, it seems that CCF may carry information about the temporal profile of the noise spikes, but ACF perhaps may not. The different asymmetry of CCF (I$( t) I,,( r + T) ) and (I:[( I) I,,,( t - T) ) we attribute to the fact that picosecond peaks in the noise structure of the depleted pump and Stokes waves have opposite temporal profiles, but cannot be considered exactly as mirror reflected replicas of each other. The picosecond fluctuations in the Stokes beam, whose time scale is comparable with the dephasing time T? = 100 ps at the used hydrogen pressure of 75 atm [ 131, may take an asymmetrical time shape with a sharp front and a long tail because of the near to transient character of the Raman scattering for individual picosecond spikes [ 41. As a consequence the picosecond spikes in the depleted pump should have a long front and sharp tail. The degree of transiency of the Stokes generation on the whole can be estimated by comparing the laser pulse duration T,, and the gain response time t, =gL/r, where g is the steady-state gain coefficient for the monochromatic pump, L the transit length through the medium, and r the Raman linewidth [ 3.5 1. In our case at the energy conversion efficiency of 30% and taking account of the defect of the gain coefticient due to nonmonochromaticity of the pump [ IS 1 the evaluation gives T,,- t,. So, on the whole the Raman scattering of the 6 ns pulse is a quasisteady-state. However, the picosecond noise structure has the time scale of the fluctuations which is much less than the gain response time. It should cause transiency and a delay in the buildup of individual spikes in the generated Stokes radiation [ 21. If the random picosecond pulse train is under consideration, the dephasing time TZ is comparable with the spikes’ widths and the molecular vibration has time IO decay between successive picosecond pulses, and phase information for the Raman process is considerably lost. According to Trippenbach and Cao Long Van [ I I. the pump-Stokes intensity correlation in the transient regime becomes the strongest when the characteristic time of the noise structure is comparable or longer than the dephasing time T2. These conditions are fultilled for the picosecond structure and, as is predicted, changes in the contrast of the correlation function. displacement of its maximum relative to the point T= 0, and asymmetry take place.
However, the situation differs for the femtosecond noise structure. We did not find any delay of the femtosecond coherent peak relative to T=O within the accuracy of the measurements because of the difficulty to account for the linear dispersion of the optical elements. In this case the relaxation time T2 of the polarization induced in compressed hydrogen is much longer than the correlation time of the femtosecond random process modulating the Stokes gain coefficient during the individual picosecond noise peak. Therefore, the Stokes gain coefficient for the randomly modulated pump pulse is essentially the same as for the case when no modulation takes place [ 41. Although the pump may be considered as a random succession of very short pulses, the molecular vibration continues to be excited and the Stokes amplitude structure follows the variations of the pump amplitude structure, i.e. the system behaves as an amplifier of parametrically generated Stokes radiation.
4. Conclusions The correlations between the intensities of a superbroad-bandwidth laser pump, depleted pump and Stokes waves in stimulated Raman scattering in compressed hydrogen have been experimentally studied in pairs. We have found that the random femtosecond fluctuations of the instantaneous intensity of the Stokes radiation follow well the ones of the pump radiation up to an energy conversion efficiency of about 30%. The picosecond noise structure of the Stokes light has changes such as asymmetry of the temporal profile of individual spikes, having a sharp front and long tail. retardation of these spikes relative to the picosecond noise peaks of the pump because of the build-up process. These changes manifest themselves as asymmetry and shift of the maximum of the CCF between the depleted pump and Stokes waves. So. CCF can be used for revealing the asymmetry of the spike’s temporal shape in noise beams. Following the criterion introduced by Raymer and Mostowski [ 51, we evaluate that the Stokes generation has to be a quasi-steady-state on the whole. The CCF between the input and depleted pump waves as well as the ACF of the depleted pump show a decrease in the contrast of the femtosecond correla-
tion peak with increasing efficiency of SRS. It indicates smoothing of the fast femtosecond amplitude fluctuations of the output pump because of the depletion. The essential cancellation of these fluctuations at a high energy conversion efficiency may be a way for preparing superbroadband light with phase fluctuations prevailing over the amplitude ones. The detail analysis of the observed intensities correlations and their changes versus the efficiency of SRS and pump depletion needs additional theoretical calculations which are in progress.
References [I ]
M. Trippenbach (1986)
121 L.A.
and Cao Long
Am.
B 3
Westling
and M.G.
Raymer.
Phys. Rev. A 36 (1987)
4835.
131Z.W.
Li. C. Radzewicz
S (1988)
141 R.L. Carman.
F. Shimizu,
Phys. Rev. A 2 (1970) 151 M.G. RaymerandJ. 161 M.G.
Raymer,
Sobolewska,
Mostowski.Phys. LA.
Walmsley,
Yu.E.
P.A. Apanasevich,
D’yakov.
(IOP. Bristol.
74 (1993) 559. 1P.A. Apanasevich, Lithuanian
[ 121M.
1.G. Zubarev.
A.B. Mironov in: Ultrafast
1992) p. 227.
V.P. Kozich
V.P. Kozicht. Opt. Spectr.
and A.I.
Vilnius,
Vodchitz,
Lithuania,
1993.
part
II.
( 199 I ) IO3 I8 ( 1993) 2132.
and J. Reintjes, Optics Comm. 83 and J. Reintjes. Optics Lett.
Sentrayan, L. Major, A. Michael and V. Kushawaha.
D: Appl. Phys. 25 (1992) SYu.
in: Proc.
J. Phys. 34 ( 1994) 61.
Bashkansky
I 15 I P.A.
9.
1991, Proc. 7th Int. UPS-Symp..
A.1. Vodchitzand
UPS-Symp.,
1 13 1M. Bashkansky
I 14 I K.
and
199 I, Vol. 126. eds. A. Leubereau and A.
Germany,
Int.
Mostowski
V.P. Kozich and A.I. Vodchitz,
Bayreuth,
8th
Rev. A24 (, 1981) 1980. 1.
Sov. Phys. JETP. 46 ( 1977) 431.
Seilmeier
[ IO I P.A. Apanaqevich.
III
Bloembergen.
Optics Len. 17 ( 1992) 435.
Processes in Spectroscopy
Acknowledgements
C.S. Wang and N
60.
Phys. Rev. A 32 ( 1985) 332.
17 1LA. Walmsley, [ 81G.P. Dzhotyan,
[ 9)
and M.G. Raymer. J. Opt. Sot. Am. B
2340.
and S.1. Mikhailov,
The research described in this publication was made possible in part by Grant N F22-044 from the Fundamental Research Foundation of Republic of Belarus and Grant N MX4000 from the International Science Foundation. We acknowledge the participation of S.Ya. Kilin in the helpful discussions concerning this research.
Van, J. Opt. Sot.
879.
Apanasevich, Nikitin
J. Phys.
1697.
Yu.E. D’yakov.
and V.A. Orlovich,
G.G. Kotaev. S.G. Kruglik. Laser Phys. 3
( 1993)
131.
IS April 1996
lliz e.
OPTICS COMMUNICATIONS
__
ELSEVIER
Optics Communications 125 ( 1996) 243-249
Correlations between the intensities of pump, depleted pump and Stokes waves in superbroadband stimulated Raman scattering A.I. Vodchitz, V.P. Kozich, P.A. Apanasevich,
V.A. Orlovich
Received 28 December 1994; revised version received 30 June 1995; accepted 9 October 199.5
Abstract The pair correlations between the intensities of input pump laser radiation with spectral bandwidth of 250 cm- ‘, which has femtosecond and picosecond noise structures, output depleted pump radiation and Stokes light generated through stimulated Raman scattering ( SRS) in compressed hydrogen have been studied experimentally under weak and strong pump depletion. The third order correlation functions were measured by means of time-delayed four-wave mixing in a Kerr-shutter scheme with two noise light beams under investigation. The data obtained show that the Stokes wave is well correlated with the input pump wave up to an energy conversion efficiency of about 30%. The measured functions display the considerable suppression of the femtosecond amplitude fluctuations in the depleted pump beam upon increasing the efficiency of SRS and pump depletion. Such a result shows a possible way for preparing superbroadband light with smooth temporal envelope and predominant phase fluctuations using SRS. The picosecond part of the correlations between the depleted pump and Stokes waves is characterized by the asymmetrical shape that is probably caused by the fact that picosecond peaks in the noise structure of the depleted pump and Stokes waves have opposite temporal profiles.
1. Introduction The statistical properties of the Stokes light and nonlinear interactions in stimulated Raman generation and amplification with broad-bandwidth pump have drawn considerable attention both from the side of investigators of the processes and users of the light generated through stimulated Raman scattering (SRS) [ I-131. The Stokes wave generation is a convenient way to produce a frequency-shifted field which is well correlated with the pump field [l-3]. Such fields can be widely used in transient spectroscopy with incoherent light [9-I I ] and other applications [ 131. Intensity cross-correlation functions in SRS of colored chaotic light without pump depletion have been studied theoretically by Trippenbach and Cao Long Van 1 I 1. 0030.40 18/96/S
12.OO0 I996 Elsevier Science E3.V. All rights
SSD/OO30-JOI 8(95)00714-8
reserved
An experimental and theoretical investigation of the temporal correlations between the intensities of multimode laser radiation and Stokes light in stimulated Raman generation was carried out by Westling and Raymer [ 21. The investigation was also done under the absence of pump depletion and small spectral bandwidth of pump radiation. In this paper we present experimental studies of the temporal correlations between the intensities of a superbroad-bandwidth pump, depleted pump and Stokes beams in pairs at SRS in compressed molecular hydrogen. Input pump broadband radiation was characterized by the presence of two noise structures in the dependence of the instantaneous intensity on time - one with femtosecond correlation time and the other with picosecond correlation time. It allowed to study and compare the transformation of noise properties through
244
A.I. Vodchitz et al. /Optics
Cotntnunications
SRS in these time scales under different levels of pump depletion from weak to strong when the pump to Stokes energy conversion efficiency varied from 3% up to about 30%.
2. Experiment The studies of temporal correlations were carried out on the set-up the scheme of which is shown in Fig. 1. A I5 mJ dye-laser (3) pumped by 50 mJ second harmonic (SH) pulses of a nanosecond Nd:YAG-laser ( I ) with nonselective resonator served as an exciting source for stimulated Raman generation. The g-shaped cavity of the dye laser without any spectral selecting elements consisted of three highly reflective mirrors and an output one with reflection coefficient of 10%. The cavity dye cell with a circulating ethanol solution of Rhodamine 6G was oriented at Brewster’s angle to the pumping SH-beam. Such a scheme of the laser allowed to realize the conditions near to superluminescent lasing with multiple passing the multimode amplitied radiation through the active medium and obtain a powerful output laser beam with a small divergence of 0.8 mrad. The 6 ns (full width at half maximum or FWHM) dye-laser pulse with a spectral bandwidth of
s/j?
1 6
Fig.
I-
!
L
!
9
10
I,
e-9
(1)
0
12
11
SRS in compressed hydrogen (see details in the
Nd:YAG-laser;
2 - KDP-crystal; 3 -broadband
dye laser;
4, 14 - fully reflective mirrors; 5 - dividing mirror: 6, 19, 20 replaceable neutral filters; 7. 9. 25 -focusing with compressed hydrogen; 10 -replaceable able dividing mirror; 12 -constant
lenses; 8 - Raman cell color filter;
I I -replace-
optical delay line; 13. 16, 18,22,
24 - replaceable fully reflective mirrors; IS - introduced opaque shield: I7
about 250 cm ’ (FWHM) had femtosecond and picosecond noise structures. The picosecond structure originated from the intensity fluctuations of the pumping SH-radiation from the multimode YAG:Nd-laser. Dyelaser light centered at a wavelength of 560 nm was shifted to the other spectral region near 730 nm through Stokes vibrational Raman generation in a molecular hydrogen gas compressed to 75 atm. For this purpose the dye-laser beam was divided in proportion of 7:3 and its more intensive part was focused into a 22 cm long hydrogen cell (8). The focal length of the focusing lens (7) was equal to 30 cm. The energy efficiency of the Stokes generation was varied from 3 to about 30% by attenuating the pump beam with neutral filters (6) to observe the effect of Raman gain and pump depletion on the intensities correlations. The output energy of dye laser was sustained at the same level in all measurements to be sure that the light statistical properties would be reproducible. The third order intensity correlations were studied in pairs between the two beams of noise light by means of time-delayed four-wave mixing (TDFWM) in a Kerr-shutter configuration. Because of the degeneracy on the two wave-vector this scheme of TDFWM has a substantial advantage in the use for coherent interactions of noise light, as phase matching is fulfilled here automatically. TDFWM was realized in a I or 3 mm thick plate of glass, a medium with instantaneous cubic nonlinear response. Under these conditions the TDFWM-signal measured as a function of’ the relative time delay Tbetween the two beams under investigation was proportional to the intensity correlation function oftype [9-II]
I
experimental setup for studying intensities correlations in
wperbroadband text ):
I
?‘
8
7
I. An
I
125 (1996) 243-249
variable optical delay line; 21. 23 - polarizers (Glan
prisms): 26 - glass plate; 27 - diaphragm; 28 - analyzer (Clan prism): 29 - photomultiplier: 30 - data acquisition system.
Here IpumpandIpmhcare the instantaneous
intensities of pumping and probing beams participating in the TDFWM-process in the Kerr-shutter scheme and the symbol (. .) means statistical averaging. Under our assumptions (see below and Refs. [9-l 1] ) that noise light is described by a stationary Gaussian random process which is ergodic, the statistical averaging was equivalent to temporal averaging. It significantly simplified the experimental measurements. Using noise radiation flows of input pump, depleted pump and Stokes as such beams with the intensities ofZi,, Iclpand I,,, respectively, we have studied the correlations between the different flows.
A.I. Vodchin et al. / Oprics Comtnunicutions
Experimentally the intensity correlations were studied in the following way. The pumping beam for TDFWM passed through the variable automatically controlled optical delay line ( 17) and a polarizer (21) and then it was focused into the glass plate (26) with a lens (25 ) having a focal length of 15 cm. The probing beam passed through the constant optical delay line ( 12) and a polarizer (23 ). It was also focused into the plate with the same lens. The polarization plane of the probing beam was horizontal and that of the pumping one was oriented at an angle of 45 degrees to the first one. The informational TDFWM-signal passed through an analyzer (28) crossed with the polarization plane of the probing beam and was detected with a photomultiplier (39) and accumulated with a data acquisition system (30). All experimental curves were registered in an automatized regime. The minima1 step of tuning the delay was equal to 28 fs. During the study of the intensity autocorrelation of input pump radiation we used the less intensive part of the output dye laser beam passing through a dividing mirror (5 1 as a pumping beam in the Kerr-shutter scheme. The beam passed through the Raman cell in the &sense of SRS and recollimating lens (9) (focal length of 30 cm) was used as a probing beam. Such a scheme was also used under measurement of the crosscorrelations between the intensities of the input and depleted pump waves and the input pump and Stokes waves. But in this case the depleted pump or Stokes radiation passed through replaceable yellow orred filter ( IO). For studying the intensity autocorrelations of the depleted pump or Stokes beams and crosscorrelations between them an opaque shield ( 15) was introduced into the beam after a mirror ( 14) and suitable replaceable mirrors ( I I ) and ( 16) were used for obtaining pumping and probing beams for the Kerr-shutter scheme. The mirrors ( l3), (l8), (22) and (24) were also replaceable and suitable for studying definite correlations. All the mirrors had broadbanddielectriccoatings with spccilied suitable reflectances in the yellow or red spectral region. For optimizing the intensities of the pumping and probing beams into the glass plate the rcplaccable neutral filters ( 19) and (20) were used. 3. Results and discussion The curve ( a) in Fig. 2 shows the measured intensity correlation function between the input and output pump
I25
(1996) 243-249
Fig. 2. The experimental laser (a) and
ACF (I;,( I) I,,,( I + 7)) of broadband
CCF (If,(r) I,,,,(/+ 7))
between the intensities
dye
of the
input pump and depleted pump beams at pump to Stokes energy conversion
efficiencies
of
IS (b)
and 30%~ ( c 1.
fields below the threshold of SRS, i.e. an autocorrelation function (ACF) of dye-laser radiation. It is seen that there are two features in this function - a picosecond-width “dome” due to the picosecond noise structure of the laser light and an ultrafast coherent spike due to the femtosecond structure [ 9-1 I 1. For the theoretical modeling of the experimental curve the amplitude of the noise light field E(t) was assumed to be represented as the product of the fast and slow independent random functions &I) and q(t), respectively which describe the stationary Gaussian random processes with different correlation times: E(r) = (y(f) x 5(r) x 77(f) ,
(2)
where a( I) is a slow function describing the pulse envelope. These random processes are characterized by the amplitude autocorrelation functions s(7)=(&f)*
<(t+7)
and H(7) =(7(f)*
v(t+~)).
(3)
Accounting these assumptions one can obtain the Ihllowing theoretical expression for ACF: G,(~)=(I~~(f)lip(t+T))l(I,p(t))~ =4[1+2~‘(~)]x(I+2H’(~)].
(3)
A.I. Vodchitz et (11./Optics Communications I25 (1996) 243-249
h \ :
a
01
1
0 Time
-1 Delay
I
1 (ps)
Fig. 3. The femtosecond parts of the correlation functions (a), (b). (c ). shown in Fig. 2 measured with higher resolution near zero time delay.
Fitting the calculated ACF (4) to the experimental, one shows that the fast random process t(t) is best described by E(T) written as S”(T) =exp(
-i/<,-)
,
pedestal ratio) of the fast part of the correlation function diminishes considerably with increasing r] and the width of the femtosecond correlation peak (FWHM) becomes slightly wider. It indicates a partial smoothing of the femtosecond noise spikes in the output pump field due to the depletion effect. The contrast of the slow part of the CCF is not changed substantially. The ACF of the Stokes radiation G,,(T) = (ZzL(t) XZ,,( t+ T)) measured at pump to Stokes energy conversion efficiency of 30% is shown in Fig. 4a, b. Fitting the model calculations based on the same assumptions as above to the experimental G,,(T) we have found that fast and slow intensities correlations are characterized by ~,r = 160 5 30 fs and rcP = 45 f. 5 ps, respectively. Comparing the curve (a) in Fig. 2 and Fig. 4. one can conclude that the statistical properties of the superbroad-bandwidth pump are well transferred to the generated Stokes wave up to an efficiency of SRS of about 30%, despite the substantial pump depletion here. The transfer of the pump light statistics to the generated Stokes radiation is corroborated as well by the measured CCF between the intensities of input undepleted pump and Stokes waves (ZfP(r) Z\,(~+T)) which is shown in Fig. 5. The two CCF (Z&(t) I,,([+ T)) between the inten-
(5)
with femtosecond correlation time ~,r= 160-130 fs. The slow process q(t) is modelled well as a random one with a phase diffusion, for which the amplitude autocorrelation function is written in the form H(T) =exp(
- 1-rj /T,~) ,
’
b
i\ I i
a
(6)
and the measured picosecond correlation time T,,, is equal to 50 + 5 ps. The curve (b) in Fig. 2 displays the measured crosscorrelation function (CCF) of the intensities (Z&(t) X I,,,( r-t T) ) between the input and depleted pump light for the pump to Stokes conversion efficiency q= 15%. The analogous CCF is represented by the curve (c) in Fig. 2 for 77= 30%. The curves (a), (b), (c ) in Fig. 3 show the fast parts of these correlation functions at the same values of 7 measured with more high resolution near zero time delay. Also we have measured the ACF of the depleted pump radiation (Z&(t) I,,,( t+ T)) at pump to Stokes conversion efliciencies of 15 and 30%. Similar data were obtained. From these results one can see that the contrast (peak/
0
i..
-50
I..
-25 Time
L _~~~~
i
0
25 Delay
5b (ps)
Fig.4. (a) ACFof Stokes radiation G,,( 7) = (I:,( r) I,,(! + 7)) measured at T= 30%; (b) the femtosecond part of G,,( ~1 measured with higher resolution near zero time delay.
A.I. Vodchitz et al. /Optics
o-i--
1
I
30
60
1
0
-30
Time
Delay
Communications
125 (1996) 243-249
OL
-100
I
-50 Time
(ps)
Fig. 7. The measured CCF (I&(f) Fig. 5. The experimental CCF between the intensities of input unde-
241
0 Delay
_l__-.
50
100
(ps)
I,,(t + 7)) between the intensities
of the depleted output pump and Stokes beams at q = 32%.
pleted pump and Stokes waves (I$( t) I,,( I + T)) at T= 30%.
sities of the depleted output pump and Stokes beams are shown in Figs. 6 and 7 for the pump to Stokes conversion efficiencies of 22 and 32%, respectively. The sharp peak corresponding to the femtosecond correlations has substantially diminished and the slow picosecond part of CCF has become very asymmetrical
(f--J I
1
-50
-25 Time
1
I
0 Delay
Fig. 6. The experimental CCF (I&(r)
25 (ps) I,,(
I + 7))
50
75
between the inten-
sities of the depleted output pump and Stokes beams at ~=22%.
with its maximum retarded relative to the point T= 0 marked by the femtosecond peak. Changing asymmetry of the CCF between the depleted pump and Stokes beams was observed by interchanging these beams in a TDFWM scheme of the nonlinear interaction, i.e. during measurement of CCF of type (Z:,(r) Z,,(r-- 7)). This CCF did not display such a strong asymmetry as the function (Z&(r) X I,,( t + T) ) did. The difference between these third order correlation functions consists in its intensity, either the intensity of the depleted pump beam or the Stokes one is squared. Because the two beams are not equivalent in the measured CCF the difference in the temporal shape of the noise spikes of these beams may result in a different shape of CCF. We did not observe a noticeable influence of interchanging the beams to the shape of the other cross-correlation functions. In the studies carried out all the ACF and CCF had a symmetrical form besides those discussed above. To understand the observed asymmetry of the correlation functions between the depleted pump and Stokes waves while the others are symmetrical, we have done a simple theoretical modeling. The third order intensity correlation functions for the pulsed signals having asymmetrical envelopes have been calculated. We have found that when the pulses have the same temporal shape then ACF and CCF do not display asymmetry. On the other hand, CCF for two pulses one
which has a sharp front and a long tail and the other a long front and a sharp tail is asymmetrical. So, it seems that CCF may carry information about the temporal profile of the noise spikes, but ACF perhaps may not. The different asymmetry of CCF (I$( t) I,,( r + T) ) and (I:[( I) I,,,( t - T) ) we attribute to the fact that picosecond peaks in the noise structure of the depleted pump and Stokes waves have opposite temporal profiles, but cannot be considered exactly as mirror reflected replicas of each other. The picosecond fluctuations in the Stokes beam, whose time scale is comparable with the dephasing time T? = 100 ps at the used hydrogen pressure of 75 atm [ 131, may take an asymmetrical time shape with a sharp front and a long tail because of the near to transient character of the Raman scattering for individual picosecond spikes [ 41. As a consequence the picosecond spikes in the depleted pump should have a long front and sharp tail. The degree of transiency of the Stokes generation on the whole can be estimated by comparing the laser pulse duration T,, and the gain response time t, =gL/r, where g is the steady-state gain coefficient for the monochromatic pump, L the transit length through the medium, and r the Raman linewidth [ 3.5 1. In our case at the energy conversion efficiency of 30% and taking account of the defect of the gain coefticient due to nonmonochromaticity of the pump [ IS 1 the evaluation gives T,,- t,. So, on the whole the Raman scattering of the 6 ns pulse is a quasisteady-state. However, the picosecond noise structure has the time scale of the fluctuations which is much less than the gain response time. It should cause transiency and a delay in the buildup of individual spikes in the generated Stokes radiation [ 21. If the random picosecond pulse train is under consideration, the dephasing time TZ is comparable with the spikes’ widths and the molecular vibration has time IO decay between successive picosecond pulses, and phase information for the Raman process is considerably lost. According to Trippenbach and Cao Long Van [ I I. the pump-Stokes intensity correlation in the transient regime becomes the strongest when the characteristic time of the noise structure is comparable or longer than the dephasing time T2. These conditions are fultilled for the picosecond structure and, as is predicted, changes in the contrast of the correlation function. displacement of its maximum relative to the point T= 0, and asymmetry take place.
However, the situation differs for the femtosecond noise structure. We did not find any delay of the femtosecond coherent peak relative to T=O within the accuracy of the measurements because of the difficulty to account for the linear dispersion of the optical elements. In this case the relaxation time T2 of the polarization induced in compressed hydrogen is much longer than the correlation time of the femtosecond random process modulating the Stokes gain coefficient during the individual picosecond noise peak. Therefore, the Stokes gain coefficient for the randomly modulated pump pulse is essentially the same as for the case when no modulation takes place [ 41. Although the pump may be considered as a random succession of very short pulses, the molecular vibration continues to be excited and the Stokes amplitude structure follows the variations of the pump amplitude structure, i.e. the system behaves as an amplifier of parametrically generated Stokes radiation.
4. Conclusions The correlations between the intensities of a superbroad-bandwidth laser pump, depleted pump and Stokes waves in stimulated Raman scattering in compressed hydrogen have been experimentally studied in pairs. We have found that the random femtosecond fluctuations of the instantaneous intensity of the Stokes radiation follow well the ones of the pump radiation up to an energy conversion efficiency of about 30%. The picosecond noise structure of the Stokes light has changes such as asymmetry of the temporal profile of individual spikes, having a sharp front and long tail. retardation of these spikes relative to the picosecond noise peaks of the pump because of the build-up process. These changes manifest themselves as asymmetry and shift of the maximum of the CCF between the depleted pump and Stokes waves. So. CCF can be used for revealing the asymmetry of the spike’s temporal shape in noise beams. Following the criterion introduced by Raymer and Mostowski [ 51, we evaluate that the Stokes generation has to be a quasi-steady-state on the whole. The CCF between the input and depleted pump waves as well as the ACF of the depleted pump show a decrease in the contrast of the femtosecond correla-
tion peak with increasing efficiency of SRS. It indicates smoothing of the fast femtosecond amplitude fluctuations of the output pump because of the depletion. The essential cancellation of these fluctuations at a high energy conversion efficiency may be a way for preparing superbroadband light with phase fluctuations prevailing over the amplitude ones. The detail analysis of the observed intensities correlations and their changes versus the efficiency of SRS and pump depletion needs additional theoretical calculations which are in progress.
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The research described in this publication was made possible in part by Grant N F22-044 from the Fundamental Research Foundation of Republic of Belarus and Grant N MX4000 from the International Science Foundation. We acknowledge the participation of S.Ya. Kilin in the helpful discussions concerning this research.
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