- Email: [email protected]
No Raman echo in liquid nitrogen
Chemical Physics 128 (1988) North-Holland, Amsterdam
549-553
NO RAMAN ECHO IN LIQUID NITROGEN M. MULLER, K. WYNNE and J.D.W. VAN VOORST Laboratoryfor Physical Chemistry, The University ofAmsterdam, Nieuwe Achtergracht 127, 1018 WSAmsterdam, The Netherlands Received
11July 1988
A combination of experimental observations and theoretical arguments leads to the conclusion that the application of the Raman echo technique to a vibrational degree of freedom in small-molecule liquids in general and to liquid nitrogen in particular is not feasible. This result is due to the inherent properties ofthe liquid state rather than to the current state of technical possibilities.
1. Introduction
Subsequently, pulse II rephases the coherence established by the first pulse. The time-resolved signal is then obtained through probing the coherence left in the system at different times after pulses I and II. In general, at least two different signals may be expected. The first - and strongest - is due to interactions of the system with only one of the two pulses and results in an ordinary Raman free induction decay (RFID). The second is due to subsequent interactions of the system with the first and the second pulse and is called the Raman echo (RE). As has been pointed out elsewhere [ 111 the RE is a seventh-order nonlinear process, whereas the RFID is only of third order. The result of this fact manifests itself mainly through the different dependence of the signal intensity of RFID and RE upon the strength of the interaction pulses. It can be shown [ 3,121 that the following relations hold for the signal intensities of RFID and RE:
Although vibrational dephasing has been studied extensively in the liquid phase in recent years, it is up till now an open question whether or not the observed lineshapes are inhomogeneously broadened or result only from homogeneous broadening [ l-41. The most appropriate experimental technique [ 5 ] available to answer this question seems to be the echo technique (denoted either by photon or Raman echo, depending on the nature of the vibrational transition). To explore this possibility we have investigated the feasibility of measuring a Raman echo in liquid nitrogen. The advantages of liquid nitrogen are several: (i) a very strong Raman transition, (ii) relatively long dephasing time (75 ps [ 6,7 ] ), (iii ) negligible population relaxation ( 1.5 s [ 8]), and (iv) extensive theoretical studies. As will be explained later in this paper, our investigations show that, contrary to an earlier report [ 91, the Raman echo technique is not applicable to liquid nitrogen, nor to any other small-molecule liquid. In the following discussion few details of the Raman echo experiment will be given. For extensive theoretical discussions of the technique, the reader is therefore referred to the literature (e.g. refs. [ 3,10,11] ) The echo signal is a result of two electromagnetic pulses (labeled I and II in the following), each consisting of a laser and a Stokes pulse Ramanresonant with the vibrational transition. Pulse I excites the system to a coherent superposition of states. 0301-0104/88/$03.50 0 Elsevier Science Publishers ( North-Holland Physics Publishing Division )
Z,,,,
cc sin’@ ,
(la)
and IRE a sin28, sin4( 8,,/2)
,
(lb)
where Si is the pulse area of the ith pulse. Note, that an estimate of 8 provides directly an estimate of the relative echo signal intensity compared to that of the RFID. The relation between RFID and RE signal intensity described by eq. (1) is central to our argument concerning the feasibility of the Raman echo technique in liquid nitrogen. B.V.
550
.Qf.Miilier et al. /No Raman echo in liquid hi2
2. Experimental In the experiments, a laser and a Stokes pulse ( 10 ps, 5 and 2 MW peak power, respectively), obtained from a combination of two synchronously pumped dye lasers and two two-stage optical pulse amplifiers, are made collinear before being split (40/60) into pulses I and II (fig. 1) _Maximal overlap in time between laser and Stokes pulses is achieved through a cross-correlation technique in a KDP crystal. The frequency difference between laser (560 nm) and Stokes (644 nm) equals the transition frequency from v=O to v= 1 (2326 cm-’ ) of the ground electronic state. Fine-tuning of the frequencies is achieved through maximizing the RFID signal intensity. The coherence of the system is probed with a pulse at the Stokes frequency generating a signal at 757 nm (fig. 2). Pulses I and 11 and the probe pulse are focused within the sample at phasematching angles (fig. 3) with a 25 cm achromat. The phasematching provides a spatial separation of RE and RFID signals, with an
Fig. 1. Schematic of the experimental setup, with OPA: optical pulse amplifiers; DBS: dichroic beamsplitter: BS: 40/60 beamsplitter: L: 25 cm achromatic lens; and PMT: photomultiplier tube.
Fig. 3. Phasematching configuration for the Raman echo. The collinear laser and Stokes pulses of pulses I and II are drawn parallel for clarity. The actual angles used in the experiments are: pulse I-pulse 11: 9’: pulse I-probe: 6.3’ ; and pulse II-probe: 2.7 ‘.
angle between the two signals of 1’. The signals are detected using a GaAs photomultiplier in combination with a transient digitizer. Frequency selectivity is obtained by the use of a RG-715 and a RG-695 colored glass filter in front of the photomultiplier. The sample is at boiling temperature (77 K) and atmospheric pressure. With the above described experimental setup several tests on the feasibility of the Raman echo technique in liquid nitrogen (Matheson Research Purity, > 99.9995% m) have been undertaken. We will only summarize the main results here: Both pulses I and II produce considerable stimulated Raman scattering (SRS). Both anti-Stokes (AS) emission (495 nm) and anti-AS (AAS) emission (444 nm) are clearly visible with the eye. Measurements revealed that both the laser -AS and AS +AAS conversion efficiencies are approximately 1%. Similar conversion efficiencies were measured for the Stokes+super-Stokes emission (757 nm) (fig. 4). The AS and AAS radiation generated by SRS was emitted in cones, with the cone of the latter wider than that of the former. The cones were not “sharp-edged” but rather diffuse at the edges. Also, the width of the cone fluctuated with fluctuating pulse powers (fig. 5 ). The spectral width of the laser pulse ( z 3 cm-‘)
I
(a)
(b)
AAS
v=2 V=l
(C)
Fig. 2. Double Feynman diagrammatic representation of (a) RFID and (b) RE (ref. [ 11 ], and references therein), with frequencies: 0,=560 nm: +=644 nm; and wi=757 nm: and (c) energy level scheme.
-
-vv=o
Fig. 4. Energy level scheme for Stokes (S), super-Stokes anti-Stokes (AS) and anti-AS (AAS) radiation generated laser pulse through stimulated Raman scattering.
(sS). by the
M. Miiller et al. /No Raman echo in liquid N2
AAS
AS
S
L
S
AS
551
AAS-
(10-4)(,0-2)(10-2)(~)(10-*)(10-*~
(10-4)
I
1
I
I
I
a
2.6
1.6
0.8
0
0.8
1.8
2.8
angle COT
I
6
Fig. 5. Observed conical emission of SRS due to the laser pulse only. The intensities are given relative to the intensity of the laser pulse.
.k
5
10
increased by a factor of ten in passing through the sample (fig. 6 ). The focus, when viewed with a telescope under 90”) did not have a fixed position within the sample, but rather assumed various positions along the focal axis. The fluctuations in focus position were strongly correlated to fluctuating pulse powers. The coherence induced by SRS showed an expected phase relaxation decay time of 70 + 10 ps, when probed under slight phase-mismatch conditions, confirming the transient nature of the excita-
8
8
4
2
0,2
4
6
8
10
i&V3
Fig. 7. Angle-dependent measurement of the generated superStokes (757 nm) radiation in a Raman echo phasematched configuration under self-focusing conditions. The arrows mark the angles of the SRS from pulses I, and II and the signal due to the probed SRS of pulse II.
tional process. The relatively large uncertainty in the decay time is due to the large instabilities in the signal strengths. Angle-dependent measurements (fig. 7 ) showed that strong (SRS) signals, mainly due to the strongest of the two pulses (pulse II), were present all through the angle of acceptance of the cryostat with even stronger signals at angles coinciding with the propagation angles of pulses I and II and of the probed SRS due to pulse II. Equal results have been obtained for the measurement of super-Stokes (757 nm) and anti-Stokes (495 nm) emission.
3. Discussion
10-l
0 .%o
a0 17600
17600
18000
16200 -
A-‘hll-1)
Fig. 6. Spectral width of the laser pulse before ( X ) and after (0 ) passing through the sample of liquid nitrogen. The curves are scaled to achieve equal maximum intensity.
Before commenting on the experimental results described above, the following should be considered. Central to the question of the feasibility of the Raman echo in liquid nitrogen is an estimate for the expected pulse area 8. A crude method for deriving a rough estimate of the maximal value of the pulse area, may be obtained from evaluating the ratio be8 Inax> tween the number of photons and the number of particles in the sample. For instance, if the number of photons equals the number of particles and if all photons are absorbed, then @max=~. In physical terms this implies that the whole population of the ensemble is transferred from ground to first excited state.
552
M. Miiller et al. /No Raman echo in liquid hi:
Of course, this method for evaluating e3,,, holds only if the number of photons is much less than the number of particles. In our experiments in liquid nitrogen the volume of the focus may be calculated from the focal length of 25 cm to be 3.6~ lo-‘2 m3. At boiling point and normal pressure this volume contains 6.2~ lOI6 nitrogen molecules. The number of photons per pulse passing through this focus may be calculated from the pulse powers to be 1.4x 1014, neglecting Gaussian beam waists. Thus, 8,,,=2.3 x 10m31r. However, it is also observed that no more than 1% of the laser pulse is converted to other frequencies in the sample. Therefore, @,,,, is even a factor hundred smaller (2.3 x 1O-5rt). From this maximal value of the pulse area one can conclude, using eq. ( 1 ), that the RE signal is at least a factor 6.3 x 10” smaller than the RFID signal. And since the RFID signal is never measured over more than eight orders of ten of dynamical range, measurement of the RE signal under these conditions can be ruled out. The above presented estimate is however inconsistent with our previously described observations. In the SRS process appreciable conversion is observed from the laser to other frequencies. It follows that in practice 8 is much greater than the theoretical maximum value of 2.3 x 1O- ‘x. Using the conversion rate of 1% as a starting point, a consistent calculation yields emax = 5 x 1O-‘rc. The number of particles in the focus, i.e. the size of the focus, is left variable in this calculation and turns out to decrease to 2 x 10” particles. Thus it is found that a consistent calculation is only possible when it is assumed that the actual focus is much smaller than that calculated from the experimental parameters. The explanation for this dramatic decrease in the size of the focus is self-focusing [ 13 1. In the experiments we have found ample evidence of this non-linear process due to the intensity-dependent refractive index, n,: (i) the frequency-shifted radiation generated by SRS is emitted in cones; (ii) the focus position is not static, but rather a function of pulse powers; (iii) the pulses are spectrally broadened as a result of self phase modulation, a process associated with the same intensity dependent refractive index as self-focusing and, consequently, (iv) large instabilities in measured signal strengths. We have checked our results against those of Hu et
Table I Comparison of our results with those of Hu et al. [ 141 and Leung et al. [ 151. Note that the experiments of refs. [ 14,151 are on a nanosecond time scale, whereas ours require picosecond resolution
present study present study ‘I ref. [ 141 ref. [ 15]
No. of particles in focus
No. of photons in focus
6.1~ IO’” 2x IO” -3x IO’
1.4x 10” 1.4x lOI %7xIo’z
zIxIo*
=zI x 10”
‘) Estimate corrected for self-focusing. al. [ 141 and Leung et al. [ 151, who performed RE experiments on solid CdS and thallium vapour respectively. In both studies the number of photons in the sample exceeded the number of particles by several orders of magnitude (table 1). Also it is noted in both papers that much SRS is generated in the process. However, in their experiments, the signals due to SRS and SRS-related processes can be suppressed by electronic gating techniques because of the nanosecond time scale and the strong inhomogeneous broadening of the observed spectral line. This is a major difference compared to the situation in liquids, where phase relaxation processes are always on a picosecond time scale [ 161 and inhomogeneous broadening is generally weak, thus disallowing the use of gating techniques to enhance discrimination of the echo signal against a large background of other, lowerorder signals. Note also, that the positive balance between photons and particles in ref. [ 141 is due to the relatively low concentration of active centres. This low concentration is however compensated for by the resonant nature of the transition (i.e. resonant with the Raman intermediate state). A similar situation for vibrational degrees of freedom in small-molecule liquids is very hard to imagine, since electronic resonance enhancement of the vibrational Raman transition is hardly ever encountered in such liquids.
4. Conclusion Summarizing the arguments which lead to the conclusion that the Raman echo technique is not applicable to liquid nitrogen, we note the following. First of all, for the generation of an appreciable echo signal
M. Miiller et al. /No Raman echo in liquid Nz
the electromagnetic pulses should be intense enough, the criterion being the generation of appreciable amounts of SRS, or equivalently large 8. In case of liquid nitrogen it is found that the powers needed equal those at which self-focusing occurs. Because of self-focusing the spatial resolution required for the detection of the small RE signal decreases drastically. To increase the Raman echo signal intensity would require still greater pulse powers than presently used ( 5.0 x 10’ ’ W/cm2 ), which in turn would lead to increase the effects of self-focusing and blooming. We have investigated a whole range of possible other candidates for measuring Raman ethos in smallmolecule liquids. The main criterion in the selection being the generation of appreciable SRS without selffocusing or blooming. This criterion was found to be a contradiction in terms: those liquids which generated much SRS showed either strong self-focusing (e.g., acetonitrile) or strong blooming (e.g., ethanol). The above arguments lead to the unavoidable conclusion that the RE technique is not feasible in smallmolecule liquids because of conflicting requirements: high-power pulses ( x 10”W/cm2), required to generate pulse areas which are large enough to obtain an appreciable RE signal, induce processes like self-focusing and blooming which obscure the detection selectivity. This inherent property of the liquid state makes other obvious methods for improving the detection resolution, e.g., orthogonal polarization of the probe or probing at a third frequency, redundant.
Acknowledgement The investigations were supported in part by the Netherlands Foundation of Chemical Research
(SON) with financial aid from the Netherlands ganization for Scientific Research (NW0 ) .
553
Or-
References [ I ] S.M. George and C.B. Harris, Phys. Rev. A 28 ( 1983) 863. [2 ] W. Zinth, H.-J. Polland, A. Laubereau and W. Kaiser, Appl. Phys. B 26 (1981) 77. [3] R.F. Loring and S. Mukamel, J. Chem. Phys. 83 (1983) 2116. [4] H.J. van Elburg and J.D.W. van Voorst, Chem. Phys. 113 (1987)463. [ 51M. Miiller, K. Wynne and J.D.W. van Voorst, Chem. Phys. 125 (1988) 225. [ 61 A. Laubereau, Chem. Phys. Letters 27 ( 1974) 600. [ 71 H.M.M. Hesp, J. Langelaar, D. Bebelaar and J.D.W. van Voorst, Phys. Rev. Letters 39 ( 1977) 1376. [S] W.F. Calaway and G.E. Ewing, Chem. Phys. Letters 30 (1975) 485. [9] J.D.W. van Voorst, D. Brandt and B.L. van Hensbergen, in: Technical Digest of Topical Meeting on Ultrafast phenomena, Snowmass, CO (Optical Society of America, 1986). [lo] S.R. Hartmann, IEEE J. Quantum Electron. QE-4 (1968) 802. [ 111 K. Wynne, M. Miiller D. Brandt and J.D.W. van Voorst, Chem. Phys. 125 (1988) 211. [ 121 P. Hu, S. Geschwind and T.M. Jedju, in: Coherence and quantum optics, Vol. 4, eds. L. Mandel and E. Wolf (Plenum Press, New York, 1978) p. 175. [ 131 S.A. Akhmanov, R.V. Khokhlov and A.P. Sukhorukov, in: Laser handbook, vol. 2, eds. F.T. Arecchi and E.O. SchulzDubois (North-Holland, Amsterdam, 1972) p. 115 1. [ 141 P. Hu, S. Geschwind and T.M. Jedju, Phys. Rev. Letters 37 (1976) 1357. [ 151 K.P. Leung, T.W. Mossberg and S.R. Hartmann, Opt. Commun. 43 (1982) 145. [ 161 D.W. Oxtoby, Advan. Chem. Phys. 40 ( 1979) 1.
549-553
NO RAMAN ECHO IN LIQUID NITROGEN M. MULLER, K. WYNNE and J.D.W. VAN VOORST Laboratoryfor Physical Chemistry, The University ofAmsterdam, Nieuwe Achtergracht 127, 1018 WSAmsterdam, The Netherlands Received
11July 1988
A combination of experimental observations and theoretical arguments leads to the conclusion that the application of the Raman echo technique to a vibrational degree of freedom in small-molecule liquids in general and to liquid nitrogen in particular is not feasible. This result is due to the inherent properties ofthe liquid state rather than to the current state of technical possibilities.
1. Introduction
Subsequently, pulse II rephases the coherence established by the first pulse. The time-resolved signal is then obtained through probing the coherence left in the system at different times after pulses I and II. In general, at least two different signals may be expected. The first - and strongest - is due to interactions of the system with only one of the two pulses and results in an ordinary Raman free induction decay (RFID). The second is due to subsequent interactions of the system with the first and the second pulse and is called the Raman echo (RE). As has been pointed out elsewhere [ 111 the RE is a seventh-order nonlinear process, whereas the RFID is only of third order. The result of this fact manifests itself mainly through the different dependence of the signal intensity of RFID and RE upon the strength of the interaction pulses. It can be shown [ 3,121 that the following relations hold for the signal intensities of RFID and RE:
Although vibrational dephasing has been studied extensively in the liquid phase in recent years, it is up till now an open question whether or not the observed lineshapes are inhomogeneously broadened or result only from homogeneous broadening [ l-41. The most appropriate experimental technique [ 5 ] available to answer this question seems to be the echo technique (denoted either by photon or Raman echo, depending on the nature of the vibrational transition). To explore this possibility we have investigated the feasibility of measuring a Raman echo in liquid nitrogen. The advantages of liquid nitrogen are several: (i) a very strong Raman transition, (ii) relatively long dephasing time (75 ps [ 6,7 ] ), (iii ) negligible population relaxation ( 1.5 s [ 8]), and (iv) extensive theoretical studies. As will be explained later in this paper, our investigations show that, contrary to an earlier report [ 91, the Raman echo technique is not applicable to liquid nitrogen, nor to any other small-molecule liquid. In the following discussion few details of the Raman echo experiment will be given. For extensive theoretical discussions of the technique, the reader is therefore referred to the literature (e.g. refs. [ 3,10,11] ) The echo signal is a result of two electromagnetic pulses (labeled I and II in the following), each consisting of a laser and a Stokes pulse Ramanresonant with the vibrational transition. Pulse I excites the system to a coherent superposition of states. 0301-0104/88/$03.50 0 Elsevier Science Publishers ( North-Holland Physics Publishing Division )
Z,,,,
cc sin’@ ,
(la)
and IRE a sin28, sin4( 8,,/2)
,
(lb)
where Si is the pulse area of the ith pulse. Note, that an estimate of 8 provides directly an estimate of the relative echo signal intensity compared to that of the RFID. The relation between RFID and RE signal intensity described by eq. (1) is central to our argument concerning the feasibility of the Raman echo technique in liquid nitrogen. B.V.
550
.Qf.Miilier et al. /No Raman echo in liquid hi2
2. Experimental In the experiments, a laser and a Stokes pulse ( 10 ps, 5 and 2 MW peak power, respectively), obtained from a combination of two synchronously pumped dye lasers and two two-stage optical pulse amplifiers, are made collinear before being split (40/60) into pulses I and II (fig. 1) _Maximal overlap in time between laser and Stokes pulses is achieved through a cross-correlation technique in a KDP crystal. The frequency difference between laser (560 nm) and Stokes (644 nm) equals the transition frequency from v=O to v= 1 (2326 cm-’ ) of the ground electronic state. Fine-tuning of the frequencies is achieved through maximizing the RFID signal intensity. The coherence of the system is probed with a pulse at the Stokes frequency generating a signal at 757 nm (fig. 2). Pulses I and 11 and the probe pulse are focused within the sample at phasematching angles (fig. 3) with a 25 cm achromat. The phasematching provides a spatial separation of RE and RFID signals, with an
Fig. 1. Schematic of the experimental setup, with OPA: optical pulse amplifiers; DBS: dichroic beamsplitter: BS: 40/60 beamsplitter: L: 25 cm achromatic lens; and PMT: photomultiplier tube.
Fig. 3. Phasematching configuration for the Raman echo. The collinear laser and Stokes pulses of pulses I and II are drawn parallel for clarity. The actual angles used in the experiments are: pulse I-pulse 11: 9’: pulse I-probe: 6.3’ ; and pulse II-probe: 2.7 ‘.
angle between the two signals of 1’. The signals are detected using a GaAs photomultiplier in combination with a transient digitizer. Frequency selectivity is obtained by the use of a RG-715 and a RG-695 colored glass filter in front of the photomultiplier. The sample is at boiling temperature (77 K) and atmospheric pressure. With the above described experimental setup several tests on the feasibility of the Raman echo technique in liquid nitrogen (Matheson Research Purity, > 99.9995% m) have been undertaken. We will only summarize the main results here: Both pulses I and II produce considerable stimulated Raman scattering (SRS). Both anti-Stokes (AS) emission (495 nm) and anti-AS (AAS) emission (444 nm) are clearly visible with the eye. Measurements revealed that both the laser -AS and AS +AAS conversion efficiencies are approximately 1%. Similar conversion efficiencies were measured for the Stokes+super-Stokes emission (757 nm) (fig. 4). The AS and AAS radiation generated by SRS was emitted in cones, with the cone of the latter wider than that of the former. The cones were not “sharp-edged” but rather diffuse at the edges. Also, the width of the cone fluctuated with fluctuating pulse powers (fig. 5 ). The spectral width of the laser pulse ( z 3 cm-‘)
I
(a)
(b)
AAS
v=2 V=l
(C)
Fig. 2. Double Feynman diagrammatic representation of (a) RFID and (b) RE (ref. [ 11 ], and references therein), with frequencies: 0,=560 nm: +=644 nm; and wi=757 nm: and (c) energy level scheme.
-
-vv=o
Fig. 4. Energy level scheme for Stokes (S), super-Stokes anti-Stokes (AS) and anti-AS (AAS) radiation generated laser pulse through stimulated Raman scattering.
(sS). by the
M. Miiller et al. /No Raman echo in liquid N2
AAS
AS
S
L
S
AS
551
AAS-
(10-4)(,0-2)(10-2)(~)(10-*)(10-*~
(10-4)
I
1
I
I
I
a
2.6
1.6
0.8
0
0.8
1.8
2.8
angle COT
I
6
Fig. 5. Observed conical emission of SRS due to the laser pulse only. The intensities are given relative to the intensity of the laser pulse.
.k
5
10
increased by a factor of ten in passing through the sample (fig. 6 ). The focus, when viewed with a telescope under 90”) did not have a fixed position within the sample, but rather assumed various positions along the focal axis. The fluctuations in focus position were strongly correlated to fluctuating pulse powers. The coherence induced by SRS showed an expected phase relaxation decay time of 70 + 10 ps, when probed under slight phase-mismatch conditions, confirming the transient nature of the excita-
8
8
4
2
0,2
4
6
8
10
i&V3
Fig. 7. Angle-dependent measurement of the generated superStokes (757 nm) radiation in a Raman echo phasematched configuration under self-focusing conditions. The arrows mark the angles of the SRS from pulses I, and II and the signal due to the probed SRS of pulse II.
tional process. The relatively large uncertainty in the decay time is due to the large instabilities in the signal strengths. Angle-dependent measurements (fig. 7 ) showed that strong (SRS) signals, mainly due to the strongest of the two pulses (pulse II), were present all through the angle of acceptance of the cryostat with even stronger signals at angles coinciding with the propagation angles of pulses I and II and of the probed SRS due to pulse II. Equal results have been obtained for the measurement of super-Stokes (757 nm) and anti-Stokes (495 nm) emission.
3. Discussion
10-l
0 .%o
a0 17600
17600
18000
16200 -
A-‘hll-1)
Fig. 6. Spectral width of the laser pulse before ( X ) and after (0 ) passing through the sample of liquid nitrogen. The curves are scaled to achieve equal maximum intensity.
Before commenting on the experimental results described above, the following should be considered. Central to the question of the feasibility of the Raman echo in liquid nitrogen is an estimate for the expected pulse area 8. A crude method for deriving a rough estimate of the maximal value of the pulse area, may be obtained from evaluating the ratio be8 Inax> tween the number of photons and the number of particles in the sample. For instance, if the number of photons equals the number of particles and if all photons are absorbed, then @max=~. In physical terms this implies that the whole population of the ensemble is transferred from ground to first excited state.
552
M. Miiller et al. /No Raman echo in liquid hi:
Of course, this method for evaluating e3,,, holds only if the number of photons is much less than the number of particles. In our experiments in liquid nitrogen the volume of the focus may be calculated from the focal length of 25 cm to be 3.6~ lo-‘2 m3. At boiling point and normal pressure this volume contains 6.2~ lOI6 nitrogen molecules. The number of photons per pulse passing through this focus may be calculated from the pulse powers to be 1.4x 1014, neglecting Gaussian beam waists. Thus, 8,,,=2.3 x 10m31r. However, it is also observed that no more than 1% of the laser pulse is converted to other frequencies in the sample. Therefore, @,,,, is even a factor hundred smaller (2.3 x 1O-5rt). From this maximal value of the pulse area one can conclude, using eq. ( 1 ), that the RE signal is at least a factor 6.3 x 10” smaller than the RFID signal. And since the RFID signal is never measured over more than eight orders of ten of dynamical range, measurement of the RE signal under these conditions can be ruled out. The above presented estimate is however inconsistent with our previously described observations. In the SRS process appreciable conversion is observed from the laser to other frequencies. It follows that in practice 8 is much greater than the theoretical maximum value of 2.3 x 1O- ‘x. Using the conversion rate of 1% as a starting point, a consistent calculation yields emax = 5 x 1O-‘rc. The number of particles in the focus, i.e. the size of the focus, is left variable in this calculation and turns out to decrease to 2 x 10” particles. Thus it is found that a consistent calculation is only possible when it is assumed that the actual focus is much smaller than that calculated from the experimental parameters. The explanation for this dramatic decrease in the size of the focus is self-focusing [ 13 1. In the experiments we have found ample evidence of this non-linear process due to the intensity-dependent refractive index, n,: (i) the frequency-shifted radiation generated by SRS is emitted in cones; (ii) the focus position is not static, but rather a function of pulse powers; (iii) the pulses are spectrally broadened as a result of self phase modulation, a process associated with the same intensity dependent refractive index as self-focusing and, consequently, (iv) large instabilities in measured signal strengths. We have checked our results against those of Hu et
Table I Comparison of our results with those of Hu et al. [ 141 and Leung et al. [ 151. Note that the experiments of refs. [ 14,151 are on a nanosecond time scale, whereas ours require picosecond resolution
present study present study ‘I ref. [ 141 ref. [ 15]
No. of particles in focus
No. of photons in focus
6.1~ IO’” 2x IO” -3x IO’
1.4x 10” 1.4x lOI %7xIo’z
zIxIo*
=zI x 10”
‘) Estimate corrected for self-focusing. al. [ 141 and Leung et al. [ 151, who performed RE experiments on solid CdS and thallium vapour respectively. In both studies the number of photons in the sample exceeded the number of particles by several orders of magnitude (table 1). Also it is noted in both papers that much SRS is generated in the process. However, in their experiments, the signals due to SRS and SRS-related processes can be suppressed by electronic gating techniques because of the nanosecond time scale and the strong inhomogeneous broadening of the observed spectral line. This is a major difference compared to the situation in liquids, where phase relaxation processes are always on a picosecond time scale [ 161 and inhomogeneous broadening is generally weak, thus disallowing the use of gating techniques to enhance discrimination of the echo signal against a large background of other, lowerorder signals. Note also, that the positive balance between photons and particles in ref. [ 141 is due to the relatively low concentration of active centres. This low concentration is however compensated for by the resonant nature of the transition (i.e. resonant with the Raman intermediate state). A similar situation for vibrational degrees of freedom in small-molecule liquids is very hard to imagine, since electronic resonance enhancement of the vibrational Raman transition is hardly ever encountered in such liquids.
4. Conclusion Summarizing the arguments which lead to the conclusion that the Raman echo technique is not applicable to liquid nitrogen, we note the following. First of all, for the generation of an appreciable echo signal
M. Miiller et al. /No Raman echo in liquid Nz
the electromagnetic pulses should be intense enough, the criterion being the generation of appreciable amounts of SRS, or equivalently large 8. In case of liquid nitrogen it is found that the powers needed equal those at which self-focusing occurs. Because of self-focusing the spatial resolution required for the detection of the small RE signal decreases drastically. To increase the Raman echo signal intensity would require still greater pulse powers than presently used ( 5.0 x 10’ ’ W/cm2 ), which in turn would lead to increase the effects of self-focusing and blooming. We have investigated a whole range of possible other candidates for measuring Raman ethos in smallmolecule liquids. The main criterion in the selection being the generation of appreciable SRS without selffocusing or blooming. This criterion was found to be a contradiction in terms: those liquids which generated much SRS showed either strong self-focusing (e.g., acetonitrile) or strong blooming (e.g., ethanol). The above arguments lead to the unavoidable conclusion that the RE technique is not feasible in smallmolecule liquids because of conflicting requirements: high-power pulses ( x 10”W/cm2), required to generate pulse areas which are large enough to obtain an appreciable RE signal, induce processes like self-focusing and blooming which obscure the detection selectivity. This inherent property of the liquid state makes other obvious methods for improving the detection resolution, e.g., orthogonal polarization of the probe or probing at a third frequency, redundant.
Acknowledgement The investigations were supported in part by the Netherlands Foundation of Chemical Research
(SON) with financial aid from the Netherlands ganization for Scientific Research (NW0 ) .
553
Or-
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