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Subpicosecond two-dimensional Raman spectroscopy applying broadband nanosecond laser radiation
13 December 1996
CHEMICAL PHYSICS LETTERS
ELSEVIER
Chemical Physics Letters 263 (1996) 435-440
Subpicosecond two-dimensional Raman spectroscopy applying broadband nanosecond laser radiation A. Lau, M. Pfeiffer, A. Kummrow Max-Born-lnstitut fftr Nichtlineare Optik und Kurzzeit~pektroskopie, D-12489 Berlin, Germany Received 5 September 1996; in final form 11 October 1996
Abstract
We report first experimental and theoretical results applying non-transform-limited nanosecond laser pulses for realizing a fifth order Raman effect in nitrobenzene. Similar to femtosecond experiments this experiment enables to distinguish principally the action of rapid and slow modulation interactions on the molecular dynamics in liquids. A fast decay time of 120 fs and a slow decay time of approximately 1.5 ps are deduced from the experiments. They are assigned to nuclear motions and the dephasing time of the v = 1345 cm-l vibration of nitrobenzene, respectively.
1. Introduction
The intensity obtained with time resolved Raman methods can be expressed by [2]
The knowledge of solvation dynamics is crucial for an understanding of the first steps of chemical reactions. Whereas most of the investigations are focused on electronic dephasing, a full understanding of the complex dynamics needs additional information on vibrational dynamics and nuclear motions. Access to the latter is usually obtained by applying coherent time resolved Raman techniques, based on third order susceptibilities. By choosing proper polarisation of the exciting beams even decay rates of isotropic and anisotropic contributions to the vibrations, acting on different time scales, can be measured separately. A very instructive overview, including line shape analysis and dynamic simulations is given in [1].
1(3)( A t) = I fd
FS( F ) fd to J( to, F ) sin( toA/)l 2 .
J(to, F ) describes a homogeneous spectral function with a molecular eigenfrequency, linewidth and a parameter of interaction with the solvent. S ( F ) represents the inhomogeneous distribution over the parameters of the spectral function, indicated by F. The intensity depends on the time delay At between the excitation and probing of the investigated modes. However, because only one variable time delay is available (At), it is in principle impossible to unambiguously distinguish between interactions, which induce rapid statistical fluctuations of the molecular transition (homogeneous linewidth) and those which
0009-2614/96/$12.00 Copyright © 1996 Published by Elsevier Science B.V. All rights reserved. ,°11 S 0 0 0 9 - 2 6 1 4 ( 9 6 ) 0 1 2 2 8 - 6
436
A. Lau et al. / Chemical Physics Letters 263 (1996) 435-440
are due to different environments in solutions acting on a slower time scale (inhomogeneous linewidth). The former process reflects just the molecular dynamics of interest, whereas the latter represents an additional mechanism of line broadening, carrying but no dynamic content. A separation of both components is desirable. In recent years two new methods have been introduced solving this problem. One of the methods applies the fifth [3,5], the other the seventh [4] order of the nonlinear polarizabilities. In fifth order the corresponding intensity is given by [2]
which is not affected by the averaging process. A femtosecond and a picosecond component in the nonlinear response of liquid nitrobenzene are clearly resolved in the experiments. We show that the signal analysis in our experiments is simpler than in femtosecond techniques, because 2 of the 5 beams in our experiments can be considered as cw beams. The broadband laser field represents a Gaussian process that can be assumed to be stationary. So our fifth order signal depending on correlation of sixth order in the broadband field can be expressed by products of correlation functions of second order.
I(5)( ,at~ , ~Xt2 ) =
I fdFS(F) fdto'S( to', 1" ) sin( ¢a'At2)
2. Experimental
× fd to J ( to, F ) {sin( toA t 1)
+sin[ t o ( A f t -
At2)]}l 2 .
i2)
In the higher order technique, two different delay times exist, the delay At: between a first excitation and the probe beam, and A t2, the time between an additional second excitation and the probe. The signal according to (2) contains one peak depending on the difference of the delay times in a manner analogous to the well-known method of photon echoes. The appearance of two different time dependencies in (2) allows to separate effects of homogeneous and inhomogeneous broadening. The application of (2) to measurements with femtosecond pulses has been discussed in Ref. [3]. The fifth order Raman process in liquid CS 2 and benzene was investigated in Ref. [5], applying impulsive excitation with isolated femtosecond pulses. In this work, a characteristic shift of the signal peak at scanning (At: -- At2) (last term in Eq. (2)) was not observed. In this Letter, we describe the first experiment applying broadband nanosecond pulses with inherent femtosecond coherence times to a fifth order nonlinear Raman effect. It extends the third order Raman investigations [6-10] on the basis of broadband nanosecond laser pulses. The broadband radiation consists of a statistical distribution of subpulses of femtosecond duration and demands for an additional time averaging of the signal field as compared to methods using femtosecond pulses. We demonstrate the femtosecond time resolution of our technique
The second or the third harmonic of a YAG laser pumps a narrow band and a broadband laser. The linewidth of the narrow band laser is less than 1 cm -1. The broadband laser is optimized to give a smooth Gaussian-like wavelength distribution, the width of which determines the time resolution and can be varied between 5 and 13 nm (FWHM). On the basis of Wiener Khintichine's theorem the spectral representation of the autocorrelation function for the broadband laser will be applied to deconvolute the signal for a determination of the molecular decay times. For some dyes we checked the validity of the relation for our radiation by direct measurements of the autocorrelation time, generating the SHG from the broadband laser as function of the delay between two parts of the broadband laser beam. For the fifth order Raman experiment we split the broadband laser in three equal beams and the narrow band laser in two. All five beams are focused in a phase-matching geometry into the sample using the condition for the wave vectors ksigna I = kb3 "l" (kb2 -- kn2 ) - ( k b l -- k n l ) ,
(3)
with kbi the wavevectors of the broadband laser and kni those of the respective narrow band laser. The time delay of each of the broadband laser beams can be separately adjusted to achieve time overlap of the beams. The time delay of two of them can be scanned by computer control. The frequency difference between the broadband and narrow band laser
437
A. Lau et al./ Chemical Physics Letters 263 (1996) 435-440
is adapted to match the Raman frequency of the investigated material. The beam pair k b l - k n ! excites the probe first. The time delay between this excitation and the probe beam (with kb3) is the variable At n. The second pair (with the index 2) provides a further excitation. A t 2 is the time delay between the second excitation and the probe (cf. Fig. 4). The signal is generated in the phase-matched direction and spatially filtered by two diaphragms before it is focused onto the entrance slit of a monochromator. A photomultiplier detects the signal, which is processed in a computer. The power densities of each of the beams in the 1 cm thick sample cell is approximately 109W/cm 2. To align the spatial and temporal overlap of the 5 beams, we used the dye Rhodamine B in a thin cell. When all beam lines are well adjusted a strong coherent signal occurs which is caused by diffraction of each of the three beams at the gratings build up by the two other beams.
3. Experimental results We first examined the order of nonlinearity of the signal by the following procedures: (i) Blocking any one of the five interacting beams results in a complete loss of the signal as shown in Fig. la. (ii) The signal is generated in the correct phasematching direction and the intensity dependence of the signal is proportional to the fifth power of the exciting laser beams. (iii) A signal is generated only with samples which show a strong Raman resonance matching the frequency difference between the narrow and broadband lasers. In the present experiments, we used nitrobenzene as the Raman active sample and investigate the homogeneously broadened Raman line at 1345 cm -1 . The spectrally resolved fifth order signal is plotted in Fig. lb (open circles). The frequency difference between the maximum of the broadband laser (squares in Fig. lb) and the narrow band laser is slightly shifted compared to the Raman frequency of 1345 cm- t. This results in an enhancement of the broadband laser frequencies just at the position of strong resonance and in a small frequency shift of the signal.
blocked laser beams
2-
/\
•
"-'~mfm¶PI~,, a l ~ P p r .
P2m/~a2
o,-d
o
mill
0
.~ "~
5
1.0-
0.4-
i
0.20.0-
mill
i
560
•
1051 20 25 shift of blocking element
solid squares:
.~
•
nitrobenzene A l/~i, ~IP'~ "~
O.S"
"---
IEIB
•
l
,Q
I
30
b) ~
opencitcle: 5. order signal
i
565 570 575 wavelength / n m
l
580
Fig. I. (a) Vanishing of the signal by blocking any of the five laser beams. (b) Spectral distribution of the broadband laser (filled squares) and of the fifth order signal due to excitation of the 1345 era- ] mode of neat nitrobenzene (open circles).
The lack of a signal for liquids without a respective Raman resonance - for example with a pairing of the exciting lasers according to ksignaI = kb3 + ( k b E - k b l ) - ( k n ] - k n 2 ) - shows that a non-resonant process with the same wavevectors but a different ordering of the incoming fields is of minor importance. This simplifies the procedure of signal analysis by exclusion of such non-Raman resonant diagrams. In Fig. 2, we present the change of the signal with the time delay At 2 between the second excitation and the probe. For At z = 0, i.e. simultaneous first and probe excitation, a rather flat time dependence of the signal is measured (Fig. 2a). In contrast, the results for At I = 300 fs in Fig. 2b show a pronounced peak on the femtosecond time scale. The logarithmic plot of those data in Fig. 2c displays a fast femtosecond decay and a slow decay on the pedestal with a decay time in the picosecond range. The latter decay time is in the order of the vibrational dephasing time of the molecular transition.
A. Lau et al. / Chemical Physics Letters 263 (1996) 435-440
438
mic plot in Fig. 3c exhibits a slow decay of the pedestal, similar to Fig. 2 (c).
'~ 2.0" t d j l l l i t l t Pir
a)
Atl = 0 fs 1.5"
4. First theoretical explanation I
0°.0
.~
0.5
2-
At=300fs
0-
~" = 571 n m
b)
For our experimental configuration, the fifth order polarization of the material depends on the broad band field according to P(s)(t) oc E ~ , ( t ) ~
dt, E ~ ( , l ) f : l d t 2 E b , ( t 2 )
....
-1-"
(4)
-2~
= =
-d5
•~
n
o'o
0:5
As index matching has to be fulfilled, a signal results from combining just one radiation component from
11o
At I = 300 fs 0.1
1.0.3 ±
0.01
.
-0.5
~. = 570.8 nm
tt~
a)
.4
.
0.0
.
0.5
..~_~
0.5
1.0
At2 / ps Fig. 2. Intensity of the fifth order signal as a function of the delay At 2 between the second pair of excitation pulses and the probe. (a) At I = 0, i.e. both excitations are simultaneously. (b) Delay At~ = 300 fs between the first and the second excitation. (c) Same as (b) plotted on a logarithmic ordinate scale, z - l / e time of the given segment.
0.0 -0.5
::i
0 0
1
0.5
=
b)
o~
0
Fig. 3 shows the fifth order signal as a function of the time delay At I (broadband laser 1 is scanned, the time positions of all others are fixed). For A t 2 ---- 0, a single peak occurs when all beams overlap in time (Fig. 3a). Two peaks occur for A t 2 ~ 0 (Fig. 3b), one for a coincidence of the first and second excitation and the second for a coincidence of the first excitation and the probe beam. The widths of the two peaks are different. The FWHM of the peak having coincidence between both excitations equals the FWHM of the peak of the A t2-scan. However, in the A t2-scan a slight time delay between the peak maximum and the At~ delay time can be observed, whereas the peak positions of the A t : s c a n a r e located strictly at the respective delay times of the second excitation and the probe beam. The logarith-
.~
i
'1
0
1
At2 = 500 fs
~1
p--
of L peak 260 fs FWHM of 2. peak = 220 fs
0.01
~
-0.5
~
0.0 At 1 / ps
015
! .0
Fig. 3. Fifth order signal in dependence of the delay At I. (a) At 2 = 0, i.e. the second excitation and the probing are coincident in time. (b) At 2 = 750 fs. One peak of the signal occurs a t coincidence of the first and the second excitation, the other at coincidence of the first excitation with the probe laser. (c) At 2 = 500 fs. The signal is plotted on a logarithmic ordinate scale. ~" - l / e time of the given segment•
A. Lau et al. / Chemical Physics Letters 263 (1996) 435-440
each of the 3 directions having different time delays. If the broadband field represents a random Gaussian process, the six-field correlator in the expression for the signal intensity breaks up in products of two-field correlators and in each two-field correlator one E* and E-component are to be contracted [11]. The main signal comes from intrachromophoric contractions and there are just two possible combinations, one for (E*(t-Att)E(t-At2)) and one for (E*(t)E(t-Atl)). This means that strong signals occur for At I = At E and for At, = 0. This prediction is fully confirmed by the experiment: The data in Fig. 2b and c exhibit a well-pronounced peak if At I ~ 0 is held fixed and At E is scanned, while two peaks occur for At 2 ~ 0 and At, being scanned. Near At~ = At E = 0, many other intra- and interchromophoric contractions contribute to the signal, giving a more complicated time structure (Fig. 2a). For a first analysis, we chose a single Raman active vibrational transition. For simplicity we assume purely homogeneous broadening (no additional distribution of the vibrational parameters). The interaction of the 5 irradiated fields with the vibrational transition is depicted in Fig. 4a. The time order of the 3 interacting broad band fields is represented by the time dependences of their fluctuating pump am-
4
At 1
a)
le--
b)
11:* I
Fig. 4. The fifth-order Raman process. (a) Time order of interaction of the 5 irradiated fields with the vibrational transition (N = narrow band and Stokes fields, B = broadband fields). The time characteristics of the 3 broadband fields applied in the theoretical model is given. (b) Two of the time dependent factorized time correlation diagrams according to Ref. [6] being responsible for the peaks at At I = At 2 and At] = 0.
439
plitudes (p(t)). The signal is determined by analyzing the Fourier transform of the autocorrelator of the polarization expression given by Eq. (4). It may be calculated applying the method proposed by Albrecht for 3 wave mixing processes with steady state fluctuating broad band radiation [12]. A first estimate on this basis performed by Ulness showed the appearance of pronounced signal peaks at At, = At E and At t = 0. The width of the observed peaks and the time dependence of the decay curves is determined by the correlation time of the broadband field (dominating influence near to the strong peaks at At z, At E = 0), and - for the actual Raman process with a homogeneous lineshape - by the transversal and longitudinal relaxation rates of the molecular vibrational transition. For the case of inhomogeneous broadening, we expect, according to the principles of the fifth order technique, to be able to discriminate both homogeneous and inhomogeneous contributions to the lineshape.
5. Discussion The most important question is if the time average over the fluctuating broadband laser radiation will smear out dynamic information. As can be seen from our experimental results, a femtosecond response of the molecules is clearly observed. The temporal width of the main peaks in the different time-resolved measurements is in the 100 fs range. The peaks are by a factor of approximately 2 broader than the width of the autocorrelation function from SHGmeasurements (96 fs). We take this as an indication that the low-frequency response of the liquid strongly influences the fifth order signal. The origin of lowfrequency motion may involve the Raman active molecule itself (a Kerr modulation with 80 fs is known for nitrobenzene [13]) or - in the general case if solutions are investigated - the solvent interaction. In the At2-scan for At~ = O, only a slow decrease of the signal occurs around At E = 0 which is related to the dephasing of the excited vibration. Except for At E = 0, the Atl-SCan reveals a strong decrease of the signal in the 100 fs range. For At] ~ 0 (Fig. 2c), a slow decay appears in the picosecond range. The reciprocal slope of the decay line in Fig. 2c is
440
A. Lau et a l . / Chemical Physics Letters 263 (1996) 435-440
~-= 1.3 + 0.4 ps. This value is close to the t2-time observed for the 1345 cm-1 vibration of nitrobenzene with third order methods. Our At 2 scans are similar to curves applying femtosecond pulses [3], including a slight time delay with respect to the coincidence time with the first excitation pulse. This delay hints to the possibility or the need to fit our data also with two different modes, as was done in [3]. Such an analysis, however, requires a thorough theoretical treatment of the time-resolved fifth order signals which is more detailed than the frequently applied model to fit the experimental curves with an underdamped and an overdamped mode. Further calculations including these processes are in progress. Instead, we use here in a first approximation a Gaussian fit (related to the Kubo model at early times), enabling us to deconvolute the signal. We find a temporal width (HWHM) of the signal peak of 120 fs (Fig. 2c), reflecting at least the time scale of the fast molecular response. This value is in the order of magnitude of time constants known for nuclear motions in Kerr substances like CS 2 [3]. Comparing the time resolved data in Fig. 2 and 3 with delay curves obtained by the respective third order process [6] the very high signal:background ratio of the fifth order signal is in contrast to the small signal:background relation of < 2 for the third order process. This originates from the 'out-of-phase' arrangement in the former process (the broadband radiations act with different signs in the interaction process, Eq. (3)), whereas the latter is described by an 'in-phase'- process (both broadband radiations have the same sign in the wavevector equation) [10]. Furthermore, it should be noted that the efficiency of our fifth order signal can be as high as 10 -4 , which seems to be much higher than the corresponding efficiency using femtosecond pulses. In conclusion, our results demonstrate the potential of broadband nanosecond radiation to measure molecular dynamics on femto- and picosecond time scales using a method based on the fifth-order susceptibilities. Similar to corresponding femtosecond techniques, our approach can in principle distinguish between fast and static interaction processes (homo-
geneous and inhomogeneous contributions to the linewidth) on vibrations in liquids. A fast process correlated with dynamics of nuclear motions and a slow decay process associated with the vibrational dephasing can clearly be identified in our experimental results. A more detailed analysis of the measured decay curves needs but a further development of theory.
Acknowledgements We gratefully acknowledge discussions with A.C. Albrecht and D.J. Ulness about the theoretical interpretation of our results and thank D.J. Ulness for a model calculation supporting our interpretation of the experimental results. We thank Prof. T. Elsaesser for stimulating discussions and Mrs. R. Goleschny for her engaged technical assistance and gratefully acknowledge support of this work by the Deutsche Forschungsgemeinschaft, contract La 742/4-4.
References [1] A. Moressi, L. Mariani, M.R. DiSmfano and M.G. Giorgini, J. Raman SpectI. 26 (1995) 179. [2] Y. Tanimura and S. Mukamel, J. Chem. Phys. 99 (1993) 9496. [3] K. Tominaga and K. Yoshihara, Phys. Rev. Lett. 74 (1995) 3061. [4] D. Vanden Bout, L. Muller and M. Berg, Phys. Rev. Lett. 67 (1991) 3700. [5] T. Steffen and K. Duppen, Phys. Rev. Lett. 76 (1996) 1224. [6] T. Hattori, A. Terasaki and T. Kobayashi, Phys. Rev. A 35 (1987) 715. [7] M.A. Dugan, J.S. Melinger and A.C. Albrecht, Chem. Phys. Lctt. 147 (1988) 411. [8] S.A. Schaertel, A.C. Albrecht, A. Lau and A. Kummrow, Appl. Phys. B 59 (1994) 377. [9] A. Kummrow and A. Lau, J. Raman Spectr. 26 (1995) 457. [10] S.A. Schaertel, D. Lee and A.C. Albrecht, J. Raman Spectr. 26 (1995) 889. [11] J.W. Goodman, Statistical Optics (Wiley, New York, 1985). [12] D.J. Ulness and A.C. Albrecht, Phys. Rev. A 53 (1996) 1081. [13] W.T. Lotshaw, D. McMorrow, C. Kalpouzos and G.A. Kenhey-Wallace, Chem. Phys. Lett. 136 (1987) 323.
CHEMICAL PHYSICS LETTERS
ELSEVIER
Chemical Physics Letters 263 (1996) 435-440
Subpicosecond two-dimensional Raman spectroscopy applying broadband nanosecond laser radiation A. Lau, M. Pfeiffer, A. Kummrow Max-Born-lnstitut fftr Nichtlineare Optik und Kurzzeit~pektroskopie, D-12489 Berlin, Germany Received 5 September 1996; in final form 11 October 1996
Abstract
We report first experimental and theoretical results applying non-transform-limited nanosecond laser pulses for realizing a fifth order Raman effect in nitrobenzene. Similar to femtosecond experiments this experiment enables to distinguish principally the action of rapid and slow modulation interactions on the molecular dynamics in liquids. A fast decay time of 120 fs and a slow decay time of approximately 1.5 ps are deduced from the experiments. They are assigned to nuclear motions and the dephasing time of the v = 1345 cm-l vibration of nitrobenzene, respectively.
1. Introduction
The intensity obtained with time resolved Raman methods can be expressed by [2]
The knowledge of solvation dynamics is crucial for an understanding of the first steps of chemical reactions. Whereas most of the investigations are focused on electronic dephasing, a full understanding of the complex dynamics needs additional information on vibrational dynamics and nuclear motions. Access to the latter is usually obtained by applying coherent time resolved Raman techniques, based on third order susceptibilities. By choosing proper polarisation of the exciting beams even decay rates of isotropic and anisotropic contributions to the vibrations, acting on different time scales, can be measured separately. A very instructive overview, including line shape analysis and dynamic simulations is given in [1].
1(3)( A t) = I fd
FS( F ) fd to J( to, F ) sin( toA/)l 2 .
J(to, F ) describes a homogeneous spectral function with a molecular eigenfrequency, linewidth and a parameter of interaction with the solvent. S ( F ) represents the inhomogeneous distribution over the parameters of the spectral function, indicated by F. The intensity depends on the time delay At between the excitation and probing of the investigated modes. However, because only one variable time delay is available (At), it is in principle impossible to unambiguously distinguish between interactions, which induce rapid statistical fluctuations of the molecular transition (homogeneous linewidth) and those which
0009-2614/96/$12.00 Copyright © 1996 Published by Elsevier Science B.V. All rights reserved. ,°11 S 0 0 0 9 - 2 6 1 4 ( 9 6 ) 0 1 2 2 8 - 6
436
A. Lau et al. / Chemical Physics Letters 263 (1996) 435-440
are due to different environments in solutions acting on a slower time scale (inhomogeneous linewidth). The former process reflects just the molecular dynamics of interest, whereas the latter represents an additional mechanism of line broadening, carrying but no dynamic content. A separation of both components is desirable. In recent years two new methods have been introduced solving this problem. One of the methods applies the fifth [3,5], the other the seventh [4] order of the nonlinear polarizabilities. In fifth order the corresponding intensity is given by [2]
which is not affected by the averaging process. A femtosecond and a picosecond component in the nonlinear response of liquid nitrobenzene are clearly resolved in the experiments. We show that the signal analysis in our experiments is simpler than in femtosecond techniques, because 2 of the 5 beams in our experiments can be considered as cw beams. The broadband laser field represents a Gaussian process that can be assumed to be stationary. So our fifth order signal depending on correlation of sixth order in the broadband field can be expressed by products of correlation functions of second order.
I(5)( ,at~ , ~Xt2 ) =
I fdFS(F) fdto'S( to', 1" ) sin( ¢a'At2)
2. Experimental
× fd to J ( to, F ) {sin( toA t 1)
+sin[ t o ( A f t -
At2)]}l 2 .
i2)
In the higher order technique, two different delay times exist, the delay At: between a first excitation and the probe beam, and A t2, the time between an additional second excitation and the probe. The signal according to (2) contains one peak depending on the difference of the delay times in a manner analogous to the well-known method of photon echoes. The appearance of two different time dependencies in (2) allows to separate effects of homogeneous and inhomogeneous broadening. The application of (2) to measurements with femtosecond pulses has been discussed in Ref. [3]. The fifth order Raman process in liquid CS 2 and benzene was investigated in Ref. [5], applying impulsive excitation with isolated femtosecond pulses. In this work, a characteristic shift of the signal peak at scanning (At: -- At2) (last term in Eq. (2)) was not observed. In this Letter, we describe the first experiment applying broadband nanosecond pulses with inherent femtosecond coherence times to a fifth order nonlinear Raman effect. It extends the third order Raman investigations [6-10] on the basis of broadband nanosecond laser pulses. The broadband radiation consists of a statistical distribution of subpulses of femtosecond duration and demands for an additional time averaging of the signal field as compared to methods using femtosecond pulses. We demonstrate the femtosecond time resolution of our technique
The second or the third harmonic of a YAG laser pumps a narrow band and a broadband laser. The linewidth of the narrow band laser is less than 1 cm -1. The broadband laser is optimized to give a smooth Gaussian-like wavelength distribution, the width of which determines the time resolution and can be varied between 5 and 13 nm (FWHM). On the basis of Wiener Khintichine's theorem the spectral representation of the autocorrelation function for the broadband laser will be applied to deconvolute the signal for a determination of the molecular decay times. For some dyes we checked the validity of the relation for our radiation by direct measurements of the autocorrelation time, generating the SHG from the broadband laser as function of the delay between two parts of the broadband laser beam. For the fifth order Raman experiment we split the broadband laser in three equal beams and the narrow band laser in two. All five beams are focused in a phase-matching geometry into the sample using the condition for the wave vectors ksigna I = kb3 "l" (kb2 -- kn2 ) - ( k b l -- k n l ) ,
(3)
with kbi the wavevectors of the broadband laser and kni those of the respective narrow band laser. The time delay of each of the broadband laser beams can be separately adjusted to achieve time overlap of the beams. The time delay of two of them can be scanned by computer control. The frequency difference between the broadband and narrow band laser
437
A. Lau et al./ Chemical Physics Letters 263 (1996) 435-440
is adapted to match the Raman frequency of the investigated material. The beam pair k b l - k n ! excites the probe first. The time delay between this excitation and the probe beam (with kb3) is the variable At n. The second pair (with the index 2) provides a further excitation. A t 2 is the time delay between the second excitation and the probe (cf. Fig. 4). The signal is generated in the phase-matched direction and spatially filtered by two diaphragms before it is focused onto the entrance slit of a monochromator. A photomultiplier detects the signal, which is processed in a computer. The power densities of each of the beams in the 1 cm thick sample cell is approximately 109W/cm 2. To align the spatial and temporal overlap of the 5 beams, we used the dye Rhodamine B in a thin cell. When all beam lines are well adjusted a strong coherent signal occurs which is caused by diffraction of each of the three beams at the gratings build up by the two other beams.
3. Experimental results We first examined the order of nonlinearity of the signal by the following procedures: (i) Blocking any one of the five interacting beams results in a complete loss of the signal as shown in Fig. la. (ii) The signal is generated in the correct phasematching direction and the intensity dependence of the signal is proportional to the fifth power of the exciting laser beams. (iii) A signal is generated only with samples which show a strong Raman resonance matching the frequency difference between the narrow and broadband lasers. In the present experiments, we used nitrobenzene as the Raman active sample and investigate the homogeneously broadened Raman line at 1345 cm -1 . The spectrally resolved fifth order signal is plotted in Fig. lb (open circles). The frequency difference between the maximum of the broadband laser (squares in Fig. lb) and the narrow band laser is slightly shifted compared to the Raman frequency of 1345 cm- t. This results in an enhancement of the broadband laser frequencies just at the position of strong resonance and in a small frequency shift of the signal.
blocked laser beams
2-
/\
•
"-'~mfm¶PI~,, a l ~ P p r .
P2m/~a2
o,-d
o
mill
0
.~ "~
5
1.0-
0.4-
i
0.20.0-
mill
i
560
•
1051 20 25 shift of blocking element
solid squares:
.~
•
nitrobenzene A l/~i, ~IP'~ "~
O.S"
"---
IEIB
•
l
,Q
I
30
b) ~
opencitcle: 5. order signal
i
565 570 575 wavelength / n m
l
580
Fig. I. (a) Vanishing of the signal by blocking any of the five laser beams. (b) Spectral distribution of the broadband laser (filled squares) and of the fifth order signal due to excitation of the 1345 era- ] mode of neat nitrobenzene (open circles).
The lack of a signal for liquids without a respective Raman resonance - for example with a pairing of the exciting lasers according to ksignaI = kb3 + ( k b E - k b l ) - ( k n ] - k n 2 ) - shows that a non-resonant process with the same wavevectors but a different ordering of the incoming fields is of minor importance. This simplifies the procedure of signal analysis by exclusion of such non-Raman resonant diagrams. In Fig. 2, we present the change of the signal with the time delay At 2 between the second excitation and the probe. For At z = 0, i.e. simultaneous first and probe excitation, a rather flat time dependence of the signal is measured (Fig. 2a). In contrast, the results for At I = 300 fs in Fig. 2b show a pronounced peak on the femtosecond time scale. The logarithmic plot of those data in Fig. 2c displays a fast femtosecond decay and a slow decay on the pedestal with a decay time in the picosecond range. The latter decay time is in the order of the vibrational dephasing time of the molecular transition.
A. Lau et al. / Chemical Physics Letters 263 (1996) 435-440
438
mic plot in Fig. 3c exhibits a slow decay of the pedestal, similar to Fig. 2 (c).
'~ 2.0" t d j l l l i t l t Pir
a)
Atl = 0 fs 1.5"
4. First theoretical explanation I
0°.0
.~
0.5
2-
At=300fs
0-
~" = 571 n m
b)
For our experimental configuration, the fifth order polarization of the material depends on the broad band field according to P(s)(t) oc E ~ , ( t ) ~
dt, E ~ ( , l ) f : l d t 2 E b , ( t 2 )
....
-1-"
(4)
-2~
= =
-d5
•~
n
o'o
0:5
As index matching has to be fulfilled, a signal results from combining just one radiation component from
11o
At I = 300 fs 0.1
1.0.3 ±
0.01
.
-0.5
~. = 570.8 nm
tt~
a)
.4
.
0.0
.
0.5
..~_~
0.5
1.0
At2 / ps Fig. 2. Intensity of the fifth order signal as a function of the delay At 2 between the second pair of excitation pulses and the probe. (a) At I = 0, i.e. both excitations are simultaneously. (b) Delay At~ = 300 fs between the first and the second excitation. (c) Same as (b) plotted on a logarithmic ordinate scale, z - l / e time of the given segment.
0.0 -0.5
::i
0 0
1
0.5
=
b)
o~
0
Fig. 3 shows the fifth order signal as a function of the time delay At I (broadband laser 1 is scanned, the time positions of all others are fixed). For A t 2 ---- 0, a single peak occurs when all beams overlap in time (Fig. 3a). Two peaks occur for A t 2 ~ 0 (Fig. 3b), one for a coincidence of the first and second excitation and the second for a coincidence of the first excitation and the probe beam. The widths of the two peaks are different. The FWHM of the peak having coincidence between both excitations equals the FWHM of the peak of the A t2-scan. However, in the A t2-scan a slight time delay between the peak maximum and the At~ delay time can be observed, whereas the peak positions of the A t : s c a n a r e located strictly at the respective delay times of the second excitation and the probe beam. The logarith-
.~
i
'1
0
1
At2 = 500 fs
~1
p--
of L peak 260 fs FWHM of 2. peak = 220 fs
0.01
~
-0.5
~
0.0 At 1 / ps
015
! .0
Fig. 3. Fifth order signal in dependence of the delay At I. (a) At 2 = 0, i.e. the second excitation and the probing are coincident in time. (b) At 2 = 750 fs. One peak of the signal occurs a t coincidence of the first and the second excitation, the other at coincidence of the first excitation with the probe laser. (c) At 2 = 500 fs. The signal is plotted on a logarithmic ordinate scale. ~" - l / e time of the given segment•
A. Lau et al. / Chemical Physics Letters 263 (1996) 435-440
each of the 3 directions having different time delays. If the broadband field represents a random Gaussian process, the six-field correlator in the expression for the signal intensity breaks up in products of two-field correlators and in each two-field correlator one E* and E-component are to be contracted [11]. The main signal comes from intrachromophoric contractions and there are just two possible combinations, one for (E*(t-Att)E(t-At2)) and one for (E*(t)E(t-Atl)). This means that strong signals occur for At I = At E and for At, = 0. This prediction is fully confirmed by the experiment: The data in Fig. 2b and c exhibit a well-pronounced peak if At I ~ 0 is held fixed and At E is scanned, while two peaks occur for At 2 ~ 0 and At, being scanned. Near At~ = At E = 0, many other intra- and interchromophoric contractions contribute to the signal, giving a more complicated time structure (Fig. 2a). For a first analysis, we chose a single Raman active vibrational transition. For simplicity we assume purely homogeneous broadening (no additional distribution of the vibrational parameters). The interaction of the 5 irradiated fields with the vibrational transition is depicted in Fig. 4a. The time order of the 3 interacting broad band fields is represented by the time dependences of their fluctuating pump am-
4
At 1
a)
le--
b)
11:* I
Fig. 4. The fifth-order Raman process. (a) Time order of interaction of the 5 irradiated fields with the vibrational transition (N = narrow band and Stokes fields, B = broadband fields). The time characteristics of the 3 broadband fields applied in the theoretical model is given. (b) Two of the time dependent factorized time correlation diagrams according to Ref. [6] being responsible for the peaks at At I = At 2 and At] = 0.
439
plitudes (p(t)). The signal is determined by analyzing the Fourier transform of the autocorrelator of the polarization expression given by Eq. (4). It may be calculated applying the method proposed by Albrecht for 3 wave mixing processes with steady state fluctuating broad band radiation [12]. A first estimate on this basis performed by Ulness showed the appearance of pronounced signal peaks at At, = At E and At t = 0. The width of the observed peaks and the time dependence of the decay curves is determined by the correlation time of the broadband field (dominating influence near to the strong peaks at At z, At E = 0), and - for the actual Raman process with a homogeneous lineshape - by the transversal and longitudinal relaxation rates of the molecular vibrational transition. For the case of inhomogeneous broadening, we expect, according to the principles of the fifth order technique, to be able to discriminate both homogeneous and inhomogeneous contributions to the lineshape.
5. Discussion The most important question is if the time average over the fluctuating broadband laser radiation will smear out dynamic information. As can be seen from our experimental results, a femtosecond response of the molecules is clearly observed. The temporal width of the main peaks in the different time-resolved measurements is in the 100 fs range. The peaks are by a factor of approximately 2 broader than the width of the autocorrelation function from SHGmeasurements (96 fs). We take this as an indication that the low-frequency response of the liquid strongly influences the fifth order signal. The origin of lowfrequency motion may involve the Raman active molecule itself (a Kerr modulation with 80 fs is known for nitrobenzene [13]) or - in the general case if solutions are investigated - the solvent interaction. In the At2-scan for At~ = O, only a slow decrease of the signal occurs around At E = 0 which is related to the dephasing of the excited vibration. Except for At E = 0, the Atl-SCan reveals a strong decrease of the signal in the 100 fs range. For At] ~ 0 (Fig. 2c), a slow decay appears in the picosecond range. The reciprocal slope of the decay line in Fig. 2c is
440
A. Lau et a l . / Chemical Physics Letters 263 (1996) 435-440
~-= 1.3 + 0.4 ps. This value is close to the t2-time observed for the 1345 cm-1 vibration of nitrobenzene with third order methods. Our At 2 scans are similar to curves applying femtosecond pulses [3], including a slight time delay with respect to the coincidence time with the first excitation pulse. This delay hints to the possibility or the need to fit our data also with two different modes, as was done in [3]. Such an analysis, however, requires a thorough theoretical treatment of the time-resolved fifth order signals which is more detailed than the frequently applied model to fit the experimental curves with an underdamped and an overdamped mode. Further calculations including these processes are in progress. Instead, we use here in a first approximation a Gaussian fit (related to the Kubo model at early times), enabling us to deconvolute the signal. We find a temporal width (HWHM) of the signal peak of 120 fs (Fig. 2c), reflecting at least the time scale of the fast molecular response. This value is in the order of magnitude of time constants known for nuclear motions in Kerr substances like CS 2 [3]. Comparing the time resolved data in Fig. 2 and 3 with delay curves obtained by the respective third order process [6] the very high signal:background ratio of the fifth order signal is in contrast to the small signal:background relation of < 2 for the third order process. This originates from the 'out-of-phase' arrangement in the former process (the broadband radiations act with different signs in the interaction process, Eq. (3)), whereas the latter is described by an 'in-phase'- process (both broadband radiations have the same sign in the wavevector equation) [10]. Furthermore, it should be noted that the efficiency of our fifth order signal can be as high as 10 -4 , which seems to be much higher than the corresponding efficiency using femtosecond pulses. In conclusion, our results demonstrate the potential of broadband nanosecond radiation to measure molecular dynamics on femto- and picosecond time scales using a method based on the fifth-order susceptibilities. Similar to corresponding femtosecond techniques, our approach can in principle distinguish between fast and static interaction processes (homo-
geneous and inhomogeneous contributions to the linewidth) on vibrations in liquids. A fast process correlated with dynamics of nuclear motions and a slow decay process associated with the vibrational dephasing can clearly be identified in our experimental results. A more detailed analysis of the measured decay curves needs but a further development of theory.
Acknowledgements We gratefully acknowledge discussions with A.C. Albrecht and D.J. Ulness about the theoretical interpretation of our results and thank D.J. Ulness for a model calculation supporting our interpretation of the experimental results. We thank Prof. T. Elsaesser for stimulating discussions and Mrs. R. Goleschny for her engaged technical assistance and gratefully acknowledge support of this work by the Deutsche Forschungsgemeinschaft, contract La 742/4-4.
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